Research Group Leader

Prof. Dr. Matthias Bethge
Prof. Dr. Matthias Bethge
Phone: +49 7071 29-89017
Fax: +49 7071 29-25015


Secretary: Heike König
Phone: +49 7071 29-89018
Fax: +49 7071 29-25015


13 May 2011

Ivana Tosic Redwood Center for Theoretical Neuroscience UC Berkeley, USA

Geometry-based sparse representation of multi-view images
Finding efficient representations of the 3D structure of the world based on multiple 2D views that we observe, still represents a fundamental challenge in vision both in biology and technology. As a foundation of next generation 3DTV and cinema technologies, multi-view imaging presents many exciting research challenges, mainly in compression and image analysis. Central to these challenges is a need for novel image models that capture the intrinsic structure of intra- and inter-view correlations in multi-view images. In this talk, I will present a new sparse generative model for stereo and multi-view image representation using over-complete geometric dictionaries, which makes multi-view geometric structure explicit in the representation. Practical application of the proposed model raises two challenges: 1) Given stereo (multi-view) images, how can we find sparse representations under the model? 2) Given a database of multi-view images, can we learn dictionaries that yield optimal sparse representations under the model? I address both challenges by introducing Multi-View Matching Pursuit (MVMP), a novel algorithm that decomposes multi-view images into sparse representations governed by the proposed model. Subsequently, I will show how MVMP can be used within a maximum-likelihood framework to optimize dictionaries for multi-view image representation. Finally, I will demonstrate the benefits of the proposed approach for camera pose estimation in omnidirectional camera networks and compression of stereo perspective images.

06 May 2011

Tom Tetzlaff Norwegian University of Life Sciences, Ås, Norway
Department of Mathematical Sciences and Technology

Decorrelation of neural-network activity by inhibitory feedback
Correlations in spike-train ensembles can seriously impair the encoding of information by their spatio-temporal structure. An inevitable source of correlation in finite neural networks is common presynaptic input to pairs of neurons. Recent studies demonstrate that spike correlations in recurrent neural networks are considerably smaller than expected based on the amount of shared presynaptic input. Here, we provide an explanation of this contradictory observation by means of a linear network model and simulations of networks of leaky integrate-and-fire neurons. We show that pairwise correlations and, hence, population-rate fluctuations are suppressed by inhibitory feedback. This assigns inhibitory neurons the new role of active decorrelation. To elucidate the effect of feedback, we compare the responses of the intact recurrent system to systems where the statistics of the feedback channel is perturbed. Perturbations of the feedback statistics can lead to a significant increase in power and coherence of the population response. In particular, neglecting correlations within the ensemble of feedback channels or between the external stimulus and the feedback amplifies population-rate fluctuations by orders of magnitude. The fluctuation suppression in homogeneous inhibitory networks is explained by a negative feedback loop in the one-dimensional dynamics of the compound activity. Similarly, a change of coordinates exposes an effective negative feedback loop in the compound dynamics of stable excitatory-inhibitory networks. The suppression of input correlations in finite networks is explained by the population averaged correlations in the linear network model: In purely inhibitory networks, shared-input correlations are canceled by negative spike-train correlations. In excitatory-inhibitory networks, spike-train correlations are typically positive. Here, the suppression of input correlations is not a result of the mere existence of correlations between excitatory (E) and inhibitory (I) neurons, but a consequence of a particular structure of correlations among the three possible pairings (EE, EI, II).
20 Jan 2011

