@STRING{colt93 = "Proceedings of the Sixth Annual ACM Conference on Computational Learning Theory" } @STRING{jacm = "Journal of the Association for Computing Machinery" } @STRING{jma = "Journal of Multivariate Analysis" } @STRING{lncs = "Lecture Notes of Computer Science, Springer" } @STRING{lncs = "Lecture Notes in Computer Science" } @STRING{nips = "Advances in Neural Information Processing Systems" } @STRING{pecs = "Colloquia Mathematica Societatis Janos Bolai, 57.\ Limit Theorem in Probability and Statistics, Pecs (Hungary)" } @STRING{spl = "Statistics \& Probability Letters" } @Article{LegensteinETAL:09b, author = {R. Legenstein and S. Chase and A. Schwartz and W. Maass}, title = {A reward-modulated {H}ebbian learning rule can explain experimentally observed network reorganization in a brain control task}, journal = {Journal of Neuroscience}, year = {2009}, volume = {}, number = {}, pages = {}, abstract = {It has recently been shown in a brain-computer interface experiment that motor cortical neurons change their tuning properties selectively to compensate for errors induced by displaced decoding parameters. In particular, it was shown that the 3D tuning curves of neurons whose decoding parameters were re-assigned changed more than those of neurons whose decoding parameters had not been re-assigned. In this article, we propose a simple learning rule that can reproduce this effect. Our learning rule uses Hebbian weight updates driven by a global reward signal and neuronal noise. In contrast to most previously proposed learning rules, this approach does not require extrinsic information to separate noise from signal. The learning rule is able to optimize the performance of a model system within biologically realistic periods of time under high noise levels. Furthermore, when the model parameters are matched to data recorded during the brain-computer interface learning experiments described above, the model produces learning effects strikingly similar to those found in the experiments.}, note = {in press} } @Article{AlonMaass:86, author = {N. Alon and W. Maass}, journal = {Proceedings of the 27th Annual IEEE Symposium on Foundations of Computer Science}, pages = {410--417}, title = {Meanders, Ramsey's theorem and lower bounds for branching programs}, year = {1986} } @Article{AlonMaass:88, author = {N. Alon and W. Maass}, journal = {J. Comput. System Sci.}, note = {Invited paper for a special issue of J. Comput. System Sci.}, pages = {118--129}, title = {Meanders and their applications in lower bound arguments}, volume = {37}, year = {1988} } @InProceedings{AuerETAL:01, author = {P. Auer and H. Burgsteiner and W. Maass}, title = {Reducing Communication for Distributed Learning in Neural Networks}, booktitle = {Proc. of the International Conference on Artificial Neural Networks -- ICANN 2002}, series = {Lecture Notes in Computer Science}, editor = {Jos\'{e} R. Dorronsoro}, pages = {123--128}, volume = {2415}, year = {2002}, publisher = {Springer}, keywords = {learning algorithm, perceptrons, parallel, aVLSI }, abstract = {A learning algorithm is presented for circuits consisting of a single layer of perceptrons. We refer to such circuits as parallel perceptrons. In spite of their simplicity, these circuits are universal approximators for arbitrary boolean and continuous functions. In contrast to backprop for multi-layer perceptrons, our new learning algorithm - the parallel delta rule (p-delta rule) - only has to tune a single layer of weights, and it does not require the computation and communication of analog values with high precision. This distinguishes our new learning rule also from other learning rules for such circuits such as MADALINE with far higher communication. Our algorithm also provides an interesting new hypothesis for the organization of learning in biological neural systems. A theoretical analysis shows that the p-delta rule does in fact implement gradient descent - with regard to a suitable error measure - although it does not require to compute derivatives. Furthermore it is shown through experiments on common real-world benchmark datasets that its performance is competitive with that of other learning approaches from neural networks and machine learning.} } @Article{AuerETAL:01a, author = {P. Auer and H. Burgsteiner and W. Maass}, title = {A learning rule for very simple universal approximators consisting of a single layer of perceptrons}, journal = {Neural Networks}, year = {2008}, volume = {21}, number = {5}, pages = {786--795}, abstract = {A learning algorithm is presented for circuits consisting of a single layer of perceptrons (= threshold gates, or equivalently gates with a Heaviside activation function). We refer to such circuits as parallel perceptrons. In spite of their simplicity, these circuits can compute any boolean function if one views the majority of the binary perceptron outputs as the binary outputs of the parallel perceptron, and they are universal approximators for arbitrary continuous functions with values in [0,1] if one views the fraction of perceptrons that output 1 as the analog output of the parallel perceptron. For a long time one has thought that there exists no competitive learning algorithms for these extremely simple circuits consisting of gates with binary outputs, which also became known as committee machines. It is commonly believed that one has to replace the hard threshold gates by sigmoidal gates and that one has to tune the weights on at least two successive layers in order to get satisfactory learning results. We show that this is not true by exhibiting a simple learning algorithm for parallel perceptrons - the parallel delta rule (p-delta rule), whose performance is comparable to that of backprop for multilayer networks consisting of sigmoidal gates. In contrast to backprop, the p-delta rule does not require the computation and communication of analog values with high precision, although it does in fact implement gradient descent - with regard to a suitable error measure. Therefore it provides an interesting new hypothesis for the organization of learning in biological neural systems.} } @InProceedings{AuerETAL:93, author = {P. Auer and P. M. Long and W. Maass and G. J. Woeginger}, booktitle = {Proceedings of the 5th Annual ACM Conference on Computational Learning Theory}, pages = {392--401}, title = {On the complexity of function learning}, year = {1993} } @Article{AuerETAL:93j, author = {P. Auer and P. M. Long and W. Maass and G. J. Woeginger}, title = {On the complexity of function learning}, journal = {Machine Learning}, note = {Invited paper in a special issue of Machine Learning}, year = {1995}, volume = {18}, pages = {187--230} } @InProceedings{AuerETAL:95, author = {P. Auer and R. C. Holte and W. Maass}, booktitle = {Proc. of the 12th International Machine Learning Conference, Tahoe City (USA)}, publisher = {Morgan Kaufmann (San Francisco)}, pages = {21--29}, title = {Theory and applications of agnostic {PAC}-learning with small decision trees}, year = {1995} } @InProceedings{AuerETAL:96, author = {P. Auer and S. Kwek and W. Maass and M. K. Warmuth}, booktitle = {Proc. of the 9th Conference on Computational Learning Theory 1996}, pages = {333--343}, publisher = {ACM-Press (New York)}, title = {Learning of depth two neural nets with constant fan-in at the hidden nodes}, year = {1996} } @Article{AuerMaass:98, author = {P. Auer and W. Maass}, title = {Introduction to the Special Issue on Computational Learning Theory}, journal = {Algorithmica}, year = {1998}, volume = {22}, number = {1/2}, pages = {1--2} } @Unpublished{BachlerMaass:06, author = {M. Bachler and W. Maass}, title = {A {B}ayesian {H}ebb Rule for Incremental Learning of Optimal Inference in {B}ayesian Networks}, note = {submitted for publication}, year = {2006} } @InCollection{BartlettMaass:03, author = {Peter L. Bartlett and W. Maass}, title = {Vapnik-{C}hervonenkis Dimension of Neural Nets}, booktitle = {The Handbook of Brain Theory and Neural Networks}, publisher = {MIT Press (Cambridge)}, year = {2003}, editor = {M. A. Arbib}, edition = {2nd}, pages = {1188--1192} } @InProceedings{BuesingMaass:07, author = {L. Buesing and W. Maass}, title = {Simplified Rules and Theoretical Analysis for Information Bottleneck Optimization and {PCA} with Spiking Neurons}, booktitle = {Proc. of NIPS 2007, Advances in Neural Information Processing Systems}, editor = {}, publisher = {MIT Press}, year = {2008}, volume = {20}, pages = {}, abstract = {We show that under suitable assumptions (primarily linearization) a simple and perspicuous online learning rule for Information Bottleneck optimization with spiking neurons can be derived. This rule performs on common benchmark tasks as well as a rather complex rule that has previously been proposed [2]. Furthermore, the transparency of this new learning rule makes a theoretical analysis of its convergence properties feasible. If this learning rule is applied to an assemble of neurons, it provides a theoretically founded method for performing principal component analysis ({PCA}) with spiking neurons. In addition it makes it possible to preferentially extract those principal components from incoming signals X that are related to some additional target signal $Y_T$ . This target signal $Y_T$ (also called relevance variable) could represent in a biological interpretation proprioception feedback, input from other sensory modalities, or top-down signals.} } @Article{BuesingMaass:09, author = {Buesing, L. and Maass, W.}, title = {A Spiking Neuron as Information Bottleneck}, journal = {submitted for publication}, year = {2009} } @InProceedings{BultmanMaass:91, author = {W. J. Bultman and W. Maass}, booktitle = {Proceedings of the 4th Annual ACM Workshop on Computational Learning Theory,}, pages = {337--353}, title = {Fast identification of geometric objects with membership queries}, year = {1991} } @Article{BultmanMaass:91j, author = {W. J. Bultman and W. Maass}, title = {Fast identification of geometric objects with membership queries}, journal = {Information and Computation}, year = 1995, volume = 118, pages = {48--64} } @Article{BuonomanoMaass:08, author = {D. Buonomano and W. Maass}, title = {State-dependent Computations: Spatiotemporal Processing in Cortical Networks.}, journal = {Nature Reviews in Neuroscience}, year = {2009}, volume = {10}, number = {2}, pages = {113--125}, note = {}, abstract = {A conspicuous ability of the brain is to seamlessly assimilate and process spatial and temporal features of sensory stimuli. This ability is indispensable for the recognition of natural stimuli. Yet, a general computational framework for processing spatiotemporal stimuli remains elusive. Recent theoretical and experimental work suggests that spatiotemporal processing emerges from the interaction between incoming stimuli and the internal dynamic state of neural networks which includes not only ongoing spiking activity, but also 'hidden' neuronal states such as short-term synaptic plasticity.} } @InProceedings{ChenMaass:92, author = {Z. Chen and W. Maass}, booktitle = {Proceedings of the 5th Annual ACM Workshop on Computational Learning Theory}, pages = {16--28}, title = {On-line learning of rectangles}, year = {1992} } @InProceedings{ChenMaass:92a, author = {Z. Chen and W. Maass}, booktitle = {Proceedings of the 3rd Int. Workshop on Analogical and Inductive Inference}, pages = {26--34}, publisher = {Springer}, series = {Lecture Notes in Artificial Intelligence}, title = {A solution of the credit assignment problem in the case of learning rectangles}, volume = {642}, year = {1992} } @Article{ChenMaass:94, author = {Z. Chen and W. Maass}, journal = {Machine Learning}, note = {Invited paper for a special issue of Machine Learning}, pages = {201--223}, title = {On-line learning of rectangles and unions of rectangles}, volume = {17}, year = {1994} } @Article{DietzfelbingerETAL:91a, author = {M. Dietzfelbinger and W. Maass and G. Schnitger}, journal = {Theoretical Computer Science}, pages = {113--129}, title = {The complexity of matrix transposition on one-tape off-line {T}uring machines}, volume = {82}, year = {1991} } @InProceedings{DietzfelbingerMaass:85, author = {M. Dietzfelbinger and W. Maass}, booktitle = {Proceedings of the 1984 Recursion Theory Week Oberwolfach, Germany}, pages = {89--120}, publisher = {Springer (Berlin)}, series = {Lecture Notes in Mathematics}, title = {Strong reducibilities in alpha- and beta-recursion theory}, volume = {1141}, year = {1985} } @InProceedings{DietzfelbingerMaass:86, author = {M. Dietzfelbinger and W. Maass}, booktitle = {Proceedings of the Structure in Complexity Theory Conference, Berkeley 1986}, pages = {163--183}, publisher = {Springer (Berlin)}, series = {Lecture Notes in Computer Science}, title = {Two lower bound arguments with ``inaccessible'' numbers}, volume = {223}, year = {1986} } @Article{DietzfelbingerMaass:88, author = {M. Dietzfelbinger and W. Maass}, journal = {J. Comput. System Sci.}, note = {Invited paper for a special issue of J. Comput. System Sci.}, pages = {313--335}, title = {Lower bound arguments with ``inaccesible'' numbers}, volume = {36}, year = {1988} } @InProceedings{DietzfelbingerMaass:88a, author = {M. Dietzfelbinger and W. Maass}, booktitle = {Proceedings of the 15th International Colloquium on Automata, Languages and Programming}, pages = {188--200}, publisher = {Springer (Berlin)}, series = {Lecture Notes in Computer Science}, title = {The complexity of matrix transposition on one-tape off-line {T}uring machines with output tape}, volume = {317}, year = {1988} } @Article{DietzfelbingerMaass:93, author = {M. Dietzfelbinger and W. Maass}, journal = {Theoretical Computer Science}, pages = {271--290}, title = {The complexity of matrix transposition on one-tape off-line {T}uring machines with output tape}, volume = {108}, year = {1993} } @Article{DobkinETAL:96, author = {D. P. Dobkin and D. Gunopulos and W. Maass}, journal = {Journal of Computer and System Sciences}, month = {June}, number = {3}, pages = {453--470}, title = {Computing the maximum biochromatic discrepancy, with applications in computer graphics and machine learning}, volume = {52}, year = {1996} } @InProceedings{FregnacETAL:05, author = {Y. Fregnac and M. Blatow and J.-P. Changeux and J. de Felipe and A. Lansner and W. Maass and D. A. McCormick and C. M. Michel and H. Monyer and E. Szathmary and R. Yuste}, title = {U{P}s and {DOWN}s in Cortical Computation}, booktitle = {The Interface between Neurons and Global Brain Function}, editor = {S. Grillner and A. M. Graybiel}, year = {2006}, pages = {393--433}, chapter = {19}, publisher = {MIT Press}, series = {Dahlem Workshop Report 93} } @Article{HaeuslerETAL:03, author = {S. Haeusler and H. Markram and W. Maass}, title = {Perspectives of the High Dimensional Dynamics of Neural Microcircuits from the Point of View of Low Dimensional Readouts}, journal = {Complexity (Special Issue on Complex Adaptive Systems)}, year = {2003}, volume = {8}, number = {4}, pages = {39--50} } @Article{HaeuslerETAL:07, author = {S. Haeusler and W. Singer and W. Maass and D. Nikolic}, title = {Superposition of information in large ensembles of neurons in primary visual cortex}, journal = {37th Annual Conference of the Society for Neuroscience, Program 176.2, Poster II23}, year = {2007}, volume = {}, number = {}, pages = {}, abstract = {We applied methods from machine learning in order to analyze the temporal evolution of stimulus-related information in the spiking activity of large ensembles of around 100 neurons in primary visual cortex of anesthetized cats. We present ed sequences of up to 3 different visual stimuli (letters) that lasted 100 ms and followed at intervals of 100 ms. We f ound that most of the information about visual stimuli extractable by advanced methods from machine learning (e.g., Sup port Vector Machines) could also be extracted by simple linear classifiers (perceptrons). Hence, in principle this info rmation can be extracted by a biological neuron. A surprising result was that new stimuli did not erase information abo ut previous stimuli. In fact, information about the nature of the preceding stimulus remained as high as the informatio n about the current stimulus. Separately trained linear readouts could retrieve information about both the current and the preceding stimulus from responses to the current stimulus. This information was encoded both in the discharge rates (response amplitudes) of the ensemble of neurons and in the precise timing of individual spikes, and persisted for seve ral 100 ms beyond the offset of stimuli. This superposition of information about sequentially presented stimuli constrains computational models for visual proce ssing. It poses a conundrum for models that assume separate classification processes for each frame of visual input and supports models for cortical computation ([Buonomano, Merzenich, 1995], [Maass, Natschlaeger, Markram, 2002]) which arg ue that a frame-by frame processing is neither feasible within highly recurrent networks nor useful for classifying and predicting rapidly changing stimulus sequences. Specific predictions of these alternative computational models are tha i) information from different frames of visual input is superimposed in recurrent circuits and ii) nonlinear combinations of different information components are immediately provided in the spike output. Our results indicate that the network from which we recorded provided nonlinear combinations of information from sequen tial frames. Such nonlinear preprocessing increases the discrimination capability of any linear readout neurons receivi ng distributed input from the kind of cells we recorded from. These readout neurons could be implemented within V1 and/ or at subsequent processing levels.