Nicolas Heess University of Edinburgh

Learning a generative model of images by factoring appearance and shape
Modeling the structure in natural images is a challenging problem. One hallmark of natural images is the variability of visual characteristics across different image regions and the presence of sharp boundaries between regions which arise, for instance, from objects occluding each other. Many generative models of generic natural images have difficulties representing this type of structure. In my talk I will discuss a model that addresses this problem. It builds on insights from the computer vision literature such as the layered representation of images and combines them with ideas from "deep" unsupervised learning. I will first describe the basic building block of the model, the Masked Restricted Boltzmann Machine, which allows occlusion boundaries to be modeled by factoring out the appearance of an image region from its shape, representing each with a separate RBM. The Masked RBM explicitly models the relative depth of image regions and allows for regions to overlap and occlude each other. In the second part of my talk I will describe how this model can be extended to deal with images of realistic size: While a straightforward application of the Masked RBM to large images would be expensive, an efficient extension can be obtained in the form of a field of Masked RBMs. The Field of Masked RBMs models an image in terms of a large number of independent small and partially overlapping "objects", each of which has an associated shape and appearance. Restricting the size of "objects" as well as limiting their number locally keeps inference and learning relatively efficient. Finally I will give an outlook of how the Field of Masked RBMs naturally gives rise to a recursive, hierarchical framework for modeling images at different scales and levels of abstraction, the "Deep Segmentation Network", and I will discuss some of the challenges ahead.
Joint work with Nicolas Le Roux, John Winn, and Jamie Shotton.
13 Jan 2011

Christian Machens Ecole Normale Supérieure Paris

Spatiotemporal Response Properties of Optic-Flow Processing Neurons
A central goal in sensory neuroscience is to fully characterize a neuron’s input-output relation. However, strong nonlinearities in the responses of sensory neurons have made it difficult to develop models that generalize to arbitrary stimuli. Typically, the standard linear-nonlinear models break down when neurons exhibit stimulus-dependent modulations of their gain or selectivity. We studied these
issues in optic-flow processing neurons in the fly. We found that the neurons’ receptive fields are fully described by a time-varying vector field that is space-time separable. Increasing the stimulus strength, however, strongly reduces the neurons’ gain and selectivity. To capture these changes in response behavior, we extended the linear-nonlinear model by a biophysically motivated gain and selectivity
mechanism. We fit all model parameters directly to the data and show that the model now characterizes the neurons’ input-output relation well over the full range of motion stimuli.

[Joint work with Franz Weber and Axel Borst]

09 Jun 2009
Matteo Carandini UCL Institute of Ophthalmology, University College London

30 Mar 2009

Michael Berry Department of Molecular Biology, Princeton University

Predictive Pattern Detection in the Retina
03 Feb 2009

Bruno Olshausen Helen Wills Neuroscience Institute & School of Optometry,
Redwood Center for Theoretical Neuroscience, UC Berkeley

Learning transformational invariants from natural movies
A key attribute of visual perception is the ability to extract invariances from visual input. Here we focus on transformational invariants - i.e., the dynamical properties that are invariant to form or spatial structure (e.g., motion). We show that a hierarchical, probabilistic model can learn to extract complex motion from movies of the natural environment. The model consists of two hidden layers: the first layer produces a sparse representation of the image that is expressed in terms of local amplitude and phase variables. The second layer learns the higher-order structure among the time-varying phase variables. After training on natural movies, the top layer units discover the structure of phase-shifts within the first layer. We show that the top layer units encode transformational invariants: they are selective for the speed and direction of a moving pattern, but are invariant to its spatial structure (orientation/spatial-frequency). The diversity of units in both the intermediate and top layers of the model provides a set of testable predictions for representations that might be found in V1 and MT. In addition, the model demonstrates how feedback from higher levels can influence representations at lower levels as a by-product of inference in a graphical model. Joint work with Charles Cadieu.
14 Nov 2008
Peter Dayan Director of the Gatsby Unit, UCL, London, UK

Perceptual Organization in the Tilt Illusion
The tilt illusion is a paradigmatic example of contextual influences on perception. We analyze it in terms of a neural population model for the perceptual organization of visual orientation. In turn, this is based on a well-found treatment of natural scene statistics, known as the Gausian Scale Mixture model. This model is closely related to divisive gain control in neural processing and has been extensively applied in the image processing and statistical learning community. In our model, oriented neural units associated with surround tilt stimuli participate in divisively normalizing the activities of the units representing a center stimulus, thereby changing their tuning curves. We show that through standard population decoding, these changes lead to the forms of repulsion and attraction observed in the tilt illusion. We also consider the relationship to other phenomena such as the tilt aftereffect. Joint work with Odelia Schwartz (Einstein) and Terry Sejnowski (Salk).
27 Aug 2008

Ralf Häfner National Eye Institute, National Institutes of Health (Bethesda)

04 Jul 2008

Richard Hahnloser Institute for Neuroinformatics (Zurich)

Neural codes and receptive fields in auditory areas of the songbird
Brains of higher vertebrates analyze the sensory world in hierarchical networks, as exemplified in the main auditory pathway in songbirds. Neural responses in this pathway to auditory stimulation become increasingly sparse and selective to behaviorally relevant stimuli such as the bird's own song or that of its tutor. In my lab we are interested both in identifying theoretical principles that may explain the increase in song selectivity along this hierarchy and in devising new methods for characterizing the receptive fields of auditory neurons.
In the first part of my talk I will report on a state-space method for computing linear receptive fields (RFs) based on Kalman filtering. This method is computationally similar to reverse correlation methods, but has the advantage of providing causal RFs and a more elaborate noise model. In the second part of my talk I will present our sparse-coding theory, in which we train a two-layer neural network to sparsely represent many tutor songs and a few conspecific songs. We find that after training, first-layer responses are not selective to tutor song for a wide range of sparseness controlled by firing thresholds. However, tutor-song selectivity arises in the second layer when sparseness there is higher than in the first layer, in qualitative agreement with experimental findings.
13 Jun 2008

Udo Ernst University of Bremen, Germany

11 Apr 2008

Jenny Read University of Newcastle, UK

The Neuronal Basis of Stereo Vision
Stereo vision has several appealing properties which make it an ideal model system for studying the neuronal basis of perception. Its underlying circuitry is understood in more detail than that of perhaps any other perceptual ability, but we are still far from the goal of a computer algorithm reproducing even this small aspect of human perception. In this talk, I aim to give an overview of several key concepts in this area, concentrating on primary visual cortex and the stereo energy model of disparity tuning. I will begin with a brief introduction to stereo geometry and the underlying anatomy, and will discuss in some detail what it means for a binocular neuron to qualify as a true disparity sensor. I will discuss the stereo correspondence problem, and the use of anti-correlated stimuli to probe whether global stereo correspondence has been achieved. I will argue that primary visual cortex shows several properties which are evidence that it is specialised to perform the initial disparity encoding which supports stereopsis. However, the neuronal correlate of stereo depth perception cannot occur in V1 itself, but in higher, extrastriate areas, whose role is as yet poorly understood. I will end with a brief overview of current research directions in my lab.
18 Feb 2008
Cornelius Schwarz Hertie Institut Tübingen, Germany

07 Feb 2008

Karsten Kruse University Saarbrücken, Germany

Protein self-organization in cells
To understand the emergence of spatiotemporal structures in biological systems remains a major challenge to this day. Self-organization of a limited number of different agents as been found to account for structure formation in sea shells, slime mold aggregation, and bee colonies. On a subcellular level, however, the importance of self-organization of proteins and other molecules for forming vital structures is still debated. In this talk I will discuss recent experimental and theoretical advances that indicate that self-organization plays an important role in cellular processes like cell division and cell locomotion.
Specifically, I will discuss the dynamics of the Min proteins in the bacterium Escherichia coli and the dynamics of the cytoskeleton in eukaryotes.
28 Jan 2008