} } @Article{HaeuslerETAL:08, author = {S. Haeusler and K. Schuch and W. Maass}, title = {Motif distribution and computational performance of two data-based cortical microcircuit templates}, journal = {J. of Physiology (Paris)}, year = {2009}, volume = {Jan-Mar;103}, number = {1-2}, pages = {73--87}, abstract = {The neocortex is a continuous sheet composed of rather stereotypical local microcircuits that consist of neurons on several laminae with characteristic synaptic connectivity patterns. An understanding of the structure and computational function of these cortical microcircuits may hold the key for understanding the enormous computational power of the neocortex. Two templates for the structure of laminar cortical microcircuits have recently been published by Thomson et al. and Binzegger et al., both resulting from long-lasting experimental studies (but based on different methods). We analyze and compare in this article the structure and computational properties of these two microcircuit templates. In particular, we examine the distribution of network motifs, i.e. of subcircuits consisting of a small number of neurons. The distribution of these building blocks of complex networks has recently emerged as a method for characterizing similarities and differences among complex networks. We show that the two microcircuit templates have quite different distribution of network motifs, although they both show a characteristic small-world property. In order to understand the computational properties of these two microcircuit templates, we have generated computer models of them, consisting of Hodgkin-Huxley point neurons with conductance based synapses that have a biologically realistic short-term plasticity. The performance of these two cortical microcircuit models was studied for 7 generic computational tasks that require accumulation and merging of information contained in two afferent spike inputs. Although the two models exhibit a different performance for some of these tasks, their average computational performance is very similar. When we changed the connectivity structure of these two microcircuit models in order to see which aspects of it are essential for computational performance, we found that the distribution of degrees of nodes is a key factor for their computational performance.} } @Article{HaeuslerETAL:08a, author = {S. Haeusler and K. Schuch and W. Maass}, title = {Motif distribution and computational performance of two data-based cortical microcircuit templates}, journal = {38th Annual Conference of the Society for Neuroscience, Program 220.9}, year = {2008}, volume = {}, number = {}, pages = {}, abstract = {The neocortex is a continuous sheet composed of rather stereotypical local microcircuits that consist of neurons on several laminae with characteristic synaptic connectivity patterns. An understanding of the structure and computational function of these cortical microcircuits may hold the key for understanding the enormous computational power of the neocortex. Two templates for the structure of laminar cortical microcircuits have recently been published by Thomson et al. (2002) and Binzegger et al. (2004), both resulting from long-lasting experimental studies (but based on different methods). We analyze and compare in this study the structure and computational properties of these two microcircuit templates. In particular, we examine the distribution of network motifs, i.e. of sub-circuits consisting of a small number of neurons. The distribution of these building blocks of complex networks has recently emerged as a method for characterizing similarities and differences among complex networks. We show that the two microcircuit templates have quite different distributions of network motifs, although they both share characteristic global structural properties, like degree distributions (distribution of the number of synapses per neuron) and small-world properties. In order to understand the computational properties of the two microcircuit templates, we have generated computer models of them, consisting of Hodgkin-Huxley point neurons with conductance based synapses that have a biologically realistic short-term plasticity. The information processing capabilities of the two cortical microcircuit models were studied for 7 generic computational tasks that require accumulation and merging of information contained in two afferent spike inputs. Although the two models exhibit a different performance for some of these tasks, their average computational performance is very similar. When we changed the connectivity structure of these two microcircuit models in order to see which aspects of it are essential for computational performance, we found that the distribution of degrees of nodes is a key factor for their computational performance. References Thomson et al. (2002), Cerebral Cortex, 12(9):936 Binzegger et al. (2004), J. Neurosci., 24(39):8441} } @Article{HaeuslerMaass:04, author = {S. Haeusler and W. Maass}, title = {A statistical analysis of information processing properties of lamina-specific cortical microcircuit models}, journal = {Cerebral Cortex}, year = 2007, volume = {17}, number = {1}, pages = {149-162} } @Article{HaeuslerMaass:06, author = {S. Haeusler and W. Maass}, title = {Computational impact of laminar structure and small world properties of cortical microcircuit models}, journal = {submitted for publication}, year = 2006 } @InProceedings{HajnalETAL:87a, author = {A. Hajnal and W. Maass and P. Pudlak and M. Szegedy and G. Turan}, booktitle = {Proceedings of the 28th Annual IEEE Symposium on Foundations of Computer Science}, pages = {99--110}, title = {Threshold circuits of bounded depth}, year = {1987} } @InProceedings{HajnalETAL:88, author = {A. Hajnal and W. Maass and G. Turan}, booktitle = {Proceedings of the 20th Annual ACM Symposium on Theory of Computing}, pages = {186--191}, title = {On the communication complexity of graph properties}, year = {1988} } @Article{HajnalETAL:93, author = {A. Hajnal and W. Maass and P. Pudlak and M. Szegedy and G. Turan}, journal = {J. Comput. System Sci.}, pages = {129--154}, title = {Threshold circuits of bounded depth}, abstract = {We examine a powerful model of parallel computation: polynomial size threshold circuits of bounded depth (the gates compute threshold functions with polynomial weights). Lower bounds are given to separate polynomial size threshold circuits of depth 2 from polynomial size threshold circuits of depth 3 and from probabilistic polynomial size circuits of depth 2. With regard to the unreliability of bounded depth circuits, it is shown that the class of functions computed reliably with bounded depth circuits of unreliable A, v , 1 gates is narrow. On the other hand, functions computable by bounded depth, polynomial-size threshold circuits can also be computed by such circuits of unreliable threshold gates. Furthermore we examine to what extent imprecise threshold gates (which behave unpredictably near the threshold value) can compute nontrivial functions in bounded depth and a bound is given for the permissible amount of imprecision. We also discuss threshold quantifiers and prove an undefinability result for graph connectivity.}, volume = {46}, year = {1993} } @InProceedings{HauserETAL:07, author = {H. Hauser and G. Neumann and A. J. Ijspeert and W. Maass}, booktitle = {Proceedings of the {IEEE}-{RAS} 7th {I}nternational {C}onference on {H}umanoid {R}obots ({H}umanoids 2007)}, title = {Biologically Inspired Kinematic Synergies Provide a New Paradigm for Balance Control of Humanoid Robots}, publisher = {}, year = {2007}, pages = {}, abstract = {Nature has developed methods for controlling the movements of organisms with many degrees of freedom which differ strongly from existing approaches for balance control in humanoid robots: Biological organisms employ kinematic synergies that simultaneously engage many joints, and which are apparently designed in such a way that their superposition is approximately linear. We show in this article that this control strategy can in principle also be applied to balance control of humanoid robots. In contrast to existing approaches, this control strategy reduces the need to carry out complex computations in real time (replacing the iterated solution of quadratic optimization problems by a simple linear controller), and it does not require knowledge of a dynamic model of the robot. Therefore it can handle unforeseen changes in the dynamics of the robot that may for example arise from wind or other external forces. We demonstrate the feasibility of this novel approach to humanoid balance control through simulations of the humanoid robot HOAP-2 for tasks that require balance control on a randomly moving surfboard.}, note = {Best {P}aper {A}ward. http://planning.cs.cmu.edu/humanoids07/p/37.pdf} } @InProceedings{HochbaumMaass:84, author = {D. Hochbaum and W. Maass}, booktitle = {Proceedings of Symp. on Theoretical Aspects of Computer Science (Paris 1984)}, pages = {55--62}, publisher = {Springer (Berlin)}, series = {Lecture Notes in Computer Science}, title = {Approximation schemes for covering and packing problems in robotics and {VLSI} (extended abstract)}, volume = {166}, year = {1984} } @Article{HochbaumMaass:85, author = {D. Hochbaum and W. Maass}, journal = {J. Assoc. Comp. Mach.}, pages = {130--136}, title = {Approximation algorithms for covering and packing problems in image processing and {VLSI}}, volume = {32}, year = {1985} } @Article{HochbaumMaass:87, author = {D. Hochbaum and W. Maass}, journal = {J. Algorithms}, pages = {305--323}, title = {Fast approximation algorithms for a nonconvex problem}, volume = {8}, year = {1987} } @Article{HomerMaass:83, author = {S. Homer and W. Maass}, journal = {Theoretical Computer Science}, pages = {279--289}, title = {Oracle dependent properties of the lattice of {NP}-sets}, volume = {24}, year = {1983} } @Article{JoshiETAL:09, author = {P. Joshi and G. Rainer and W. Maass}, title = {Computational role of theta oscillations in delayed-decision tasks}, journal = {in preparation}, year = {2009}, pages = {}, volume = {} } @InProceedings{JoshiMaass:03, author = {P. Joshi and W. Maass}, title = {Movement Generation and Control with Generic Neural Microcircuits}, booktitle = {Biologically Inspired Approaches to Advanced Information Technology. First International Workshop, Bio{ADIT} 2004, Lausanne, Switzerland, January 2004, Revised Selected Papers}, pages = {258--273}, year = {2004}, editor = {A. J. Ijspeert and M. Murata and N. Wakamiya}, volume = {3141}, series = {Lecture Notes in Computer Science}, publisher = {Springer Verlag}, abstract = {Simple linear readouts from generic neural microcircuit models consisting of spiking neurons and dynamic synapses can be trained to generate and control basic movements, for example, reaching with an arm to various target points. After suitable training of these readouts on a small number of target points; reaching movements to other target points can also be generated. Sensory or proprioceptive feedback turns out to be essential for such movement control, even if it is noisy and substantially delayed. Such feedback turns out to optimally improve the performance of the neural microcircuit model if it arrives with a biologically realistic delay of 100 to 200 ms. Furthermore, additional feedbacks of ``prediction of sensory variables'' are shown to improve the performance significantly. The proposed model also provides a new approach for movement control in robotics. Existing control methods in robotics that take the particular dynamics of the sensors and actuators into account (``embodiment of robot control'') are taken one step further by this approach, which provides methods for also using the ``embodiment of computation'', i.e. the inherent dynamics and spatial structure of neural circuits, for the design of robot movement controllers.} } @Article{JoshiMaass:04, author = {P. Joshi and W. Maass}, journal = {Neural Computation}, title = {Movement Generation with Circuits of Spiking Neurons}, year = {2005}, volume = 17, number = 8, pages = {1715--1738}, abstract = {How can complex movements that take hundreds of milliseconds be generated by stereotypical neural microcircuits consisting of spiking neurons with a much faster dynamics? We show that linear readouts from generic neural microcircuit models can be trained to generate basic arm movements. Such movement generation is independent of the arm-model used and the type of feedbacks that the circuit receives. We demonstrate this by considering two different models of a two-jointed arm, a standard model from robotics and a standard model from biology, that each generate different kinds of feedback. Feedbacks that arrive with biologically realistic delays of 50--280 ms turn out to give rise to the best performance. If a feedback with such desirable delay is not available, the neural microcircuit model also achieves good performance if it uses internally generated estimates of such feedback. Existing methods for movement generation in robotics that take the particular dynamics of sensors and actuators into account (``embodiment of motor systems'') are taken one step further with this approach, which provides methods for also using the ``embodiment of motion generation circuitry'', i.e., the inherent dynamics and spatial structure of neural circuits, for the generation of movements.} } @Article{KaskeMaass:04, author = {A. Kaske and W. Maass}, title = {A model for the interaction of oscillations and pattern generation with real-time computing in generic neural microcircuit models}, journal = {Neural Networks}, year = {2006}, volume = {19}, number = {5}, pages = {600--609}, abstract = {It is shown that real-time computations on spike patterns and temporal integration of information in neural microcircuit models are compatible with potentially discruptive additional inputs such as oscillations. A minor change in the connection statistics of such circuits (making synaptic connections to more distal target neurons more likely for excitatory than for inhibitory neurons) endows such generic neural microcircuit model with the ability to generate periodic patterns autonomously. We show that such pattern generation can also be multiplexed with pattern classi�cation and temporal integration of information in the same neural circuit. These results can be interpreted as showing that periodic activity provides a second channel for communication in neural systems which can be used to synchronize or coordinate spatially separated processes, without encumbering local real-time computations on spike trains in diverse neural circuits.} } @Article{KlampflETAL:07, author = {S. Klampfl and R. Legenstein and W. Maass}, title = {Spiking neurons can learn to solve information bottleneck problems and to extract independent components}, journal = {Neural Computation}, year = {2009}, volume = {21}, number = {4}, pages = {911--959}, abstract = {Independent Component Analysis (or blind source separation) is assumed to be an essential component of sensory processing in the brain and could provide a less redundant representation about the external world. Another powerful processing strategy is the optimization of internal representations according to the information bottleneck method. This method would allow to extract preferentially those components from high-dimensional sensory input streams that are related to other information sources, such as internal predictions or proprioceptive feedback. However there exists a lack of models that could explain how spiking neurons could learn to execute either of these two processing strategies. We show in this article how stochastically spiking neurons with refractoriness could in principle learn in an unsupervised manner to carry out both information bottleneck optimization and the extraction of independent components. We derive suitable learning rules, which extend the well known BCM-rule, from abstract information optimization principles. These rules will simultaneously keep the firing rate of the neuron within a biologically realistic range.} } @InProceedings{KlampflETAL:07b, author = {S. Klampfl and R. Legenstein and W. Maass}, title = {Information Bottleneck Optimization and Independent Component Extraction with Spiking Neurons}, booktitle = {Proc. of NIPS 2006, Advances in Neural Information Processing Systems}, editor = {}, publisher = {MIT Press}, year = {2007}, volume = {19}, pages = {713--720}, abstract = {The extraction of statistically independent components from high-dimensional multi-sensory input streams is assumed to b e an essential component of sensory processing in the brain. Such independent component analysis (or blind source separat ion) could provide a less redundant representation of inform ation about the external world. Another powerful processing strategy is to extract preferentially those components from high-dimensional input streams that are related to other inf ormation sources, such as internal predictions or propriocep tive feedback. This strategy allows the optimization of inte rnal representation according to the information bottleneck method. However, concrete learning rules that implement thes e general unsupervised learning principles for spiking neuro ns are still missing. We show how both information bottlenec k optimization and the extraction of independent components can in principle be implemented with stochastically spiking neurons with refractoriness. The new learning rule that achi eves this is derived from abstract information optimization principles.} } @Article{KlampflETAL:09, author = {S. Klampfl and S.V. David and P. Yin and S.A. Shamma and W. Maass}, title = {Integration of stimulus history in information conveyed by neurons in primary auditory cortex in response to tone sequences}, journal = {39th Annual Conference of the Society for Neuroscience, Program 163.8, Poster T6 }, year = {2009}, volume = {}, number = {}, pages = {}, abstract = {A critical component of auditory processing is integrating information about sound features that change over time. Previous studies have shown that the context of a sound -- the immediate history of auditory stimulation -- can have a substantial effect on responses of auditory neurons to a current sound. In order to characterize these effects, we measured the information contained in the neural activity in primary auditory cortex (A1) about both current and preceding sounds. Neural recordings were made from single A1 neurons (n=122) isolated from 23 multi-channel recordings in 4 passively listening ferrets. The stimulus was a sequence of tones (150 ms duration). The frequency step between two consecutive tones was always half an octave up or down. For each neuron, we measured at particular points in time the mutual information (MI) between its response during a sliding window (20ms) and the identity of the current and preceding tone. Since direct estimates of MI from spike trains typically suffer from a systematic error (bias) due to the limited number of available response trials for a given stimulus, we used a recently proposed shuffling-based estimator with additional quadratic extrapolation bias correction (Panzeri et al., 2007). This method produces reliable information estimates for this particular setup. We found that most responses (102 out of 122 neurons) contained significant information about the stimulus throughout the duration of the tone. Of this information, on average, 60\% was about the current tone, while 40\% was about the previous tone. We also trained linear classifiers (Support Vector Machines with linear kernel) on the low-pass filtered response spike trains of multiple simultaneously recorded neurons (4-10) to discriminate between the two possible predecessors for a given tone. The performance the linear classifier can be viewed as a lower bound on the information contained in the responses about the previous tone. Performance of up to 80\% was achieved. These results quantify the amount of information contained in the responses of A1 neurons about both currently and previously played tones and demonstrate that neurons in A1 integrate information about previous input into their current responses. References: Panzeri et al. (2007), J Neurophysiol, 98(3):1064} } @Article{KlampflMaass:09, author = {S. Klampfl and W. Maass}, title = {A neuron can learn anytime classification of trajectories of network states without supervision}, journal = {submitted for publication}, year = {Feb. 2009}, volume = {}, number = {}, pages = {}, note = {} } @Article{KlampflMaass:09a, author = {S. Klampfl and W. Maass}, title = {A theoretical basis for emergent pattern discrimination in neural systems through slow feature extraction}, journal = {submitted}, year = {2009}, pages = {}, volume = {} } @InProceedings{KlampflMaass:09b, author = {S. Klampfl and W. Maass}, title = {Replacing supervised classification learning by {S}low {F}eature {A}nalysis in spiking neural networks}, booktitle = {Proc. of NIPS 2009: Advances in Neural Information Processing Systems}, editor = {}, publisher = {MIT Press}, year = {2010}, volume = {22}, pages = {}, abstract = {Many models for computations in recurrent networks of neurons assume that the network state moves from some initial state to some fixed point attractor or limit cycle that represents the output of the computation. However experimental data show that in response to a sensory stimulus the network state moves from its initial state through a trajectory of network states and eventually returns to the initial state, without reaching an attractor or limit cycle in between. This type of network response, where salient information about external stimuli is encoded in characteristic trajectories of continuously varying network states, raises the question how a neural system could compute with such code, and arrive for example at a temporally stable classification of the external stimulus. We show that a known unsupervised learning algorithm, Slow Feature Analysis (SFA), could be an important ingredient for extracting stable information from these network trajectories. In fact, if sensory stimuli are more often followed by another stimulus from the same class than by a stimulus from another class, SFA approaches the classification capability of Fisher�s Linear Discriminant (FLD), a powerful algorithm for supervised learning. We apply this principle to simulated cortical microcircuits, and show that it enables readout neurons to learn discrimination of spoken digits and detection of repeating firing patterns within a stream of spike trains with the same firing statistics, without requiring any supervision for learning.} } @Article{LegensteinETAL:03, author = {R. Legenstein and H. Markram and W. Maass}, title = {Input Prediction and Autonomous Movement Analysis in Recurrent Circuits of Spiking Neurons}, year = {2003}, journal = {Reviews in the Neurosciences (Special Issue on Neuroinformatics of Neural and Artificial Computation)}, volume = {14}, number = {1--2}, pages = {5--19}, abstract = {Temporal integration of information and prediction of future sensory inputs are assumed to be important computational tasks of generic cortical microcircuits. However it has remained open how cortical microcircuits could possibly achieve this, especially since they consist in contrast to most neural network models of neurons and synapses with heterogeneous dynamic responses. However it turns out that the diversity of computational units increases the capability of microcircuit models for temporal integration. Furthermore the prediction of future input may be rather easy for such circuits since it suffices to train the readouts from such microcircuits. In this article we show that very simple readouts from a generic recurrently connected circuit of integrate-and-fire neurons with diverse dynamic synapses can be trained in an unsupervised manner to predict movements of different objects, that move within an unlimited number of combinations of speed, angle, and offset over a simulated sensor field. The autonomously trained microcircuit model is also able to compute the direction of motion, which is a computationally difficult problem ("aperture problem") since it requires disambiguation of local sensor readings through the context of other sensor readings at the current and preceding moments. Furthermore the same circuit can be trained simultaneously in a supervised manner to also report the shape and velocity of the moving object. Finally it is shown that the trained neural circuit supports novelty detection and the generation of "imagined movements". Altogether the results of this article suggest that it is not necessary to construct specific and biologically unrealistic neural circuit models for specific sensory processing tasks, since "found" generic cortical microcircuit models in combination with very simple perceptron-like readouts can easily be trained to solve such computational tasks.} } @Article{LegensteinETAL:04, author = {R. Legenstein and C. Naeger and W. Maass}, title = {What can a Neuron Learn with Spike-Timing-Dependent Plasticity?}, journal = {Neural Computation}, year = {2005}, volume = {17}, number = {11}, pages = {2337--2382}, abstract = {Leaky integrate-and-fire neurons ("spiking neurons") can implement with different values of their adjustable synaptic parameters an enormous variety of different transformations $F$ from input spike trains to output spike trains. We examine in this article the question to what extent a spiking neuron with biologically realistic models for dynamic synapses can {\em learn} via spike-timing-dependent plasticity (STDP) to implement any such transformation $F$. We show that in contrast to the Perceptron Convergence Theorem for simplified neuron models (McCulloch-Pitts neuron) no theoretical guarantee can be given for the convergence of STDP applied to spiking neurons. On the other hand we demonstrate through extensive computer simulations that for many common distributions of correlated and uncorrelated input spike trains this convergence result holds at least in an approximate sense for spiking neurons with STDP. This suggests that STDP can practically be viewed as a universal learning rule for spiking neurons, since it enables a spiking neuron to approximately learn any transformation $F$ from input spike trains to output spike trains that it could possibly implement in a stable manner. We show that this result not only holds for the common interpretation of STDP where it modulates the weights of (usually static) synapses, but also for an alternative interpretation suggested by experimental data where it modulates the initial release probability of biologically more realistic models for dynamic synapses.} } @InProceedings{LegensteinETAL:04a, author = {R. Legenstein and W. Maass}, title = {A criterion for the convergence of learning with spike timing dependent plasticity}, booktitle = {Advances in Neural Information Processing Systems}, editor = {Y. Weiss and B. Schoelkopf and J. Platt}, volume = {18}, pages = {763--770}, year = 2006, publisher = {MIT Press}, abstract = {We investigate under what conditions a neuron can learn by experimentally supported rules for spike timing dependent plasticity (STDP) to predict the arrival times of strong ``teacher inputs'' to the same neuron. It turns out that in contrast to the famous Perceptron Convergence Theorem, which predicts convergence of the perceptron learning rule for a strongly simplified neuron model whenever a stable solution exists, no equally strong convergence guarantee can be given for spiking neurons with STDP. But we derive a criterion on the statistical dependency structure of input spike trains which characterizes exactly when learning with STDP will converge on average for a simple model of a spiking neuron. This criterion is reminiscent of the linear separability criterion of the Perceptron Convergence Theorem, but it applies here to the rows of a correlation matrix related to the spike inputs. In addition we show through computer simulations for more realistic neuron models that the resulting analytically predicted positive learning results not only hold for the common interpretation of STDP where STDP changes the weights of synapses, but also for a more realistic interpretation suggested by experimental data where STDP modulates the initial release probability of dynamic synapses.} } @InProceedings{LegensteinETAL:08, author = {R. Legenstein and D. Pecevski and W. Maass}, title = {Theoretical Analysis of Learning with Reward-Modulated Spike-Timing-Dependent Plasticity}, booktitle = {Proc. of NIPS 2007, Advances in Neural Information Processing Systems}, editor = {}, publisher = {MIT Press}, year = {2008}, volume = {20}, pages = {881--888}, abstract = {Reward-modulated spike-timing-dependent plasticity ({STDP}) has recently emerged as a candidate for a learning rule that could explain how local learning rules at single synapses support behaviorally relevant adaptive changes in complex networks of spiking neurons. However the potential and limitations of this learning rule could so far only be tested through computer simulations. This article provides tools for an analytic treatment of reward-modulated {STDP}, which allow us to predict under which conditions reward-modulated {STDP} will be able to achieve a desired learning effect. In particular, we can produce in this way a theoretical explanation and a computer model for a fundamental experimental finding on biofeedback in monkeys (reported in [1])} } @Article{LegensteinETAL:08a, author = {R. Legenstein and D. Pecevski and W. Maass}, title = {A Learning Theory for Reward-Modulated Spike-Timing-Dependent Plasticity with Application to Biofeedback}, journal = {PLoS Computational Biology}, year = {2008}, volume = {4}, number = {10}, pages = {1--27}, abstract = {Reward-modulated spike-timing-dependent plasticity ({STDP}) has recently emerged as a candidate for a learning rule that could explain how behaviorally relevant adaptive changes in complex networks of spiking neurons could be achieved in a self-organizing manner through local synaptic plasticity. However the capabilities and limitations of this learning rule could so far only be tested through computer simulations. This article provides tools for an analytic treatment of reward-modulated {STDP}, which allows us to predict under which conditions reward-modulated {STDP} will achieve a desired learning effect. These analytical results imply that neurons can learn through reward-modulated {STDP} to classify not only spatial, but also temporal firing patterns of presynaptic neurons. They also can learn to respond to specific presynaptic firing patterns with particular spike patterns. Finally, the resulting learning theory predicts that even difficult credit-assignment problems, where it is very hard to tell which synaptic weights should be modified in order to increase the global reward for the system, can be solved in a self-organizing manner through reward-modulated {STDP}. This yields an explanation for a fundamental experimental result on biofeedback in monkeys by Fetz and Baker. In this experiment monkeys were rewarded for increasing the firing rate of a particular neuron in the cortex, and were able to solve this extremely difficult credit assignment problem. Our model for this experiment relies on a combination of reward-modulated {STDP} with variable spontaneous firing activity. Hence it also provides a possible functional explanation for trial-to-trial variability, which is characteristic for cortical networks of neurons, but has no analogue in currently existing artificial computing systems. In addition our model demonstrates that reward-modulated {STDP} can be applied to all synapses in a large recurrent neural network without endangering the stability of the network dynamics.} } @Article{LegensteinETAL:08b, author = {R. Legenstein and D. Pecevski and W. Maass}, title = {Supplementary Information to: "{A} Learning Theory for Reward-Modulated Spike-Timing-Dependent Plasticity with Application to Biofeedback"}, journal = {PLoS Computational Biology}, year = {2008}, volume = {4}, number = {10}, pages = {} } @Article{LegensteinETAL:08c, author = {R. Legenstein and S. A. Chase and A. B. Schwartz and W. Maass}, title = {A model for learning effects in motor cortex that may facilitate the brain control of neuroprosthetic devices}, journal = {38th Annual Conference of the Society for Neuroscience, Program 517.6}, year = {2008}, volume = {}, number = {}, pages = {}, abstract = {Recent experimental results have shown that the direction preference of neurons in monkey motor cortex changes in order to compensate for purposeful misreading of preferred directions for brain control of a robot arm. We show that a simple neural network model in combination with a new rule for reward-modulated Hebbian plasticity can explain this effect. This rule requires substantial trial-to-trial variability of the neuronal output for exploration. In contrast to previously proposed rules for reward-modulated Hebbian plasticity, the new rule does not require that the plasticity mechanism `knows' the noise explicitly. It is able to optimize the performance of the model system within biologically realistic periods of time and under high noise levels. When the neuronal noise is fitted to experimental data, the model produces learning effects similar to those found in monkey experiments. We quantified these effects and found a surprisingly good match to those observed in experiments. This study shows that reward-modulated learning can explain detailed experimental results about neuronal tuning changes in a motor control task and suggests that reward-modulated learning is an essential plasticity mechanism in the cortex for the acquisition of goal-directed behavior. Self-tuning effects of the type considered in this model are obviously important for successful use of neuroprosthetic devices.} } @InProceedings{LegensteinETAL:09a, author = {R. Legenstein and S. A. Chase and A. B. Schwartz and W. Maass}, title = {Functional network reorganization in motor cortex can be explained by reward-modulated {H}ebbian learning}, booktitle = {Proc. of NIPS 2009: Advances in Neural Information Processing Systems}, editor = {}, publisher = {MIT Press}, year = {2010}, volume = {22}, pages = {}, note = {in press}, abstract = {The control of neuroprosthetic devices from the activity of motor cortex neurons benefits from learning effects where the function of these neurons is adapted to the control task. It was recently shown that tuning properties of neurons in monkey motor cortex are adapted selectively in order to compensate for an erroneous interpretation of their activity. In particular, it was shown that the tuning curves of those neurons whose preferred directions had been misinterpreted changed more than those of other neurons. In this article, we show that the experimentally observed self-tuning properties of the system can be explained on the basis of a simple learning rule. This learning rule utilizes neuronal noise for exploration and performs Hebbian weight updates that are modulated by a global reward signal. In contrast to most previously proposed reward-modulated Hebbian learning rules, this rule does not require extraneous knowledge about what is noise and what is signal. The learning rule is able to optimize the performance of the model system within biologically realistic periods of time and under high noise levels. When the neuronal noise is fitted to experimental data, the model produces learning effects similar to those found in monkey experiments.} } @TechReport{LegensteinMaass:04, author = {R. Legenstein and W. Maass}, title = {Additional material to the paper: What can a Neuron Learn with Spike-Timing-Dependent Plasticity?}, institution = {Institute for Theoretical Computer Science, Graz University of Technology}, htmlnote = {(PDF)}, year = {2004} } @InCollection{LegensteinMaass:05, author = {R. Legenstein and W. Maass}, title = {What makes a dynamical system computationally powerful?}, booktitle = {New Directions in Statistical Signal Processing: From Systems to Brains}, publisher = {MIT Press}, editor = {S. Haykin and J. C. Principe and T.J. Sejnowski and J.G. McWhirter}, pages = {127--154}, year = {2007}, abstract = {We review methods for estimating the computational capability of a complex dynamical system. The main examples that we discuss are models for cortical neural microcircuits with varying degrees of biological accuracy, in the context of online computations on complex input streams. We address in particular the question to what extent earlier results ab out the relationship between the edge of chaos and the compu tational power of dynamical systems in discrete time for off -line computing also apply to this case.} } @Article{LegensteinMaass:05a, author = {R. Legenstein and W. Maass}, title = {Edge of Chaos and Prediction of Computational Performance for Neural Microcircuit Models}, journal = {Neural Networks}, year = {2007}, volume = {20}, number = {3}, pages = {323--334}, note = {}, abstract = {We analyze in this article the significance of the edge of chaos for real time computations in neural microcircuit models consisting of spiking neurons and dynam ic synapses. We find that the edge of chaos predicts quite well those values of circuit parameters that yield maximal computational performance. But obviously it makes no predic tion of their computational performance for other parameter values. Therefore, we propose a new method for predicting t he computational performance of neural microcircuit models. The new measure estimates directly the kernel property and the generalization capability of a neural microcircuit. We validate the proposed measure by comparing its prediction w ith direct evaluations of the computational performance of various neural microcircuit models. The proposed method als o allows us to quantify differences in the computational pe rformance and generalization capability of neural circuits in different dynamic regimes ({UP}- and {DOWN}-states) that have been demonstrated through intracellular recordings in vivo.