Philipp Lies TU Darmstadt, Germany

12 Jan 2008

Matthias Kaschube Princeton University Carl-Icahn Laboratory, USA

Quantitative universality and self-organization in visual cortical development
The occurrence of universal quantitative laws in strongly interacting multi-component systems indicates that their behavior can be elucidated through the identification of general mathematical principles rather than by the detailed characterization of their individual components. Here we demonstrate that universal quantitative laws govern the spatial layout of orientation selective neurons in the visual cortex in three mammalian species separated in evolution by more than 50 million years. The spatial layout adheres to these laws even if visual cortical organization exhibits marked overall inhomogeneities and when neuronal response properties are altered by visual deprivation. Most suggestive of a mathematical structure underlying this universality, the average number of pinwheel centers per orientation hyper-column in all species is statistically indistinguishable from the constant pi . Mathematical models of cortical self-organization reproduce all observed universal layout properties if long-range interactions are dominant. We conclude that long-range interactions are constitutive in visual cortical development, dynamically organizing cortical architecture with a high degree of quantitative precision.
14 Dec 2007

Mario Dipoppa Ecole Normale Superieure de Lyon, France

13 Nov 2007

Nima Keshvari FU Berlin, Germany

Analysis of functional protein sequences using mutual information
I will talk about a novel method for analyzing protein sequences that we developed at the MPI for Molecular Plant Physiology. The method is based on estimating the mutual information between amino acid positions in different organisms. It provides new insights into C2H2 Zinkfingers, a certain class of transcription factors. I will also give a short introduction to our web-based tool which we developed on the basis of this method.
18 Oct 2007
Greg Stevens Princeton University, New Jersey

Dimensionality and dynamics in the behavior of C. elegans
A major challenge in analyzing animal behavior is to discover some underlying simplicity in complex motor actions. Here we show that the space of shapes adopted by the nematode C. elegans is surprisingly low dimensional, with just four dimensions accounting for 95% of the shape variance, and we partially reconstruct ‘equations of motion’ for the dynamics in this space. These dynamics have multiple attractors, and we find that the worm visits these in a rapid and almost completely deterministic response to weak thermal stimuli. Stimulus-dependent correlations among the different modes suggest that one can generate more reliable behaviors by synchronizing stimuli to the state of the worm in shape space. We confirm this prediction, effectively "steering" the worm in real time.
17 Oct 2007

Misha Ahrens Gatsby Unit, UCL, UK

A new class of compact neural encoding models that capture nonlinearities and dependence on stimulus context
The fitting of meaningful models to the stimulus-response functions of neurons is often hampered by several factors. Compact models might lack the flexibility to adequately capture the nonlinear dynamics of the neural responses, but elaborate models may be hard to estimate due to a lack of good estimation algorithms and large numbers of model parameters. Here we describe a class of nonlinear neural encoding models based on multilinear (tensor) mathematics, which share many of the conveniences of linear models -- such as robust estimation algorithms and low numbers of parameters -- yet are able to capture nonlinear effects such as short-term stimulus-specific adaptation. They achieve this through an (interpretable) multiplicative factorization in an extended stimulus space. The effectiveness of the methods is illustrated on firing rate (PSTH) data from primary auditory cortex.
I will also briefly discuss extensions of the fitting algorithms: first, joint regularization in the various factorized stimulus dimensions using a variational approximation, and second, a variant of IRLS (iteratively re-weighted least squares) that can be used to efficiently fit the models to spike trains through the point-process likelihood.
12 Oct 2007

Michael Bach University of Freiburg, Germany

Towards objective measures of visual acuity
Visual acuity (VA) is the most basic and widely used measure of visual function. Much hinges on it, for instance the outcome of clinical studies or medico-legal issues of RENTE. Thus a reliable (goal 1) and speedy (2) measure is required, and both the influence of the examiner (3) and the examinee (4) needs to be minimized. Signal detection theory helps towards goals 1 & 2: Adaptive staircase procedures optimize speed and accuracy, forced choice reduces the observer criterion. Goal 3 is addressed by automating the procedure. These ideas are embodied in the Freiburg Acuity Test (FrACT), which will be demonstrated with members of the audience as subjects.
For patients who cannot or will not fully cooperate (goal 4), visual evoked potentials provide non-invasive objective assessment of VA. We have advanced that methodology employing signal statistics, Fourier techniques and fully automatic algorithms to a state where we close in on subjective acuity within ± 1 octave in 95% of the cases. Plans will be outlined to address the question to what degree subjective perception coincides with the visual resolution of V1.