} } @Article{LegensteinMaass:07, author = {R. Legenstein and W. Maass}, title = {On the classification capability of sign-constrained perceptrons}, journal = {Neural Computation}, volume = {20}, number = {1}, pages = {288--309}, year = {2008}, abstract = {The perceptron (also referred to as McCulloch-Pitts neuron, or linear threshold gate) is commonly used as a simplified model for the discrimination and learning capability of a biological neuron. Criteria that tell us when a perceptron can implement (or learn to implement) all possible dichotomies over a given set of input patterns are well-known, but only for the idealized case where one assumes that the sign of a synaptic weight can be switched during learning. We present in this article an analysis of the classification capability of the biologically more realistic model of a sign-constrained perceptron, where the signs of synaptic weights remain fixed during learning (which is the case for most types of biological synapses). In particular, the VC-dimension of sign-constrained perceptrons is determined, and a necessary and sufficient criterion is provided that tells us when all $2^m$ dichotomies over a given set of m patterns can be learned by sign-constrained perceptron. We also show that uniformity of {L1} norms of input patterns is a sufficient condition for full representation power in the case where all weights are required to be nonnegative. Finally, we also exhibit cases where the sign-constraint of a perceptron drastically reduces its classification capability. Our theoretical analysis is complemented by computer simulations, which demonstrate in particular that sparse input patterns improve the classification capability of sign-constrained perceptrons.} } @Article{LegensteinMaass:09, author = {R. Legenstein and W. Maass}, title = {An integrated learning rule for branch strength potentiation and {STDP}}, journal = {39th Annual Conference of the Society for Neuroscience, Program 895.20, Poster HH36}, year = {2009}, volume = {}, number = {}, pages = {}, abstract = {Recent experimental data (Losonczy, Makara, and Magee, Nature 2008) show that not only the strength of synaptic efficacy is plastic, but also the coupling between dendritic branches and the soma (via dendritic spikes). More precisely, the strength of this coupling can be increased both through a coincidence of dendritic branch activations with action potential generation, and through a coincidence of branch activation with ACh. This effect has been called Branch Strength Potentiation (BSP). We show through theoretical analysis and computer simulations that the learning capability of single neurons is substantially increased if STDP is combined with BSP. More precisely, we show that a simple learning rule, based on a error-minimization principle, contains both BSP and STDP as special cases. The learning rule includes a homeostatic mechanism which acts locally at the site of the dendritic branch. The depression that was observed for post-before-pre pairings in standard STDP experiments is also observed in simulations of this learning rule. It can be explained by the combined effect of this local homeostatic mechanism and the backpropagating action potential. This powerful new learning rule endows single neurons with learning capabilities which were previously unattainable. For example, a single neuron acquires through this new learning rule the capability to solve a "binding problem". I.e., a single neuron can learn to respond to fire upon activation of presynaptic pools A and B, and also upon activation of presynaptic pools C and D, but NOT in response to concurrent activation of presynaptic pools A and C, or B and D. We also consider a variation of this learning rule where changes at synapses and branches are not only based on local activity, but also on a global reward signal that is indicated to the neuron by the concentration of a neuromodulatory signal such as ACh. We show that this biologically plausible learning rule for reward-based learning is much more efficient than previously proposed rules based on simple neuron models without nonlinear branches.} } @Article{LiebeETAL:09, author = {S. Liebe and G. Hoerzer and N.K. Logothetis and W. Maass and G. Rainer}, title = {Long range coupling between {V4} and {PF} in theta band during visual short-term memory}, journal = {39th Annual Conference of the Society for Neuroscience, Program 652.20, Poster Y31}, year = {2009}, volume = {}, number = {}, pages = {}, abstract = {Both extrastriate area V4 and the lateral prefrontal cortex (PF) are thought to be part of a neural network contributing to sensory and mnemonic processing of visual information. However, it is not well understood how V4 and PF might interact during visual memory. Here, we addressed this question by recording Local Field Potentials (LFP) simultaneously in both brain regions while two rhesus monkeys performed a delayed matching-to sample task. In the task, a sample stimulus (250ms) was presented followed by a probe stimulus (600ms) after a delay period (1500ms). A lever press was required if the sample stimulus matched the probe. We assessed coupling between LFP sites within and between the different brain regions by both measuring pair-wise phase-synchrony (phase locking value, PLV) using a wavelet based method and employing a coupling measure that relies on the concept of Granger causality (partial-directed coherence; PDC) using multivariate autoregressive (MVAR) modeling. In both monkeys we consistently found increases in theta-band phase synchrony (3.5-7 Hz) between V4 and PF LFP site pairs during the delay period of the task. Specifically, a significant proportion of pairs (26.1\%, 62/231 for monkey 1 and 25\%, 40/160 for monkey 2, p<0.001) showed increased coherence during the delay phase compared to the pre-stimulus baseline period. In contrast, only a small proportion of sites showed significant coupling in gamma (42-97 Hz, 5.9\%/13\% for monkeys 1/2, respectively) or beta (16-36Hz, 6.9\%/16\%) frequencies. In addition, we obtained comparable results using PDC, which also assesses the directionality of information flow between the brain areas. Our preliminary results indicate that the interaction between V4 and PF during short-term memory might be primarily mediated through neuronal coherence in the theta band. Furthermore, our analyses using MVAR modeling suggest that this interaction can be characterized by a bidirectional information flow between these areas. These findings support the idea that long-range interactions play an important role in short-term maintenance of short-term memory.} } @InCollection{Maass:00, author = {W. Maass}, title = {Spike trains -- Im {R}hythmus neuronaler {Z}ellen}, booktitle = {Katalog der steirischen Landesausstellung gr2000az}, pages = {36--42}, publisher = {Springer Verlag}, year = {2000}, editor = {H. Konrad, R. Kriesche} } @InCollection{Maass:00a, author = {W. Maass}, title = {Lernende {M}aschinen}, booktitle = {Katalog der steirischen Landesausstellung gr2000az}, pages = {50--56}, publisher = {Springer Verlag}, year = 2000, editor = {H. Konrad, R. Kriesche} } @InCollection{Maass:00b, author = {W. Maass}, title = {Neural computation: a research topic for theoretical computer science? {S}ome thoughts and pointers}, booktitle = {Current Trends in Theoretical Computer Science, Entering the 21th Century}, publisher = {World Scientific Publishing}, year = {2001}, pages = {680--690}, editor = {Rozenberg G. and Salomaa A. and Paun G.} } @InProceedings{Maass:00c, author = {W. Maass}, title = {Neural computation: a research topic for theoretical computer science? {S}ome thoughts and pointers}, booktitle = {Bulletin of the European Association for Theoretical Computer Science (EATCS)}, pages = {149--158}, year = {2000}, volume = {72} } @InProceedings{Maass:01a, author = {W. Maass}, title = {wetware ({E}nglish version)}, booktitle = {{TAKEOVER}: {W}ho is {D}oing the {A}rt of {T}omorrow ({A}rs {E}lectronica 2001)}, pages = {148--152}, year = {2001}, publisher = {Springer} } @InProceedings{Maass:01b, author = {W. Maass}, title = {wetware (deutsche {V}ersion)}, booktitle = {{TAKEOVER}: {W}ho is {D}oing the {A}rt of {T}omorrow ({A}rs {E}lectronica 2001)}, year = {2001}, pages = {153--157}, publisher = {Springer} } @Article{Maass:02, author = {W. Maass}, title = {Computing with Spikes}, journal = {Special Issue on Foundations of Information Processing of {TELEMATIK}}, year = {2002}, pages = {32--36}, volume = {8}, number = {1} } @InProceedings{Maass:02a, author = {W. Maass}, title = {On the Computational Power of Neural Microcircuit Models: Pointers to the Literature}, booktitle = {Proc. of the International Conference on Artificial Neural Networks -- ICANN 2002}, pages = {254--256}, year = {2002}, editor = {Jos\'{e} R. Dorronsoro}, volume = {2415}, series = {Lecture Notes in Computer Science}, publisher = {Springer} } @InCollection{Maass:03, author = {W. Maass}, title = {Computation with Spiking Neurons}, booktitle = {The Handbook of Brain Theory and Neural Networks}, edition = {2nd}, publisher = {MIT Press (Cambridge)}, editor = {M. A. Arbib}, year = {2003}, pages = {1080--1083} } @Article{Maass:06, author = {W. Maass}, title = {Book Review of "{I}mitation of life: how biology is inspiring computing" by {N}ancy {F}orbes}, journal = {Pattern Analysis and Applications}, year = {2006}, volume = {8}, number = {4}, pages = {390--391}, note = {Springer (London)} } @InProceedings{Maass:07, author = {W. Maass}, booktitle = {Proceedings of the Conference CiE'07: {COMPUTABILITY IN EUROPE} 2007, Siena (Italy)}, title = {Liquid Computing}, publisher = {Springer (Berlin)}, series = {Lecture Notes in Computer Science}, volume = {}, year = {2007}, pages = {}, note = {in press}, abstract = {This review addresses structural differences between that type of computation on which computability theory and computational complexity theory have focused so far, and those computations that are usually carried out in biological organisms (either in the brain, or in the form of gene regulation within a single cell). These differences concern the role of time, the way in which the input is presented, the way in which an algorithm is implemented, and in the end also the definition of what a computation is. This article describes liquid computing as a new framework for analyzing those types of computations that are usually carried out in biological organisms.} } @InCollection{Maass:09, author = {W. Maass}, title = {Motivation, Theory, and Applications of Liquid State Machines}, booktitle = {Computability in Context: Computation and Logic in the Real World}, editor = {B. Cooper and A. Sorbi}, year = {2009}, publisher = {Imperial College Press}, pages = {}, keywords = {}, note = {in press}, abstract = {The Liquid State Machine (LSM) has emerged as a computational model that is more adequate than the Turing machine for describing computations in biological networks of neurons. Characteristic features of this new model are (i) that it is a model for adaptive computational systems, (ii) that it provides a method for employing randomly connected circuits, or eve "found" physical objects for meaningful computations, (iii) that it provides a theoretical context where heterogeneous, rather than stereotypical, local gates or processors increase the computational power of a circuit, (iv) that it provides a method for multiplexing different computations (on a common input) within the same circuit. This chapter reviews the motivation for this model, its theoretical background, and current work on implementations of this model in innovative artificial computing devices.} } @InProceedings{Maass:75, author = {W. Maass}, booktitle = {Proof Theory Symposium Kiel 1974}, editor = {J. Diller and G. H. Mueller}, journal = {Lecture Notes in Mathematics, Springer (Berlin)}, pages = {257--263}, publisher = {Springer (Berlin)}, series = {Lecture Notes in Mathematics}, title = {Church Rosser Theorem fuer Lambda-Kalkuele mit unendlich langen Termen}, volume = {500}, year = {1975} } @Article{Maass:76, author = {W. Maass}, journal = {Archive Math. Logik Grundlagen}, pages = {27--46}, title = {Eine {F}unktionalinterpretation der praedikativen {A}nalysis}, volume = {18}, year = {1976} } @Article{Maass:77, author = {W. Maass}, journal = {Archive Math. Logik Grundlagen}, pages = {169--186}, title = {On minimal pairs and minimal degrees in higher recursion theory}, volume = {18}, year = {1977} } @Article{Maass:78, author = {W. Maass}, journal = {Ann. of Math. Logic}, pages = {149--170}, title = {Inadmissibility, tame r.e. sets and the admissible collapse}, volume = {13}, year = {1978} } @Article{Maass:78a, author = {W. Maass}, journal = {J. Symbolic Logic}, pages = {270-279}, title = {The uniform regular set theorem in alpha-recursion theory}, volume = {43}, year = {1978} } @InProceedings{Maass:78b, author = {W. Maass}, booktitle = {Higher Set Theory}, editor = {G. H. Mueller and D. Scott}, pages = {339--359}, publisher = {Springer (Berlin)}, series = {Lecture Notes in Mathematics}, title = {Fine structure theory of the constructible universe in alpha- and beta-recursion theory}, volume = {669}, year = {1978} } @Conference{GuptaMaass:91, author = {A. Gupta and W. Maass}, booktitle = {Advances in Neural Information Processing Systems}, editor = {R. P. Lippmann and J. E. Moody and D. S. Touretzky}, pages = {825--831}, publisher = {Morgan Kaufmann, (San Mateo)}, title = {A method for the efficient design of {B}oltzmann machines for classification problems}, volume = {3}, year = {1991} } @MastersThesis{Maass:78c, author = {W. Maass}, note = {Minerva Publikation (Muenchen)}, school = {Ludwig-Maximilians-Universitaet Muenchen}, title = {Contributions to alpha- and beta-recursion theory}, type = {Habilitationsschrift}, year = {1978} } @InCollection{Maass:78d, author = {W. Maass}, booktitle = {Generalized Recursion Theory II}, editor = {E. Fenstad and R. O. Gandy and G. E. Sacks}, pages = {239--269}, publisher = {North-Holland (Amsterdam)}, title = {High alpha-recursively enumerable degrees}, year = {1978} } @Article{Maass:79, author = {W. Maass}, journal = {Ann. of Math. Logic}, pages = {205--231}, title = {On alpha- and beta-recursively enumerable degrees}, volume = {16}, year = {1979} } @InProceedings{Maass:81, author = {W. Maass}, booktitle = {Proceedings of the Conf. on Recursion Theory and Computational Complexity}, editor = {G. Lolli}, pages = {229--236}, publisher = {Liguori editore (Napoli)}, title = {Recursively invariant beta-recursion theory -- a preliminary survey}, year = {1981} } @Article{Maass:81a, author = {W. Maass}, journal = {Proceedings Amer. Math. Soc.}, pages = {267--270}, title = {A countable basis for sigma-one-two sets and recursion theory on aleph-one}, volume = {82}, year = {1981} } @Article{Maass:81b, author = {W. Maass}, journal = {Ann. of Math. Logic}, pages = {27--73}, title = {Recursively invariant beta-recursion theory}, volume = {21}, year = {1981} } @Article{Maass:83, author = {W. Maass}, journal = {J. Symbolic Logic}, pages = {809--823}, title = {Recursively enumerable generic sets}, volume = {47}, year = {1983} } @Article{Maass:83a, author = {W. Maass}, journal = {Trans. Amer. Math. Soc.}, pages = {311--336}, title = {Characterization of recursively enumerable sets with supersets effectively isomorphic to all recursively enumerable sets}, volume = {279}, year = {1983} } @Article{Maass:84, author = {W. Maass}, journal = {J. Symbolic Logic}, pages = {51--62}, title = {On the orbits of hyperhypersimple sets}, volume = {49}, year = {1984} } @InProceedings{Maass:84a, author = {W. Maass}, booktitle = {Proceedings of 16th Annual ACM Symp. on Theory of Computing}, pages = {401--408}, title = {Quadratic lower bounds for deterministic and nondeterministic one-tape {T}uring machines}, abstract = {We introduce new techniques for proving quadratic lower bounds for deterministic and nondeterministic i-tape Turing machines (all considered Turing machines have an additional oneway input tape). In particular we produce quadratic lower bounds for the simulation of 2-tape TM's by l-tape TM's and thus answer a rather old question (problem No.1 and No.7 in the l i s t of Duris, Galil, Paul, Reischuk [3]). Further we demo6strate a substantial superiority of nondeterminism over determinism and of co-nondeterminism over nondeterminism for l-tape TM's.}, year = {1984} } @Article{Maass:85, author = {W. Maass}, journal = {J. Symbolic Logic}, pages = {138--148}, title = {Variations on promptly simple sets}, volume = {50}, year = {1985} } @Article{Maass:85a, author = {W. Maass}, journal = {Proceedings of Symposia in Pure Mathematics}, pages = {21--32}, title = {Major subsets and automorphisms of recursively enumerable sets}, volume = {42}, year = {1985} } @Article{Maass:85b, author = {W. Maass}, journal = {Transactions of the American Mathematical Society}, pages = {675--693}, title = {Combinatorial lower bound arguments for deterministic and nondeterministic {T}uring machines}, abstract = {We introduce new techniques for proving quadratic lower bounds for deterministic and nondeterminisitc 1-tape {T}uring machines (all considered {T}uring machines have an additional one-way input tape). In particular, we derive for the simulation of 2-tape {T}uring machines by 1-tape {T}uring machines an optimal quadratic lower bound in the deterministic case and a nearly optimal lower bound in the nonderterministic case. This answers the rather old question whether the computing power of the considered types of {T}uring machines is significantly increased when more than one tape is used (problem Nos. 1 and 7 in the list of {D}uris, {G}alil, {P}aul, {R}eischuk [3]). Further, we demonstrate a substantial superiority of nonderterminism over determinism and of co-nondeterminism over nondeterminism for 1-tage {T}uring machines}, volume = {292}, number = {2}, year = {1985}, note = {hard copy} } @InProceedings{Maass:86, author = {W. Maass}, booktitle = {Proceedings of the International Conference on Logic, Methodology and Philosphy of Science, Salzburg 1983}, pages = {141--158}, publisher = {North-Holland (Amsterdam)}, title = {Are recursion theoretic arguments useful in complexity theory}, year = {1986} } @Article{Maass:86a, author = {W. Maass}, journal = {SIAM J. Computing}, pages = {453--467}, title = {On the complexity of nonconvex covering}, volume = {15}, year = {1986} } @Article{Maass:88, author = {W. Maass}, journal = {J. Symbolic Logic}, pages = {1098--1109}, title = {On the use of inaccessible numbers and order indiscernibles in lower bound arguments for random access machines}, volume = {53}, year = {1988} } @InProceedings{Maass:91, author = {W. Maass}, booktitle = {Proceedings of the 4th Annual ACM Workshop on Computational Learning Theory}, pages = {167--175}, publisher = {Morgan Kaufmann (San Mateo)}, title = {On-line learning with an oblivious environment and the power of randomization}, year = {1991} } @InProceedings{Maass:93, author = {W. Maass}, booktitle = {Proceedings of the 25th Annual ACM Symposium on Theory Computing}, pages = {335-344}, title = {Bounds for the computational power and learning complexity of analog neural nets}, year = {1993} } @Article{Maass:93j, author = {W. Maass}, title = {Bounds for the computational power and learning complexity of analog neural nets}, journal = {SIAM J. on Computing}, year = 1997, volume = 26, number = 3, pages = {708--732} } @InProceedings{Maass:94, author = {W. Maass}, booktitle = {Advances in Neural Information Processing Systems}, pages = {311--318}, title = {Agnostic {PAC}-learning of functions on analog neural nets}, editors = {G. Tesauro and D. S. Touretzky and T. K. Leen}, volume = {7}, year = {1995} } @InProceedings{Maass:94a, author = {W. Maass}, booktitle = {Proceedings of the International Conference on Artificial Neural Networks 1994 (ICANN'94)}, pages = {581--584}, publisher = {Springer (Berlin)}, title = {Neural nets with superlinear {VC}-dimension}, year = {1994} } @InCollection{Maass:94b, author = {W. Maass}, booktitle = {Theoretical Advances in Neural Computation and Learning}, editor = {V. P. Roychowdhury and K. Y. Siu and A. Orlitsky}, pages = {295-336}, publisher = {Kluwer Academic Publishers (Boston)}, title = {Perspectives of current research about the complexity of learning on neural nets}, year = {1994} } @InProceedings{Maass:94c, author = {W. Maass}, booktitle = {Theoretical Andvances in Neural Computation and Learning}, editor = {V. P. Roychowdhury and K. Y. Siu and A. Orlitsky}, pages = {153--172}, publisher = {Kluwer Academics Publisher (Boston)}, title = {Computing on analog neural nets with arbitrary real weights}, year = {1994} } @InProceedings{Maass:94d, author = {W. Maass}, booktitle = {Proc. of the 7th Annual ACM Conference on Computational Learning Theory}, pages = {67--75}, title = {Efficient agnostic {PAC}-learning with simple hypotheses}, year = {1994} } @InCollection{Maass:94e, author = {W. Maass}, booktitle = {Computational Learning Theory: EuroColt'93}, editor = {J. Shawe-Taylor and M. Anthony}, pages = {1--17}, publisher = {Oxford University Press (Oxford)}, title = {On the complexity of learning on neural nets}, year = {1994} } @Article{Maass:94f, author = {W. Maass}, title = {Agnostic {PAC}-learning of functions on analog neural nets}, journal = {Neural Computation}, year = 1995, volume = 7, pages = {1054--1078} } @Article{Maass:94j, author = {W. Maass}, title = {Neural nets with superlinear {VC}-dimension}, journal = {Neural Computation}, year = 1994, volume = 6, pages = {877--884} } @InProceedings{Maass:95, author = {W. Maass}, booktitle = {Proc. of the 7th Italian Workshop on Neural Nets 1995}, pages = {99--104}, publisher = {World Scientific (Singapore)}, title = {Analog computations on networks of spiking neurons (extended abstract)}, year = {1996} } @InCollection{Maass:95a, author = {W. Maass}, booktitle = {The Handbook of Brain Theory and Neural Networks}, editor = {M.