Bach M, Maurer JP, Wolf ME VEP-based acuity assessment in normal vision, artificially degraded vision, and in patients. Brit J Ophthalmol (to be published) Bach M (2007) The Freiburg Visual Acuity Test – Variability unchanged by post-hoc re-analysis. Graefe’s Arch Clin Exp Ophthalmol 245:965–971 Schulze-Bonsel K, Feltgen N, Burau H, Hansen LL, Bach M (2006) Visual acuities "Hand Motion" and "Counting Fingers" can be quantified using the Freiburg Visual Acuity Test. Invest Ophthalmol Vis Sci 47:1236–1240 Bach M (1996) The "Freiburg Visual Acuity Test" – Automatic measurement of visual acuity. Optometry and Vision Science 73:49-53
20 Jul 2007

Youn Jin Kim Colour & Imaging Group
Department of Colour Science, University of Leeds (UK)

Illumination-Adaptive Image Quality Evaluation And Enhancement
09 Jul 2007

Antonino Casile Hertie Institut, Tübingen

The role of fixational eye movements in the neuronal encoding of natural visual input.
06 Jul 2007

Jonathan Pillow Gatsby Unit, UCL, UK

Assessing the role of correlations in multi-neuronal spike coding
A central problem in systems neuroscience is to understand how ensembles of neurons convey information in their collective spiking activity. Correlations, or statistical dependencies between neural responses, are of critical importance to understanding the neural code, as they affect both the amount of information carried by population responses and the manner in which downstream brain areas are able decode it. I will show that multi-neuronal correlations can be understood using a simple, highly tractable computational model. The model captures both the stimulus dependence and detailed spatio-temporal correlation structure in the light responses of a complete population of parasol retinal ganglion cells (27 cells), making it possible to assess how correlations affect the encoding of stimulus-related information. We find that correlations strongly influence the precise timing of spike trains, explaining a large fraction of trial-to-trial response variability in individual neurons that otherwise would be attributed to intrinsic noise. We can assess the importance of correlations by performing Bayesian decoding of multi-neuronal spike trains; we find that exploiting the full correlation structure of the population response preserves 20% more stimulus-related information than decoding under the assumption of independent encoding. These results provide a framework for understanding the role that correlated activity plays in encoding and decoding sensory signals, and should be applicable to the study of population coding in a wide variety of neural circuits.
25 May 2007

Andreas Steimer Institute of Neuroinformatics, Uni/ETH-Zürich, Zürich (Switzerland)

Implementing the Belief-Propagation Algorithm with Networks of Spiking Neurons-An approach based on Liquid-State-Machines
Andreas Steimer, Rodney J. Douglas Institute of Neuroinformatics, Uni/ETH-Zürich, Zürich (Switzerland)
In many real world situations living beings have to deal with incomplete knowledge about their environment and still have to be able to act reasonably. For example, think of a herbivore who sees just parts of a predator hiding in high grass. Based on this incomplete visual information, the animal has to infer the 'true' stimulus (the predator) in order to initiate an appropriate behavioral response (to flee).
A large variety of such problems, e.g. in the general framework of object recognition, can be described by so called 'graphical models' like Bayesian Networks or Markov Random Fields [Löliger(2004),Weiss&Freeman(2001)]. These models describe statistical relationships between a set of variables and give rise to algorithms computing probabilities about states of unknown variables based on the observed information. 'Belief-Propagation' is an efficient method for this task [Kschischang et al.(2001), Rao(2006)] and is also a potential candidate for a biological implementation in the brain, because it is entirely based on local information processing [Rao(2006)]. Computational units (the nodes of a graphical model) communicate with each other by distributing so called 'messages' exclusively to their neighbors in the graph.
Within this contextual framework, our working hypothesis is that the experimentally observed patches of synaptic boutons, prominent in layer 2/3 all over the cortex [Angelucci et al.(2002)], are a physical representation of nodes in a graphical model. At the same time we assume that a patch constitutes a canonical microcircuit of neurons which is able to calculate the Belief-Propagation message update equations. For that, each patch is interpreted as a collection of 'Liquid State Machines' [Maass et al.(2002)] consisting of a common liquid-pool of recurrently connected neurons, and several readout units. Each combination of the liquid-pool and any readout, realizes a particular message signal transmitted from a node to one of its neighbors. Messages arriving at a node are all fed into the common liquid-pool, whose main task is to implement nonlinear projections of the low-dimensional input into a high-dimensional space [Maass et al.(2002)]. This operation is crucial for the Belief-Propagation algorithm which utilizes highly nonlinear message update rules [Löliger(2004)].
'pDelta' learning [Auer et al.(2005)] is used for the supervised training of the readouts. It is based on populations of perceptron units, however it can also be applied to spiking neurons when message signals are represented in space rate code [Maass et al.(2002)]. Therefore, our aim is to formulate microcircuits with a modular character, i.e. with the same input and output coding of spikes. This work is funded by the EU within the 'DAISY'-project (Grant No: FP6-2005-015803)
11 May 2007