~A.~Arbib}, pages = {1000--1003}, publisher = {MIT Press (Cambridge)}, title = {Vapnik-{C}hervonenkis dimension of neural nets}, year = {1995} } @InProceedings{Maass:95b, author = {W. Maass}, booktitle = {Advances in Neural Information Processing Systems}, editor = {G. Tesauro and D. S. Touretzky and T. K. Leen}, pages = {183--190}, publisher = {MIT Press (Cambridge)}, title = {On the computational complexity of networks of spiking neurons}, volume = {7}, year = {1995} } @Article{Maass:95c, author = {W. Maass}, journal = {Telematik}, pages = {53--60}, volume = {1}, title = {{N}euronale {N}etze und {M}aschinelles {L}ernen am {I}nstitut fuer {G}rundlagen der {I}nformationsverarbeitung an der {T}echnischen {U}niversitaet {G}raz}, year = {1995} } @Article{Maass:96, author = {W. Maass}, journal = {Neural Computation}, pages = {1--40}, title = {Lower Bounds for the Computational Power of Networks of Spiking Neurons}, volume = {8}, number = {1}, year = {1996} } @InProceedings{Maass:96a, author = {W. Maass}, booktitle = {Advances in Neural Information Processing Systems}, editor = {D. Touretzky and M. C. Mozer and M. E. Hasselmo}, pages = {211--217}, publisher = {MIT Press (Cambridge)}, title = {On the computational power of noisy spiking neurons}, volume = {8}, year = {1996} } @InProceedings{Maass:96b, author = {W. Maass}, title = {Networks of spiking neurons: the third generation of neural network models}, booktitle = {Proc. of the 7th Australian Conference on Neural Networks 1996 in Canberra, Australia}, pages = {1-10}, year = {1996} } @Article{Maass:97a, author = {W. Maass}, journal = {Neural Computation}, pages = {279--304}, title = {Fast sigmoidal networks via spiking neurons}, volume = {9}, year = {1997} } @Article{Maass:97b, author = {W. Maass}, howpublished = {FTP-host: archive.cis.ohio-state.edu FTP-filename: /pub/neuroprose/maass.third-generation.ps.Z}, journal = {Neural Networks}, pages = {1659--1671}, title = {Networks of spiking neurons: the third generation of neural network models}, volume = {10}, year = {1997} } @InProceedings{Maass:97c, author = {W. Maass}, booktitle = {Computational Neuroscience: Trends in research}, editor = {James Bower}, pages = {123--127}, title = {A model for fast analog computations with noisy spiking neurons}, year = {1997} } @InCollection{Maass:97d, author = {W. Maass}, booktitle = {Spatiotemporal Models in Biological and Artificial Systems}, editor = {F. L. Silva}, pages = {97-104}, publisher = {IOS-Press}, title = {Analog computations with temporal coding in networks of spiking neurons}, year = {1997} } @InProceedings{Maass:97e, author = {W. Maass}, booktitle = {Advances in Neural Information Processing Systems}, editor = {M. Mozer and M. I. Jordan and T. Petsche}, pages = {211--217}, publisher = {MIT Press (Cambridge)}, title = {Noisy spiking neurons with temporal coding have more computational power than sigmoidal neurons}, volume = {9}, year = {1997} } @InProceedings{Maass:97f, author = {W. Maass}, booktitle = {Proc. of the 8th International Conference on Algorithmic Learning Theory in Sendai (Japan)}, editor = {M. Li and A. Maruoka}, pages = {364--384}, publisher = {Springer (Berlin)}, series = {Lecture Notes in Computer Science}, title = {On the relevance of time in neural computation and learning}, volume = {1316}, year = {1997} } @Article{Maass:97g, author = {W. Maass}, title = {On the relevance of time in neural computation and learning}, journal = {Theoretical Computer Science}, year = 2001, volume = {261}, pages = {157-178} } @InProceedings{Maass:98a, author = {W. Maass}, booktitle = {Proc. of the Federated Conference of CLS'98 and MFCS'98, Mathematical Foundations of Computer Science 1998}, title = {On the role of time and space in neural computation}, publisher = {Springer (Berlin)}, series = {Lecture Notes in Computer Science}, volume = {1450}, year = {1998}, pages = {72-83}, note = {Invited talk} } @Article{Maass:98b, author = {W. Maass}, journal = {Network: Computation in Neural Systems}, number = {3}, pages = {381-397}, title = {A simple model for neural computation with firing rates and firing correlations}, volume = {9}, year = {1998} } @InProceedings{Maass:98d, author = {W. Maass}, title = {Models for fast analog computation with spiking neurons}, booktitle = {Proc. of the International Conference on Neural Information Processing 1998 (ICONIP'98) in Kytakyusyu, Japan}, pages = {187--188}, year = 1998, publisher = {IOS Press (Amsterdam)}, note = {Invited talk at the special session on ``Dynamic Brain''} } @InProceedings{Maass:98e, author = {W. Maass}, title = {Spiking neurons}, booktitle = {Proceedings of the ICSC/IFAC Symposium on Neural Computation 1998 (NC'98)}, pages = {16--20}, year = 1998, publisher = {ICSC Academic Press (Alberta)}, note = {Invited talk} } @InCollection{Maass:98f, author = {W. Maass}, title = {Computing with spiking neurons}, booktitle = {Pulsed Neural Networks}, pages = {55--85}, publisher = {MIT Press (Cambridge)}, year = {1999}, editor = {W. Maass and C.~M.~Bishop} } @InProceedings{Maass:99, author = {W. Maass}, title = {Neural Computation with Winner-Take-All as the only Nonlinear Operation}, booktitle = {Advances in Information Processing Systems}, editor = {Sara A. Solla and Todd K. Leen and Klaus-Robert Mueller}, volume = {12}, publisher = {MIT Press (Cambridge)}, year = {2000}, pages = {293--299} } @InCollection{Maass:99a, author = {W. Maass}, title = {Das menschliche {G}ehirn -- nur ein {R}echner?}, booktitle = {Zur Kunst des Formalen Denkens}, publisher = {Passagen Verlag (Wien)}, year = 2000, pages = {209-233}, editor = {R. E. Burkard and W. Maass and P. Weibel} } @InCollection{Maass:99c, author = {W. Maass}, title = {Paradigms for computing with spiking neurons}, booktitle = {Models of Neural Networks. Early Vision and Attention}, publisher = {Springer (New York)}, year = {2002}, editor = {J. L. van Hemmen and J. D. Cowan and E. Domany}, volume = {4}, chapter = {9}, pages = {373--402} } @Article{Maass:99e, author = {W. Maass}, title = {On the computational power of winner-take-all}, year = {2000}, journal = {Neural Computation}, volume = {12}, number = {11}, pages = {2519--2536} } @Article{MaassETAL:00, author = {W. Maass and A. Pinz and R. Braunstingl and G. Wiesspeiner and T. Natschlaeger and O. Friedl and H. Burgsteiner}, title = {Konstruktion von {L}ernfaehigen {R}obotern im {S}tudentenwettbewerb ``{R}obotik 2000'' an der {T}echnischen {U}niversitaet {G}raz}, journal = {in: Telematik}, year = {2000}, pages = {20--24} } @Article{MaassETAL:01a, author = {W. Maass and T. Natschlaeger and H. Markram}, title = {Real-time Computing Without Stable States: A New Framework for Neural Computation Based on Perturbations}, journal = {Neural Computation}, volume = 14, number = 11, pages = {2531-2560}, year = 2002, abstract = {A key challenge for neural modeling is to explain how a continuous stream of multi-modal input from a rapidly changing environment can be processed by stereotypical recurrent circuits of integrate-and-fire neurons in real-time. We propose a new framework for neural computation that provides an alternative to previous approaches based on attractor neural networks. It is shown that the inherent transient dynamics of the high-dimensional dynamical system formed by a neural circuit may serve as a universal source of information about past stimuli, from which readout neurons can extract particular aspects needed for diverse tasks in real-time. Stable internal states are not required for giving a stable output, since transient internal states can be transformed by readout neurons into stable target outputs due to the high dimensionality of the dynamical system. Our approach is based on a rigorous computational model, the liquid state machine, that unlike Turing machines, does not require sequential transitions between discrete internal states. Like the Turing machine paradigm it allows for universal computational power under idealized conditions, but for real-time processing of time-varying input. The resulting new framework for neural computation has novel implications for the interpretation of neural coding, for the design of experiments and data-analysis in neurophysiology, and for neuromorphic engineering.} } @InProceedings{MaassETAL:02, author = {W. Maass and G. Steinbauer and R. Koholka}, title = {Autonomous fast learning in a mobile robot}, booktitle = {Sensor Based Intelligent Robots. International Workshop, Dagstuhl Castle, Germany, October 15--25, 2000, Selected Revised Papers }, pages = {345--356}, year = {2002}, editor = {G. D. Hager and H. I. Christensen and H. Bunke and R. Klein}, volume = {2238}, series = lncs, publisher = {Springer (Berlin)} } @InProceedings{MaassETAL:02a, author = {W. Maass and R. Legenstein and H. Markram}, title = {A New Approach towards Vision suggested by Biologically Realistic Neural Microcircuit Models}, booktitle = {Biologically Motivated Computer Vision. Proc. of the Second International Workshop, BMCV 2002, Tuebingen, Germany, November 22--24, 2002}, editor = {H. H. Buelthoff and S. W. Lee and T. A. Poggio and C. Wallraven}, series = {Lecture Notes in Computer Science}, volume = {2525}, pages = {282--293}, year = {2002}, publisher = {Springer (Berlin)}, abstract = {We propose an alternative paradigm for processing time-varying visual inputs, in particular for tasks involving temporal and spatial integration, which is inspired by hypotheses about the computational role of cortical microcircuits. Since detailed knowledge about the precise structure of the microcircuit is not needed for that, it can in principle also be implemented with partially unknown or faulty analog hardware. In addition, this approach supports parallel realtime processing of time-varying visual inputs for diverse tasks, since different readouts can be trained to extract concurrently from the same microcircuit completely different information components.} } @InProceedings{MaassETAL:02b, author = {W. Maass and T. Natschlaeger and H. Markram}, title = {A Model for Real-Time Computation in Generic Neural Microcircuits}, booktitle = {Proc. of NIPS 2002, Advances in Neural Information Processing Systems}, editor = {S. Becker and S. Thrun and K. Obermayer}, publisher = {MIT Press}, year = {2003}, volume = {15}, pages = {229--236}, abstract = {A key challenge for neural modeling is to explain how a continuous stream of multi-modal input from a rapidly changing environment can be processed by stereotypical recurrent circuits of integrate-and-fire neurons in real-time. We propose a new computational model that does not require a task-dependent construction of neural circuits. Instead it is based on principles of high dimensional dynamical systems in combination with statistical learning theory, and can be implemented on generic evolved or found recurrent circuitry.} } @Article{MaassETAL:02c, author = {W. Maass and T. Natschlaeger and H. Markram}, title = {Fading Memory and Kernel Properties of Generic Cortical Microcircuit Models}, journal = {Journal of Physiology -- Paris}, year = {2004}, pages = {315--330}, volume = {98}, number = {4--6}, abstract = {It is quite difficult to construct circuits of spiking neurons that can carry out complex computational tasks. On the other hand even randomly connected circuits of spiking neurons can in principle be used for complex computational tasks such as time-warp invariant speech recognition. This is possible because such circuits have an inherent tendency to integrate incoming information in such a way that simple linear readouts can be trained to transform the current circuit activity into the target output for a very large number of computational tasks. Consequently we propose to analyze circuits of spiking neurons in terms of their roles as analog fading memory and nonlinear kernels, rather than as implementations of specific computational operations and algorithms. This article is a sequel to \cite{LSM}, and contains new results about the performance of generic neural microcircuit models for the recognition of speech that is subject to linear and nonlinear time-warps, as well as for computations on time-varying firing rates. These computations rely, apart from general properties of generic neural microcircuit models, just on capabilities of simple linear readouts trained by linear regression. This article also provides detailed data on the fading memory property of generic neural microcircuit models, and a quick review of other new results on the computational power of such circuits of spiking neurons.} } @InCollection{MaassETAL:03, author = {W. Maass and T. Natschlaeger and H. Markram}, title = {Computational Models for Generic Cortical Microcircuits}, booktitle = {Computational Neuroscience: A Comprehensive Approach}, publisher = {Chapman \& Hall/CRC}, year = {2004}, editor = {J. Feng}, chapter = {18}, pages = {575--605}, address = {Boca Raton}, abstract = {The human nervous system processes a continuous stream of multi-modal input from a rapidly changing environment. A key challenge for neural modeling is to explain how the neural microcircuits (columns, minicolumns, etc.) in the cerebral cortex whose anatomical and physiological structure is quite similar in many brain areas and species achieve this enormous computational task. We propose a computational model that could explain the potentially universal computational capabilities and does not require a task-dependent construction of neural circuits. Instead it is based on principles of high dimensional dynamical systems in combination with statistical learning theory, and can be implemented on generic evolved or found recurrent circuitry. This new approach towards understanding neural computation on the micro-level also suggests new ways of modeling cognitive processing in larger neural systems. In particular it questions traditional ways of thinking about neural coding.} } @InProceedings{MaassETAL:04, author = {W. Maass and R. Legenstein and N. Bertschinger}, booktitle = {Advances in Neural Information Processing Systems}, title = {Methods for Estimating the Computational Power and Generalization Capability of Neural Microcircuits}, year = {2005}, volume = {17}, pages = {865--872}, editor = {L. K. Saul and Y. Weiss and L. Bottou}, publisher = {MIT Press}, abstract = {What makes a neural microcircuit computationally powerful? Or more precisely, which measurable quantities could explain why one microcircuit $C$ is better suited for a particular family of computational tasks than another microcircuit $C'$? We propose in this article quantitative measures for evaluating the computational power and generalization capability of a neural microcircuit, and apply them to generic neural microcircuit models drawn from different distributions. We validate the proposed measures by comparing their prediction with direct evaluations of the computational performance of these microcircuit models. This procedure is applied first to microcircuit models that differ with regard to the spatial range of synaptic connections and with regard to the scale of synaptic efficacies in the circuit, and then to microcircuit models that differ with regard to the level of background input currents and the level of noise on the membrane potential of neurons. In this case the proposed method allows us to quantify differences in the computational power and generalization capability of circuits in different dynamic regimes (UP- and DOWN-states) that have been demonstrated through intracellular recordings in vivo.