Michael Schnabel Bernstein Center for Computational Neuroscience, Göttingen

A symmetry of the visual world in the architecture of the visual cortex
We provide evidence that signatures of shift-twist symmetry (STS), a fundamental symmetry of visual cortical architecture [6,7], are present in the layout of tree shrew V1 orientation maps. On the theoretical side, we investigate the possible effects of STS on orientation map layout by modeling OPMs within two different frameworks, Gaussian random fields and complex planforms and find in both cases that STS leads to a specific coupling of orientation map to the visuotopic map. This coupling can occur in two different ways, related to "even" and "odd" solutions previously introduced in [6,7]. However, our data analysis reveals that just one case - the "odd" one - is realized in tree shrew OPMs. Due to the prevalence of collinear contours in natural images [9] STS is an inherent feature of natural image statistics. However, in terms of the two symmetry classes, natural images belong to the opposite - the "even" - class.
In order to address the question of whether STS observed in tree shrew OPMS may reflect natural image statistics, i.e. collinearity, we simulated map development using a modified elastic net model [4]. In this model, instead of presenting isolated, pointlike contour elements (as originally done in [4]) we used elongated collinear arrangements of contour elements for network training. Resulting maps showed an increasing degree of STS with increasing degree of collinearity of the stimuli used.
Their correlation functions as well as geometric arrangement of separate columns with given orientation preferences were found to be consistent with the layout of OPMs in tree shrew V1. These results suggest that the signatures of STS observed in tree shrew OPMs might originate from the structure of natural scene statistics.
[1] Swindale, N.V. Network, 7:161 (1996)
[2] Wolf et al., Nature, 395:73 (1998)
[3] Schnabel et al., Soc. of Neurosc. Abstr., (2004,2005)
[4] Durbin and Mitchison, Nature, 343:646 (1990)
[5] Bosking et al., J.Neurosci., 17(6) (1997)
[6] Bressloff et al., Phil.Trans.R.Soc.London. B 356 (2001)
[7] Thomas and Cowan Phys.Rev.Lett. 92 (2004)
[8] Wolf, Phys.Rev.Lett. 95 (2005)
[9] Sigman et al., PNAS 98 (2001)
23 Apr 2007

Hans-Peter Frey Institute of Cognitive Science at the University of Osnabrück, Germany

How much bottom-up is overt visual attention?
Bottom-up stimulus features and top-down control both contribute to the allocation of visual attention. The aim of my research was to gain a better understanding of how and when these processes control attention. The talk comprises 2 parts that illuminate the problem from somewhat different, but complementary angles.
In the first part, the most prominent model in the field of bottom-up control, the saliency map, is analyzed. We compared its predictions to eye-movements made by human observers in different categories of grayscale as well as colored images. We analyzed the models performance for different numbers of fixations, with an unexpected result.
In the second part, different image features at fixated image regions are considered. I show that color-contrast influences eye-movements, but that this is not a sign for a causal relation. Top-down influences override the features’ effect, as soon as we manipulate the stimuli.
19 Apr 2007

Ahna Girshick University of California at Berkeley, Banks Lab

Probabilistic combination of disparity and texture slant information: weighted averaging and robust estimation as optimal percepts
Human depth perception involves combining multiple, possibly conflicting, sensory measurements.Previous work with slightly conflicting cues has shown that this process is performed by statistical optimal weighted averaging.Here we ask whether the brain has a mechanism to be robust to large cue conflicts.We investigated how disparity and texture are combined in estimating slant as a function of their conflict. When the two cues only had a small conflict, we found evidence for optimally weighted averaging. At larger conflicts, we observed robust behavior in which one of the discrepant cues was rejected. Interestingly, the ignored cue could be either disparity or texture, and was not necessarily the less reliable cue. Optimally weighted averaging has previously been modeled as the combination of Gaussian sensory estimates. We show that both weighted averaging and robustness are predicted if the tails of the sensory estimates are heavier than a Gaussian. Lastly, we probed to see whether access to single-cue estimates determined robustness behavior. We found no evidence for access, suggesting nearly full cue fusion. We used this data to estimate a 'coupling prior' for disparity-texture combination.
11 Apr 2007

Andreas Kotowisz University Würzburg
currently preparing his diploma thesis in the lab of Christof Koch at Caltech

Modeling feature based top-down attention during visual search
07 Mar 2007

Christian Machens Ludwig-Maximilians-Universität, München, Germany

From complex electrophysiological data to a simple model
During short-term memory maintenance, different neurons in prefrontal cortex (PFC), recorded under identical conditions, show a wide variety of temporal dynamics and response properties [1]. These data are a specific example of the more general finding that neural recordings from frontal cortices often reveal that different neurons have very different response characteristics. Modeling this complexity of responses has been difficult. Most commonly, some features of the responses are focused on, and models that fit those reduced features are built (e.g., [2]). But can the full complexity of responses be easily captured?
We have previously reported that the complex responses in PFC during short-term memory can be summarized in 5 dimensions (i.e., 5 parameters suffice to capture most of the variance in the data across neurons; Machens et al., COSYNE ’06). Olasagasti, Goldman, and colleagues have described a method to fit experimentally-obtained steady-state firing rates (that is, no dynamics) in a network model of persistent activity (Olasagasti et al., COSYNE ’05, COSYNE ’06). We now combine and extend these two approaches, and show how a simple linear fitting procedure leads to a model that describes the data in few dimensions yet captures most of the complexity and dynamics of the neural responses.
Let us assume we have observed, experimentally, M timepoints in the firing rates of N neurons– a total of M ⋅ N data points. Let us model this data in a recurrent network of N neurons, with full connectivity. Such a network will have Nˆ2 weights (i.e., as yet undetermined connection strengths). If N > M we have more unknowns than data points, and we could in principle solve the system exactly, reproducing all of the measured neural firing rates. The fitting procedure we use to achieve this requires the inversion of a matrix D representing all the data. To avoid overfitting the data, we use the singular value decomposition to represent, and then easily invert, the data matrix D: setting small singular values to zero corresponds to reducing the dimensionality of the model, which avoids overfitting. For the PFC data during short-term memory that we have previously analyzed, we find, in accordance with our previous results, that five dimensions suffice to describe the data (Machens et al., COSYNE ’06). The current approach now maps these data directly onto a neural network model, reproducing the dynamics of the data with most of their experimentally-observed richness and variety.
[1] Timing and Neural Encoding of Somatosensory Parametric Working Memory in Macaque Prefrontal Cortex. C.D. Brody, A. Hernandez, A. Zainos, and R. Romo, Cereb. Cortex 13:1196-1207, 2003.
[2] Flexible control of mutual inhibition: a neural model of two- interval discrimination. C.K. Machens, R. Romo, and C.D. Brody, Science, 307:1121-1124, 2005.
Last updated: Wednesday, 27.02.2013