} } @InProceedings{MaassETAL:06, author = {W. Maass and P. Joshi and E. D. Sontag}, title = {Principles of real-time computing with feedback applied to cortical microcircuit models}, booktitle = {Advances in Neural Information Processing Systems}, abstract = {The network topology of neurons in the brain exhibits an abundance of feedback connections, but the computational function of these feedback connections is largely unknown. We present a computational theory that characterizes the gain in computational power achieved through feedback in dynamical systems with fading memory. It implies that many such systems acquire through feedback universal computational capabilities for analog computing with a non-fading memory. In particular, we show that feedback enables such systems to process time-varying input streams in diverse ways according to rules that are implemented through internal states of the dynamical system. In contrast to previous attractor-based computational models for neural networks, these flexible internal states are {\em high-dimensional} attractors of the circuit dynamics, that still allow the circuit state to absorb new information from online input streams. In this way one arrives at novel models for working memory, integration of evidence, and reward expectation in cortical circuits. We show that they are applicable to circuits of conductance-based Hodgkin-Huxley (HH) neurons with high levels of noise that reflect experimental data on in-vivo conditions. }, year = {2006}, volume = {18}, pages = {835--842}, publisher = {MIT Press}, editor = {Y. Weiss and B. Schoelkopf and J. Platt} } @Article{MaassETAL:06a, author = {W. Maass and P. Joshi and E. D. Sontag}, title = {Computational aspects of feedback in neural circuits}, journal = {PLoS Computational Biology}, year = 2007, volume = {3}, number = {1}, pages = {e165, 1--20} } @Article{MaassETAL:07, author = {H. Jaeger and W. Maass and J. Principe}, title = {Introduction to the Special Issue on Echo State Networks and Liquid State Machines}, journal = {Neural Networks}, year = {2007}, volume = {20}, number = {3}, pages = {287--289}, note = {} } @Article{MaassETAL:81, author = {W. Maass and A. Shore and M. Stob}, journal = {Israel J. Math.}, pages = {210--224}, title = {Splitting properties and jump classes}, volume = {39}, year = {1981} } @InProceedings{MaassETAL:87, author = {W. Maass and G. Schnitger and E. Szemeredi}, booktitle = {Proceedings of the 19th Annual ACM Symposium on Theory of Computing}, pages = {94--100}, title = {Two tapes are better than one for off-line Turing machines}, year = {1987} } @InProceedings{MaassETAL:91, author = {W. Maass and G. Schnitger and E. Sontag}, booktitle = {Proc. of the 32nd Annual IEEE Symposium on Foundations of Computer Science 1991}, pages = {767-776}, title = {On the computational power of sigmoid versus boolean threshold circuits}, year = {1991} } @InCollection{MaassETAL:91a, author = {W. Maass and G. Schnitger and E. Sontag}, title = {On the computational power of sigmoid versus boolean threshold circuits}, booktitle = {Theoretical Advances in Neural Computation and Learning}, pages = {127--151}, publisher = {Kluwer Academic Publishers (Boston)}, year = {1994}, editor = {V.~P.~Roychowdhury and K.~Y.~Siu and A.~Orlitsky} } @Article{MaassETAL:93, author = {W. Maass and G. Schnitger and E. Szemeredi and G. Turan}, journal = {Computational Complexity}, pages = {392--401}, title = {Two tapes versus one for off-line {T}uring machines}, volume = {3}, year = {1993} } @InProceedings{MaassLegenstein:01, author = {R. A. Legenstein and W. Maass}, title = {Foundations for a circuit complexity theory of sensory processing}, booktitle = {Proc. of NIPS 2000, Advances in Neural Information Processing Systems}, editor = {T. K. Leen and T. G. Dietterich and V. Tresp}, year = {2001}, volume = {13}, pages = {259--265}, publisher = {MIT Press}, address = {Cambridge}, htmlnote = {The poster presented at NIPS is available as gzipped Postscript.}, abstract = {We introduce {\em total wire length} as salient complexity measure for an analysis of the circuit complexity of sensory processing in biological neural systems and neuromorphic engineering. Furthermore we introduce a set of basic computational problems that apparently need to be solved by circuits for translation- and scale-invariant sensory processing. Finally we exhibit a number of circuit design strategies for these new benchmark functions that can be implemented within realistic complexity bounds, in particular with linear or almost linear total wire length.} } @Article{MaassLegenstein:01a, author = {R. A. Legenstein and W. Maass}, title = {Wire Length as a Circuit Complexity Measure}, journal = {Journal of Computer and System Sciences}, year = {2005}, volume = {70}, pages = {53--72}, abstract = { We introduce {\em wire length} as a salient complexity measure for analyzing the circuit complexity of sensory processing in biological neural systems. This new complexity measure is applied in this paper to two basic computational problems that arise in translation- and scale-invariant pattern recognition, and hence appear to be useful as benchmark problems for sensory processing. We present new circuit design strategies for these benchmark problems that can be implemented within realistic complexity bounds, in particular with linear or almost linear wire length. Finally we derive some general bounds which provide information about the relationship between new complexity measure wire length and traditional circuit complexity measures.} } @Article{MaassLegenstein:01c, author = {R. A. Legenstein and W. Maass}, title = {Neural circuits for pattern recognition with small total wire length}, journal = {Theoretical Computer Science}, volume = {287}, pages = {239--249}, year = {2002}, abstract = {One of the most basic pattern recognition problems is whether a certain local feature occurs in some linear array to the left of some other local feature. We construct in this article circuits that solve this problem with an asymptotically optimal number of threshold gates. Furthermore it is shown that much fewer threshold gates are needed if one employs in addition a small number of winner-take-all gates. In either case the circuits that are constructed have linear or almost linear total wire length, and are therefore not unrealistic from the point of view of physical implementations.} } @Article{MaassLegenstein:01d, author = {R. A. Legenstein and W. Maass}, title = {Optimizing the Layout of a Balanced Tree}, journal = {Technical Report}, year = {2001}, abstract = { It is shown that the total wire length of layouts of a balanced binary tree on a 2-dimensional grid can be reduced by 33% if one does not choose the obvious ``symmetric'' layout strategy. Furthermore it is shown that the more efficient layout strategy that is presented in this article is optimal, not only for binary trees but for m-ary trees with any m >= 2.} } @Article{MaassMarkram:00, author = {W. Maass and H. Markram}, title = {Synapses as dynamic memory buffers}, journal = {Neural Networks}, volume = {15}, pages = {155--161}, year = {2002} } @Article{MaassMarkram:02, author = {W. Maass and H. Markram}, title = {On the Computational Power of Recurrent Circuits of Spiking Neurons}, journal = {Journal of Computer and System Sciences}, year = {2004}, volume = {69}, number = {4}, pages = {593--616} } @InCollection{MaassMarkram:02a, author = {W. Maass and H. Markram}, title = {Temporal Integration in Recurrent Microcircuits}, booktitle = {The Handbook of Brain Theory and Neural Networks}, publisher = {MIT Press (Cambridge)}, year = {2003}, editor = {M. A. Arbib}, edition = {2nd}, pages = {1159--1163} } @InProceedings{MaassMarkram:04, author = {W. Maass and H. Markram}, title = {Theory of the Computational Function of Microcircuit Dynamics}, booktitle = {The Interface between Neurons and Global Brain Function}, editor = {S. Grillner and A. M. Graybiel}, year = {2006}, pages = {371--390}, chapter = {18}, publisher = {MIT Press}, series = {Dahlem Workshop Report 93} } @Article{MaassNatschlaeger:97a, author = {W. Maass and T. Natschlaeger}, title = {Networks of Spiking Neurons can Emulate Arbitrary {H}opfield nets in Temporal Coding}, journal = {Network: Computation in Neural Systems}, year = 1997, volume = 8, number = 4, pages = {355--372}, keywords = {spiking neurons, hopfield net, temporal coding}, userlabel = {4}, abstract = {A theoretical model for analog computation with temporal coding is introduced and tested through simulations in GENESIS. It turns out that the use of multiple synapses yields very noise robust mechanisms for analog computations with temporal coding in networks of detailed compartmental neuron models. One arrives in this way at a method for emulating arbitrary Hopfield nets with spiking neurons in temporal coding, yielding new models for associative recall of spatio-temporal firing patterns. A corresponding layered architecture yields a refinement of the synfire-chain model that can assume a fairly large set of different firing patterns for different inputs.} } @InProceedings{MaassNatschlaeger:98, author = {W. Maass and T. Natschlaeger}, title = {Associative Memory with Networks of Spiking Neurons in Temporal Coding}, booktitle = {Neuromorphic Systems: Engineering Silicon from Neurobiology}, editor = {L. S. Smith and A. Hamilton}, year = 1998, publisher = {World Scientific}, pages = {21--32}, keywords = {spiking neurons, hopfield net, temporal coding}, abstract = {A theoretical model for analog computation with temporal coding is introduced and tested through simulations in GENESIS. It turns out that the use of multiple synapses yields very noise robust mechanisms for analog computations with temporal coding in networks of detailed compartmental neuron models. One arrives in this way at a method for emulating arbitrary Hopfield nets with spiking neurons in temporal coding, yielding new models for associative recall of spatio-temporal firing patterns.} } @InProceedings{MaassNatschlaeger:98b, author = {W. Maass and T. Natschlaeger}, title = {Emulation of {H}opfield Networks with Spiking Neurons in Temporal Coding}, booktitle = {Computational Neuroscience: Trends in Research}, editor = {J. M. Bower}, year = 1998, publisher = {Plenum Press}, pages = {221--226}, keywords = {spiking neurons, hopfield net, temporal coding}, abstract = {A theoretical model for analog computation with temporal coding is introduced and tested through simulations in GENESIS. It turns out that the use of multiple synapses yields very noise robust mechanisms for analog computations with temporal coding in networks of detailed compartmental neuron models. One arrives in this way at a method for emulating arbitrary Hopfield nets with spiking neurons in temporal coding, yielding new models for associative recall of spatio-temporal firing patterns. A corresponding layered architecture yields a refinement of the synfire-chain model that can assume a fairly large set of different firing patterns for different inputs.} } @Article{MaassNatschlaeger:99, author = {W. Maass and T. Natschlaeger}, title = {A model for Fast Analog Computation Based on Unreliable Synapses}, journal = {Neural Computation}, year = 2000, pages = {1679--1704}, volume = {12}, number = {7}, keywords = {unreliable synapses, universal function approximation, fast analog computation, time series, hebbian learning, space rate coding, population activity}, abstract = {We investigate through theoretical analysis and computer simulations the consequences of unreliable synapses for fast analog computations in networks of spiking neurons, with analog variables encoded by the current firing activities of pools of spiking neurons. Our results suggest that the known unreliability of synaptic transmission may be viewed as a useful tool for analog computing, rather than as a ``bug'' in neuronal hardware. We also investigate computations on time series and Hebbian learning in this context of space-rate coding.} } @InProceedings{MaassOrponen:97, author = {W. Maass and P. Orponen}, booktitle = {Advances in Neural Information Processing Systems}, editor = {M. Mozer and M. I. Jordan and T. Petsche}, pages = {218--224}, publisher = {MIT Press (Cambridge)}, title = {On the effect of analog noise in discrete-time analog computations}, volume = {9}, year = {1997} } @Article{MaassOrponen:97j, author = {W. Maass and P. Orponen}, title = {On the effect of analog noise in discrete-time analog computations}, journal = {Neural Computation}, year = 1998, volume = 10, pages = {1071--1095} } @InProceedings{MaassRuf:95, author = {W. Maass and B. Ruf}, address = {Paris}, booktitle = {Proc. of the International Conference on Artificial Neural Networks ICANN}, pages = {515--520}, publisher = {EC2\&Cie}, title = {On the Relevance of the Shape of Postsynaptic Potentials for the Computational Power of Networks of Spiking Neurons}, year = {1995}, keywords = {spiking neuron, postsynaptic potential, computational complexity} } @Article{MaassRuf:97, author = {W. Maass and B. Ruf}, journal = {Information and Computation}, title = {On computation with pulses}, year = {1999}, volume = {148}, pages = {202--218}, keywords = {spiking neuron, computational complexity, postsynaptic potential} } @InProceedings{MaassSchmitt:97, author = {W. Maass and M. Schmitt}, booktitle = {Proc. of the 10th Conference on Computational Learning Theory 1997}, note = {See also Electronic Proc. of the Fifth International Symposium on Artificial Intelligence and Mathematics (http://rutcor.rutgers.edu/\~{}amai)}, pages = {54--61}, publisher = {ACM-Press (New York)}, title = {On the complexity of learning for a spiking neuron}, year = {1997} } @Article{MaassSchmitt:98, author = {W. Maass and M. Schmitt}, journal = {Information and Computation}, title = {On the complexity of learning for spiking neurons with temporal coding}, year = {1999}, volume = {153}, pages = {26--46} } @InProceedings{MaassSchnitger:86, author = {W. Maass and G. Schnitger}, booktitle = {Proceedings of the Structure in Complexity Theory Conference, Berkeley 1986}, pages = {249--264}, publisher = {Springer (Berlin)}, series = {Lecture Notes in Computer Science}, title = {An optimal lower bound for {T}uring machines with one Work Tape and Two-Way Input Tape}, year = {1986}, volume = {223} } @Article{MaassSchorr:87, author = {W. Maass and A. Schorr}, journal = {SIAM J. Comput.}, pages = {195--202}, title = {Speed-up of {T}uring machines with one work tape and a two-way input tape}, volume = {16}, year = {1987} } @InProceedings{MaassSlaman:89, author = {W. Maass and T. A. Slaman}, booktitle = {Proceedings of the Logic Colloquium '88, Padova, Italy}, editor = {Ferro and Bonotto and Valentini and Zanardo}, pages = {79-89}, publisher = {Elsevier Science Publishers (North-Holland)}, title = {Some problems and results in the theory of actually computable functions}, year = {1989} } @InProceedings{MaassSlaman:89a, author = {W. Maass and T. A. Slaman}, booktitle = {Proceedings of the 4th Annual Conference on Structure in Complexity Theory}, pages = {231--239}, publisher = {IEEE Computer Society Press (Washington)}, title = {The complexity types of computable sets (extended abstract)}, year = {1989} } @InProceedings{MaassSlaman:89b, author = {W. Maass and T. A. Slaman}, booktitle = {Proceedings of the 7th International Conference on Fundamentals of Computation Theory}, pages = {318--326}, publisher = {Springer (Berlin)}, series = {Lecture Notes in Computer Science}, title = {Extensional properties of sets of time bounded complexity (extended abstract)}, volume = {380}, year = {1989} } @InProceedings{MaassSlaman:90, author = {W. Maass and T. A. Slaman}, booktitle = {Proceedings of the 1989 Recursion Theory Week Oberwolfach}, pages = {297--322}, publisher = {Springer (Berlin)}, title = {On the relationship between the complexity, the degree, and the extension of a computable set}, year = {1990} } @InProceedings{MaassSlaman:91, author = {W. Maass and T. A. Slaman}, booktitle = {Proceedings of a Workshop on Logic from Computer Science}, editor = {Y. N. Moschovakis}, pages = {359--372}, publisher = {Springer (Berlin)}, title = {Splitting and density for the recursive sets of a fixed time complexity}, year = {1991} } @Article{MaassSlaman:92, author = {W. Maass and T. A. Slaman}, journal = {J. Comput. Syst. Sci.}, note = {Invited paper for a special issue of the J. Comput. Syst. Sci.}, pages = {168--192}, title = {The complexity types of computable sets}, volume = {44}, year = {1992} } @Article{MaassSontag:97, author = {W. Maass and E. Sontag}, journal = {Neural Computation}, title = {Analog neural nets with {G}aussian or other common noise distribution cannot recognize arbitrary regular languages}, year = {1999}, volume = {11}, pages = {771--782} } @Article{MaassSontag:99a, author = {W. Maass and E. D. Sontag}, title = {Neural systems as nonlinear filters}, journal = {Neural Computation}, volume = {12}, number = {8}, year = {2000}, pages = {1743--1772} } @InProceedings{MaassSontag:99b, author = {W. Maass and E. D. Sontag}, title = {A precise characterization of the class of languages recognized by neural nets under {G}aussian and other common noise distributions}, booktitle = {Advances in Neural Information Processing Systems}, year = 1999, volume = {11}, pages = {281--287}, editor = {M.~S.~Kearns and S.~S.~Solla and D.~A.~Cohn}, publisher = {MIT Press (Cambridge)} } @Article{MaassStob:83, author = {W. Maass and M. Stob}, journal = {Ann. of Pure and Applied Logic}, pages = {189--212}, title = {Intervals of the lattice of recursively enumerable sets determined by major subsets}, volume = {24}, year = {1983} } @Article{MaassSutner:88, author = {W. Maass and K. Sutner}, journal = {Acta Informatica}, pages = {93-122}, title = {Motion planning among time dependent abstacles}, volume = {26}, year = {1988} } @InProceedings{MaassTuran:89, author = {W. Maass and G. Turan}, booktitle = {Proceedings of the 30th Annual IEEE Symposium on Foundations of Computer Science}, pages = {262--267}, title = {On the complexity of learning from counterexamples (extended abstract)}, year = {1989} } @InProceedings{MaassTuran:90, author = {W. Maass and G. Turan}, booktitle = {Proceedings of the 31th Annual IEEE Symposium on Foundations of Computer Science}, pages = {203--210}, title = {On the complexity of learning from counterexamples and membership queries}, year = {1990} } @Article{MaassTuran:92, author = {W. Maass and G. Turan}, journal = {Machine Learning}, note = {Invited paper for a special issue of Machine Learning}, pages = {107--145}, title = {Lower bound methods and separation results for on-line learning models}, volume = {9}, year = {1992} } @InCollection{MaassTuran:94, author = {W. Maass and G. Turan}, booktitle = {Computational Learning Theory and Natural Learning System: Constraints and Prospects}, editor = {S. J. Hanson and G. A. Drastal and R. L. Rivest}, pages = {381--414}, publisher = {MIT Press (Cambridge)}, title = {How fast can a threshold gate learn}, year = {1994} } @Article{MaassTuran:94a, author = {W. Maass and G. Turan}, journal = {Machine Learning}, pages = {251--269}, title = {Algorithms and lower bounds for on-line learning of geometrical concepts}, volume = {14}, year = {1994} } @InProceedings{MaassTuran:95, author = {W. Maass and G. Turan}, address = {Jerusalem}, booktitle = {Proc. of the 4th Bar-Ilan Symposium on Foundations of Artificial Intelligence (BISFAI'95)}, title = {On learnability and predicate logic (extended abstract)}, year = {1995}, pages = {75--85} } @InProceedings{MaassWarmuth:95, author = {W. Maass and M. Warmuth}, booktitle = {Proc. of the 12th International Machine Learning Conference, Tahoe City, USA}, editor = {Morgan Kaufmann (San Francisco)}, pages = {378-386}, title = {Efficient learning with virtual threshold gates}, year = {1995} } @Article{MaassWarmuth:95j, author = {W. Maass and M. Warmuth}, title = {Efficient learning with virtual threshold gates}, journal = {Information and Computation}, year = 1998, volume = 141, number = 1, pages = {66--83} } @InCollection{MaassWeibel:97, author = {W. Maass and P. Weibel}, booktitle = {{Jenseits von Kunst}}, editor = {P. Weibel}, pages = {745--747}, publisher = {Passagen Verlag}, title = {{I}st die {V}ertreibung der {V}ernunft reversibel? {U}eberlegungen zu einem {W}issenschafts- und {M}edienzentrum}, year = {1997} } @InProceedings{MaassZador:98, author = {W. Maass and A. M. Zador}, booktitle = {Advances in Neural Processing Systems}, publisher = {MIT Press (Cambridge)}, title = {Dynamic stochastic synapses as computational units}, volume = {10}, pages = {194--200}, year = {1998} } @InCollection{MaassZador:98a, author = {W. Maass and A. Zador}, booktitle = {Pulsed Neural Networks}, editor = {W. Maass and C. Bishop}, publisher = {MIT-Press (Cambridge)}, title = {Computing and learning with dynamic synapses}, year = {1998}, pages = {321-336} } @Article{MaassZador:98j, author = {W. Maass and A. M. Zador}, title = {Dynamic stochastic synapses as computational units}, journal = {Neural Computation}, year = 1999, volume = 11, number = 4, pages = {903--917} } @Article{MelamedETAL:03, author = {O. Melamed and W. Gerstner and W. Maass and M. Tsodyks and H. Markram}, title = {Coding and Learning of Behavioral Sequences}, journal = {Trends in Neurosciences}, volume = 27, number = 1, year = {2004}, pages = {11--14} } @InProceedings{NatschlaegerETAL:01, author = {T. Natschlaeger and W. Maass and E. D. Sontag and A. Zador}, title = {Processing of Time Series by Neural Circuits with Biologically Realistic Synaptic Dynamics}, booktitle = {Advances in Neural Information Processing Systems 2000 ({NIPS '2000})}, editor = {Todd K. Leen and Thomas G. Dietterich and Volker Tresp}, year = 2001, volume = 13, pages = {145--151}, address = {Cambridge}, publisher = {MIT Press}, abstract = {Experimental data show that biological synapses behave quite differently from the symbolic synapses in common artificial neural network models. Biological synapses are dynamic, i.e., their weight changes on a short time scale by several hundred percent in dependence of the past input to the synapse. In this article we explore the consequences that this synaptic dynamics entails for the computational power of feedforward neural networks. It turns out that even with just a single hidden layer such networks can approximate a surprisingly large class of nonlinear filters: all filters that can be characterized by Volterra series. This result is robust with regard to various changes in the model for synaptic dynamics. Furthermore we show that simple gradient descent suffices to approximate a given quadratic filter by a rather small neural system with dynamic synapses. We demonstrate that with this approach the nonlinear filter considered in (Back and Tsoi 93) can be approximated even better than by their model.}, htmlnote = {The poster presented at NIPS is available as Acrobat PDF file.} } @Article{NatschlaegerETAL:01a, author = {T. Natschlaeger and W. Maass and A. Zador}, title = {Efficient Temporal Processing with Biologically Realistic Dynamic Synapses}, journal = {Network: Computation in Neural Systems}, year = 2001, pages = {75--87}, volume = 12, abstract = {Experimental data show that biological synapses behave quite differently from the symbolic synapses in common artificial neural network models. Biological synapses are dynamic, i.e., their ``weight'' changes on a short time scale by several hundred percent in dependence of the past input to the synapse. Here we describe a general model of computation that exploits dynamic synapses, and use a backpropagation-like algorithm to adjust the synaptic parameters. We show that such gradient descent suffices to approximate a given quadratic filter by a rather small neural system with dynamic synapses. We demonstrate that with this approach the nonlinear filter considered in (Back and Tsoi, 1993) can be approximated slightly better than by their model. Our numerical results are complemented by theoretical analysis which show that even with just a single hidden layer such networks can approximate a surprisingly large class of nonlinear filters: all filters that can be characterized by Volterra series. This result is robust with regard to various changes in the model for synaptic dynamics. } } @Article{NatschlaegerETAL:02, author = {T. Natschlaeger and W. Maass and H. Markram}, title = {The "Liquid Computer": A Novel Strategy for Real-Time Computing on Time Series}, journal = {Special Issue on Foundations of Information Processing of {TELEMATIK}}, year = {2002}, pages = {39--43}, volume = {8}, number = {1}, abstract = {We will discuss in this survey article a new framework for analysing computations on time series and in particular on spike trains, introduced in (Maass et. al. 2002). In contrast to common computational models this new framework does not require that information can be stored in some stable states of a computational system. It has recently been shown that such models where all events are transient can be successfully applied to analyse computations in neural systems and (independently) that the basic ideas can also be used to solve engineering tasks such as the design of nonlinear controllers. Using an illustrative example we will develop the main ideas of the proposed model. This illustrative example is generalized and cast into a rigorous mathematical model: the Liquid State Machine. A mathematical analysis shows that there are in principle no computational limitations of liquid state machines in the domain of time series computing. Finally we discuss several successful applications of the framework in the area of computational neuroscience and in the field of artificial neural networks.} } @InCollection{NatschlaegerETAL:03, author = {T. Natschlaeger and H. Markram and W. Maass}, title = {Computer Models and Analysis Tools for Neural Microcircuits}, booktitle = {Neuroscience Databases. A Practical Guide}, publisher = {Kluwer Academic Publishers (Boston)}, year = {2003}, editor = {R. Koetter}, chapter = {9}, pages = {123--138}, abstract = {This chapter surveys web resources regarding computer models and analysis tools for neural microcircuits. In particular it describes the features of a new website (www.lsm.tugraz.at) that facilitates the creation of computer models for cortical neural microcircuits of various sizes and levels of detail, as well as tools for evaluating the computational power of these models in a Matlabenvironment.} } @Article{NatschlaegerMaass:01a, author = {T. Natschlaeger and W. Maass}, title = {Computing the Optimally Fitted Spike Train for a Synapse}, journal = {Neural Computation}, year = 2001, volume = 13, number = 11, pages = {2477--2494}, abstract = {Experimental data have shown that synapses are heterogeneous: different synapses respond with different sequences of amplitudes of postsynaptic responses to the same spike train. Neither the role of synaptic dynamics itself nor the role of the heterogeneity of synaptic dynamics for computations in neural circuits is well understood. We present in this article two computational methods that make it feasible to compute for a given synapse with known synaptic parameters the spike train that is optimally fitted to the synapse in a certain sense. With the help of these methods one can compute for example the temporal pattern of a spike train (with a given number of spikes) that produces the largest sum of postsynaptic responses for a specific synapse. Several other applications are also discussed. To our surprise we find that most of these optimally fitted spike trains match common firing patterns of specific types of neurons that are discussed in the literature. Hence our analysis provides a possible functional explanation for the experimentally observed regularity in the combination of specific types of synapses with specific types of neurons in neural circuits. } } @InProceedings{NatschlaegerMaass:01b, author = {T. Natschlaeger and W. Maass}, title = {Finding the Key to a Synapse}, booktitle = {Advances in Neural Information Processing Systems ({NIPS '2000})}, editor = {Todd K. Leen and Thomas G. Dietterich and Volker Tresp}, year = 2001, pages = {138--144}, volume = 13, address = {Cambridge}, publisher = {MIT Press}, abstract = {Experimental data have shown that synapses are heterogeneous: different synapses respond with different sequences of amplitudes of postsynaptic responses to the same presynaptic spike train. Neither the role of synaptic dynamics itself nor the role of the heterogeneity of synaptic dynamics for computations in neural circuits is well understood. We present in this article methods that make it feasible to compute for a given synapse with known synaptic parameters the spike train that is optimally fitted to the synapse, in the sense that it produces the largest sum of postsynaptic responses. To our surprise we find that most of these optimally fitted spike trains match common firing patterns of specific types of neurons that are discussed in the literature. Hence our analysis provides a possible functional explanation for the experimentally observed regularity in the combination of specific types of synapses with specific types of neurons in neural circuits.}, htmlnote = {The poster presented at NIPS is available as Acrobat PDF file.} } @InProceedings{NatschlaegerMaass:03, author = {T. Natschlaeger and W. Maass}, title = {Information Dynamics and Emergent Computation in Recurrent Circuits of Spiking Neurons}, booktitle = {Proc. of NIPS 2003, Advances in Neural Information Processing Systems}, year = {2004}, volume = {16}, pages = {1255--1262}, editor = {S. Thrun and L. Saul and B. Schoelkopf}, publisher = {MIT Press}, address = {Cambridge}, abstract = {An efficient method using Bayesian and linear classifiers is presented for analyzing the dynamics of information in high dimensional circuit states, and applied to investigate emergent computation in generic cortical microcircuit models. It is shown that such recurrent circuits of spiking neurons have an inherent capability to carry out rapid computations on complex spike patterns, merging information contained in the order of spike arrival with previously acquired context information.} } @Article{NatschlaegerMaass:04, author = {T. Natschlaeger and W. Maass}, title = {Dynamics of Information and Emergent Computation in Generic Neural Microcircuit Models}, journal = {Neural Networks}, volume = {18}, number = {10}, pages = {1301--1308}, year = {2005}, abstract = {Numerous methods have already been developed to estimate the information contained in single spike trains. In this article we explore efficient methods for estimating the information contained in the simultaneous firing activity of hundreds of neurons. Obviously such methods are needed to analyze data from multi-unit recordings. We test these methods on generic neural microcircuit models consisting of 800 neurons, and analyze the temporal dynamics of information about preceding spike inputs in such circuits. It turns out that information spreads with high speed in such generic neural microcircuit models, thereby supporting -- without the postulation of any additional neural or synaptic mechanisms -- the possibility of ultra-rapid computations on the first input spikes.} } @Article{NatschlaegerMaass:2001, author = {T. Natschlaeger and W. Maass}, title = {Spiking Neurons and the Induction of Finite State Machines}, journal = {Theoretical Computer Science: Special Issue on Natural Computing}, volume = 287, year = 2002, pages = {251--265}, abstract = {We discuss in this short survey article some current mathematical models from neurophysiology for the computational units of biological neural systems: neurons and synapses. These models are contrasted with the computational units of common artificial neural network models, which reflect the state of knowledge in neurophysiology 50 years ago. We discuss the problem of carrying out computations in circuits consisting of biologically realistic computational units, focusing on the biologically particularly relevant case of computations on time series. Finite state machines are frequently used in computer science as models for computations on time series. One may argue that these models provide a reasonable common conceptual basis for analyzing computations in computers and biological neural systems, although the emphasis in biological neural systems is shifted more towards asynchronous computation on analog time series. In the second half of this article some new computer experiments and theoretical results are discussed, which address the question whether a biological neural system can in principle learn to behave like a given simple finite state machine. } } @InProceedings{NatschlaegerMaass:99, author = {T. Natschlaeger and W. Maass}, title = {Fast Analog Computation in Networks of Spiking Neurons Using Unreliable Synapses}, booktitle = {{ESANN'99} Proceedings of the European Symposium on Artificial Neural Networks}, year = 1999, address = {Bruges, Belgium}, pages = {417--422}, keywords = {unreliable synapses, universal function approximation, fast analog computation, time series, hebbian learning, space rate coding, population activity}, abstract = {We investigate through theoretical analysis and computer simulations the consequences of unreliable synapses for fast analog computations in networks of spiking neurons, with analog variables encoded by the firing activities of pools of spiking neurons. Our results suggest that the known unreliability of synaptic transmission may be viewed as a useful tool for analog computing, rather than as a ``bug'' in neuronal hardware. We also investigate computations on analog time series encoded by the firing activities of pools of spiking neurons.} } @Article{NesslerETAL:08, author = {B. Nessler and M. Pfeiffer and W. Maass}, title = {Hebbian learning of {B}ayes optimal decisions}, journal = {In Proc. of NIPS 2008: Advances in Neural Information Processing Systems}, year = {2009}, volume = {21}, number = {}, pages = {}, note = {MIT Press}, abstract = {When we perceive our environment, make a decision, or take an action, our brain has to deal with multiple sources of uncertainty. The Bayesian framework of statistical estimation provides computational methods for dealing optimally with uncertainty. Bayesian inference however is algorithmically quite complex, and learning of Bayesian inference involves the storage and updating of probability tables or other data structures that are hard to implement in neural networks. Hence it is unclear how our nervous system could acquire the capability to approximate optimal Bayesian inference and action selection. This article shows that the simplest and experimentally best supported type of synaptic plasticity, Hebbian learning, can in principle achieve this. Even inference in complex Bayesian networks can be approximated by Hebbian learning in combination with population coding and lateral inhibition (``Winner-Take-All'') in cortical microcircuits that produce a sparse encoding of complex sensory stimuli. We also show that a corresponding reward-modulated Hebbian plasticity rule provides a principled framework for understanding how Bayesian inference could support fast reinforcement learning in the brain. In particular we show that recent experimental results by Yang and Shadlen on reinforcement learning of probabilistic inference in primates can be modeled in this way.} } @InProceedings{NesslerETAL:10, author = {B. Nessler and M. Pfeiffer and W. Maass}, title = {{STDP} enables spiking neurons to detect hidden causes of their inputs}, booktitle = {Proc. of NIPS 2009: Advances in Neural Information Processing Systems}, editor = {}, publisher = {MIT Press}, year = {2010}, volume = {22}, pages = {}, abstract = {The principles by which spiking neurons contribute to the astounding computational power of generic cortical microcircuits, and how spike-timing-dependent plasticity (STDP) of synaptic weights could generate and maintain this computational function, are unknown. We show here that STDP, in conjunction with a stochastic soft winner-take-all (WTA) circuit, induces spiking neurons to generate through their synaptic weights implicit internal models for subclasses (or �causes�) of the high-dimensional spike patterns of hundreds of pre-synaptic neurons. Hence these neurons will fire after learning whenever the current input best matches their internal model. The resulting computational function of soft WTA circuits, a common network motif of cortical microcircuits, could therefore be a drastic dimensionality reduction of information streams, together with the autonomous creation of internal models for the probability distributions of their input patterns. We show that the autonomous generation and maintenance of this computational function can be explained on the basis of rigorous mathematical principles. In particular, we show that STDP is able to approximate a stochastic online Expectation-Maximization (EM) algorithm for modeling the input data. A corresponding result is shown for Hebbian learning in artificial neural networks.} } @InProceedings{NeumannETAL:07, author = {G. Neumann and M. Pfeiffer and W. Maass}, booktitle = {Proceedings of the 18th European Conference on Machine Learning (ECML) and the 11th European Conference on Principles and Practice of Knowledge Discovery in Databases (PKDD) 2007, Warsaw (Poland)}, title = {Efficient Continuous-Time Reinforcement Learning with Adaptive State Graphs}, publisher = {Springer (Berlin)}, year = {2007}, pages = {}, note = {in press}, abstract = {We present a new reinforcement learning approach for deterministic continuous control problems in environments with unknown, arbitrary reward functions. The difficulty of finding solution trajectories for such problems can be reduced by incorporating limited prior knowledge of the approximative local system dynamics. The presented algorithm builds an adaptive state graph of sample points within the continuous state space. The nodes of the graph are generated by an efficient principled exploration scheme that directs the agent towards promising regions, while maintaining good online performance. Global solution trajectories are formed as combinations of local controllers that connect nodes of the graph, thereby naturally allowing continuous actions and continuous time steps. We demonstrate our approach on various movement planning tasks in continuous domains.} } @InProceedings{NeumannETAL:09, author = {G. Neumann and W. Maass and J. Peters}, title = {Learning Complex Motions by Sequencing Simpler Motion Templates}, booktitle = {Proc. of the Int. Conf. on Machine Learning (ICML 2009), Montreal}, year = {2009}, volume = {}, number = {}, pages = {}, note = {in press}, abstract = {Abstraction of complex, longer motor tasks into simpler elemental movements enables humans and animals to exhibit motor skills which have not yet been matched by robots. Humans intuitively decompose complex motions into smaller, simpler segments. For example when describing simple movements like drawing a triangle with a pen, we can easily name the basic steps of this movement. Surprisingly, such abstractions have rarely been used in artificial motor skill learning algorithms. These algorithms typically choose a new action (such as a torque or a force) at a very fast time-scale. As a result, both policy and temporal credit assignment problem become unnecessarily complex - often beyond the reach of current machine learning methods. We introduce a new framework for temporal abstractions in reinforcement learning (RL), i.e. RL with motion templates. We present a new algorithm for this framework which can learn high-quality policies by making only few abstract decisions. } } @Article{NikolicETAL:06, author = {D. Nikolic and S. Haeusler and W. Singer and W. Maass}, title = {Temporal dynamics of informational contents carried by neurons in the primary visual cortex}, journal = {submitted for publication}, year = 2006 } @Article{NikolicETAL:07, author = {D. Nikolic and S. Haeusler and W. Singer and W. Maass}, title = {Distributed fading memory for stimulus properties in the primary visual}, journal = {submitted for publication}, year = {2009}, volume = {}, number = {}, pages = {}, abstract = {} } @InProceedings{NikolicETAL:07a, author = {D. Nikoli\'{c} and S. Haeusler and W. Singer and W. Maass}, title = {Temporal dynamics of information content carried by neurons in the primary visual cortex}, booktitle = {Proc. of NIPS 2006, Advances in Neural Information Processing Systems}, editor = {}, publisher = {MIT Press}, year = {2007}, volume = {19}, pages = {1041--1048}, abstract = {We use multi-electrode recordings from cat primary visual cortex and investigate whether a simple linear classifier ca n extract information about the presented stimuli. We find that information is extractable and that it even las ts for several hundred milliseconds after the stimulus has b een removed. In a fast sequence of stimulus presentation, information about both new and old stimuli is present simultaneously and nonlinear relations between these stimuli can be extracted. These results suggest nonlinear properties of cortical representat ions. The implications of these properties for the nonlinear brain theory are discussed.} } @Article{NikolicETAL:09, author = {D. Nikolic and S. Haeusler and W. Singer and W. Maass}, title = {Distributed fading memory for stimulus properties in the primary visual cortex}, journal = {PLoS Biology}, year = {2009}, volume = {7}, number = {12}, pages = {1--19}, abstract = {It is currently not known how distributed neuronal responses in early visual areas carry stimulus-related information. We made multi-electrode recordings from cat primary visual cortex and applied methods from machine learning in order to analyze the temporal evolution of stimulus-related information in the spiking activity of large ensembles of around 100 neurons. We used sequences of up to three different visual stimuli (letters) presented for 100 ms and with intervals of 100 ms or larger. Most of the information about visual stimuli extractable by sophisticated methods of machine learning, i.e. support vector machines with non-linear kernel functions, was also extractable by simple linear classification such as can be achieved by individual neurons. New stimuli did not erase information about previous stimuli. The responses to the most recent stimulus contained about equal amounts of information about both this and the preceding stimulus. This information was encoded both in the discharge rates (response amplitudes) of the ensemble of neurons and, when using short time-constants for integration (e.g., 20 ms), in the precise timing of individual spikes (<= $~20$ ms), and persisted for several 100 ms beyond the offset of stimuli. The results indicate that the network from which we recorded is endowed with fading memory and is capable of performing online computations utilizing information about temporally sequential stimuli. This result challenges models assuming frame-by-frame analyses of sequential inputs.}, note = {} } @Article{PfeifferETAL:09, author = {M. Pfeiffer and B. Nessler and W. Maass and R. J. Douglas}, title = {Reward-modulated {H}ebbian Learning of Optimal Decision Making}, journal = {Neural Computation}, year = {2009}, pages = {}, volume = {} } @Article{PfeifferETAL:09b, author = {M. Pfeiffer and B. Nessler and W. Maass}, title = {{STDP} approximates Expectation Maximization in networks of spiking neurons with lateral inhibition}, journal = {in preparation}, year = {2009}, pages = {}, volume = {} } @Article{PfeifferETAL:09c, author = {M. Pfeiffer and B. Nessler and R. Douglas and W. Maass}, title = {Reward-modulated {H}ebbian {L}earning of {D}ecision {M}aking}, journal = {Neural Computation}, year = {2009}, volume = {}, number = {}, pages = {}, abstract = {We introduce a framework for decision making in which the learning of decision making is reduced to its simplest and biologically most plausible form: Hebbian learning on a linear neuron. We cast our Bayesian-Hebb learning rule as reinforcement learning in which certain decisions are rewarded, and prove that each synaptic weight will on average converge exponentially fast to the log-odd of receiving a reward when its pre- and post-synaptic neurons are active. In our simple architecture, a particular action is selected from the set of candidate actions by a winner-take-all operation. The global reward assigned to this action then modulates the update of each synapse. Apart from this global reward signal our reward-modulated Bayesian Hebb rule is a pure Hebb update that depends only on the co-activation of the pre- and postsynaptic neurons, and not on the weighted sum of all presynaptic inputs to the post-synaptic neuron as in the perceptron learning rule or the Rescorla-Wagner rule. This simple approach to action-selection learning requires that information about sensory inputs be presented to the Bayesian decision stage in a suitably pre-processed form resulting from other adaptive processes (acting on a larger time scale) that detect salient dependencies among input features. Hence our proposed framework for fast learning of decisions also provides interesting new hypotheses regarding neural nodes and computational goals of cortical areas that provide input to the final decision stage.}, note = {in press} } @TechReport{RaschETAL:06, author = {M. Rasch and S. Haeusler and Z. Kisvarday and W. Maass and N. Logothetis}, title = {Comparison of a detailed model for area {V}1 with simultaneous recordings from {LGN} and {V}1}, institution = {Technische Universitaet Graz and MPI Tuebingen}, year = {2006} } @TechReport{RaschETAL:06b, author = {M. Rasch and A. Gretton and Y. Murayama and W. Maass and N. Logothetis}, title = {Interaction of local field potential and spiking activity in area {V}1}, institution = {Technische Universitaet Graz and MPI Tuebingen}, year = {2006} } @Article{RaschETAL:07, author = {M. J. Rasch and A. Gretton and Y. Murayama and W. Maass and N. K. Logothetis}, title = {Inferring spike trains from local field potentials}, journal = {Journal of Neurophysiology}, year = {2008}, volume = {99}, number = {}, pages = {1461--1476}, note = {}, abstract = {We investigated whether it is possible to infer spike trains solely on the basis of the underling local field potentials ({LFP}s). Employing support vector machines and linear regression models, we found that in the primary visual cortex ({V}1) of monkeys, spikes can indeed be inferred from {LFP}s, at least with moderate success. Although there is a considerable degree of variation across electrodes, the low-frequency structure in spike trains (in the 100 ms range) can be inferred with reasonable accuracy, whereas exact spike positions are not reliably predicted. Two kinds of features of the {LFP} are exploited for prediction: the frequency power of bands in the high $\gamma$-range (40-90 {H}z), and information contained in low-frequency oscillations (<10 {H}z), where both phase and power modulations are informative. Information analysis revealed that both features code (mainly) independent aspects of the spike-to-{LFP} relationship, with the low-frequency {LFP} phase coding for temporally clustered spiking activity. Although both features and prediction quality are similar during semi-natural movie stimuli and spontaneous activity, prediction performance during spontaneous activity degrades much more slowly with increasing electrode distance. The general trend of data obtained with anesthetized animals is qualitatively mirrored in that of a more limited data set recorded in {V}1 of awake monkeys. In contrast to the cortical field potentials, thalamic {LFP}s (e.g. {LFP}s derived from recordings in d{LGN}) hold no useful information for predicting spiking activity.} } @Article{RaschETAL:09, author = {M. J. Rasch and K. Schuch and N. K. Logothetis and W. Maass}, title = {Statistical characterization of the spike response to natural stimuli in monkey area {V}1 and in a detailed model for a patch of {V}1}, journal = {submitted}, year = {2009}, pages = {}, volume = {} } @Article{SteimerETAL:09, author = {A. Steimer and W. Maass and R. Douglas}, title = {Belief-propagation in networks of spiking neurons}, journal = {Neural Computation}, year = {2009}, volume = {21}, number = {}, pages = {2502--2523}, abstract = {From a theoretical point of view, statistical inference is an attractive model of brain operation. However, it is unclear how to implement these inferential processes in neuronal networks. We offer a solution to this problem by showing in detailed simulations how the Belief-Propagation algorithm on a factor graph can be embedded in a network of spiking neurons. We use pools of spiking neurons as the function nodes of the factor graph. Each pool gathers 'messages' in the form of population activities from its input nodes and combines them through its network dynamics. The various output messages to be transmitted over the edges of the graph are each computed by a group of readout neurons that feed in their respective destination pools. We use this approach to implement two examples of factor graphs. The first example is drawn from coding theory. It models the transmission of signals through an unreliable channel and demonstrates the principles and generality of our network approach. The second, more applied example, is of a psychophysical mechanism in which visual cues are used to resolve hypotheses about the interpretation of an object's shape and illumination. These two examples, and also a statistical analysis, all demonstrate good agreement between the performance of our networks and the direct numerical evaluation of beliefpropagation.} } @Article{SteinbauerETAL:02, author = {G. Steinbauer and R. Koholka and W. Maass}, title = {A very short story about autonomous robots}, journal = {Special Issue on Foundations of Information Processing of {TELEMATIK}}, year = {2002}, volume = {8}, number = {1}, pages = {26--29} } @Article{SussilloETAL:07, author = {D. Sussillo and T. Toyoizumi and W. Maass}, title = {Self-tuning of neural circuits through short-term synaptic plasticity}, journal = {Journal of Neurophysiology}, year = {2007}, volume = {97}, pages = {4079--4095}, abstract = {Circuits of neurons in the cortex have a remarkable capability to maintain functional and dynamic stability in spite of changes in the level of external inputs, synaptic plasticity and changes in the circuit structure that occur during development and adult learning. The source of this characteristic stability of cortical circuits has remained a mystery, especially since even stronglysimplified models of such circuits do not exhibit similar stability properties. One simplification that is usually made in such models is that the empirically found nonlinear and diverse inherent short term dynamics (paired-pulse facilitation and depression) of biological synapses is replaced by static and uniform linear synapse models. We show in this article that this is a mistake, since the complex and diverse nonlinear dynamics of biological synapses supports the implementation of powerful control principles that endow circuits of spiking neurons with almost in-vivo like stability properties.} } @Article{BuesingMaass:10, author = {L. Buesing and W. Maass}, title = {A Spiking Neuron as Information Bottleneck}, journal = {Neural Computation}, year = {2010}, volume = {}, number = {}, pages = {}, abstract = {Neurons receive thousands of presynaptic input spike trains while emitting a single output spike train. This drastic dimensionality reduction suggests to consider a neuron as a bottleneck for information transmission. Extending recent results, we propose a simple learning rule for the weights of spiking neurons derived from the Information Bottleneck (IB) framework that minimizes the loss of relevant information transmitted in the output spike train. In the IB framework relevance of information is defined with respect to contextual information, the latter entering the proposed learning rule as a "third" factor besides pre- and postsynaptic activities. This renders the theoretically motivated learning rule a plausible model for experimentally observed synaptic plasticity phenomena involving three factors. Furthermore, we show that the proposed IB learning rule allows spiking neurons to learn a "predictive code",i.e. to extract those parts of their input that are predictive for future input.}, note = {in press} } @Article{UchizawaETAL:06, author = {K. Uchizawa and R. Douglas and W. Maass}, title = {On the Computational Power of Threshold Circuits with Sparse Activity}, journal = {Neural Computation}, year = 2006, volume = 18, number = 12, pages = {2994--3008}, abstract = {Circuits composed of threshold gates (McCulloch-Pitts neurons, or perceptrons) are simplified models of neural circuits with the advantage that they are theoretically more tractable than their biological counterparts. However, when such threshold circuits are designed to perform a specific computational task they usually differ in one important respect from computations in the brain: they require very high activity. On average every second threshold gate fires (sets a ``1'' as output) during a computation. By contrast, the activity of neurons in the brain is much more sparse, with only about 1\% of neurons firing. This mismatch between threshold and neuronal circuits is due to the particular complexity measures (circuit size and circuit depth) that have been minimized in previous threshold circuit constructions. In this article we investigate a new complexity measure for threshold circuits, {\em energy complexity}, whose minimization yields computations with sparse activity. We prove that all computations by threshold circuits of polynomial size with entropy $O(\log n)$ can be restructured so that their energy complexity is reduced to a level near the {\em entropy of circuit states}. This entropy of circuit states is a novel circuit complexity measure, which is of interest not only in the context of threshold circuits, but for circuit complexity in general. As an example of how this measure can be applied we show that any polynomial size threshold circuit with entropy $O(\log n)$ can be simulated by a polynomial size threshold circuit of depth 3. Our results demonstrate that the structure of circuits which result from a minimization of their energy complexity is quite different from the structure which results from a minimization of previously considered complexity measures, and potentially closer to the structure of neural circuits in the nervous system. In particular, different pathways are activated in these circuits for different classes of inputs. This article shows that such circuits with sparse activity have a surprisingly large computational power.} } @InProceedings{UchizawaETAL:06a, author = {K. Uchizawa and R. Douglas and W. Maass}, booktitle = {Proceedings of the 33rd International Colloquium on Automata, Languages and Programming, ICALP (1) 2006, Venice, Italy, July 10-14, 2006, Part I}, title = {Energy Complexity and Entropy of Threshold Circuits}, year = {2006}, volume = {4051}, pages = {631--642}, publisher = {Springer}, series = {Lecture Notes in Computer Science}, editor = {M. Bugliesi and B. Preneel and V. Sassone and I. Wegener}, abstract = {Circuits composed of threshold gates (McCulloch-Pitts neurons, or perceptrons) are simplified models of neural circuits with the advantage that they are theoretically more tractable than their biological counterparts. However, when such threshold circuits are designed to perform a specific computational task they usually differ in one important respect from computations in the brain: they require very high activity. On average every second threshold gate fires (sets a ``1'' as output) during a computation. By contrast, the activity of neurons in the brain is much more sparse, with only about 1\% of neurons firing. This mismatch between threshold and neuronal circuits is due to the particular complexity measures (circuit size and circuit depth) that have been minimized in previous threshold circuit constructions. In this article we investigate a new complexity measure for threshold circuits, {\em energy complexity}, whose minimization yields computations with sparse activity. We prove that all computations by threshold circuits of polynomial size with entropy $O(\log n)$ can be restructured so that their energy complexity is reduced to a level near the {\em entropy of circuit states}. This entropy of circuit states is a novel circuit complexity measure, which is of interest not only in the context of threshold circuits, but for circuit complexity in general. As an example of how this measure can be applied we show that any polynomial size threshold circuit with entropy $O(\log n)$ can be simulated by a polynomial size threshold circuit of depth 3.} } @TechReport{WinterETAL:06, author = {M. Winter and H. Bischof and M. Rasch and W. Maass}, title = {Results and open problems regarding the role of local feature descriptors for image classification in computer vision, and image representations in primary visual cortex}, institution = {Technische Universitaet Graz}, year = {2006} }