Department of Computational Sciences

Group leader: Gergő Orbán

Mihály Bányai, Merse Előd Gáspár, Dávid Gergely Nagy#, Balázs Török#

# Ph.D. student

The website of the group:

Our research focuses on understanding how the nervous system works. In particular, we aim to explore the computations executed by the brain. We apply two approaches in our research. On the one hand, we use high-level computational models to try and understand how people represent the different elements of the outside world in perception and learning. In order to do this, we examine behavioural data from cognitive psychology experiments in machine learning systems, often using the tools of Bayesian statistics. On the other hand, we carry out research on low-level computations in order to reveal the way in which the network of neurons solves the problems that extremely rich stimuli make them face. For this, we describe the optimal behaviour expected in the given situation, with the help of ideal observation models. Then we use optimality criteria to try and describe how neural behaviour relates to the expected optimum and why and how it differs from the latter. Main research areas:


  • Studying the visual system, understanding computations organised in a hierarchy
  • Examining memory processes, the dynamics of learning and forgetting


Understanding how the brain processes
visual information requires computational models that decompose images in a way that
facilitates object recognition. To validate such models, we need to derive predictions from
them that may be compared to experimental recordings, while controlling for measurement

A critical aspect of modelling neural response is to assess the sources of variability in the
measurable spike trains. We compared two widely used models of neural spiking in terms of
predictive power regarding higher-order statistics of neural responses. Comparing our
simulation results to publicly available recordings from awake monkeys revealed that the
Doubly Poissonian model, which assumes that the source of variability is at he level of spike
generation, is not consistent with observed changes in the correlations in response to
changes in stimulus features including contrast and orientation. On the other hand, a model
that assumes noise to emerge at the level of membrane potential, the Rectified Gaussian
model, was demonstrated to account for stimulus-dependent modulations in repsonse
statistics. We presented these results in two international conferences, and they are under
review at an international journal.

The key prediction of the hierarchical model of visual responses we developed earlier is that
trial-to-trial correlations of evoked spike counts in the primary visual cortex (V1) are
dependent on the stimulus content. Importantly, a part of this stimulus dependence of
correlations is assumed to originate from areas processing higher-level percepts. A critical
consequence of this assumption is that stimulus-dependence of correlations are present
when complex, highly structured stimuli are precessed by the visual system, but vanish
when higher-level structure is absent from images. We designed experiments that
specifically test whether visual stimuli eliciting higher-order percepts elicit more specific
correlational patterns than stimuli containing independent features. We recorded neural
responses from the V1 of macaques performing an attention task at the Ernst Strüngmann
Institute in Frankfurt. The results confirmed the prediction of our model. We also
investigated what types of image structure elicit similar specificities without photorealistic
information, revealing intermediate stages of cortical processing. Our results corroborated
the earlier finding that the secondary visual cortex is involved in the representation of
textures. The results are currently being prepared for publication.

Normative analysis of memory processes. — In the preceding years we have developed a
theory of the interactions of episodic a semantic memory, according to which the dynamics
of these memory systems is optimised for dealing with the problem of iterative structure
learning and model selection in high dimensional data and complex model spaces. Our

sequential Monte Carlo approximation algorithm made it possible to apply this model to
larger datasets. We have published these results in a proceedings article, while also
presenting them in multiple international and Hungarian conferences. The scaling up made
possible by the approximation revealed that the selection of episodes from the contents of
episodic memory to integrate into the statistical model is critical. Consequently, we have
developed a procedure for the optimisation of this selection, however this requires further
It would be an important extension of our model if we were able to show that episodic
memory makes structure learning possible in the more realistic situation where episodes
are compressed in a non-invertible way. For modelling this compression, we propose an
encoding where the brain uses latent state variables in a hierarchical probabilistic model of
the environment, and higher level variables are prioritised over lower level details. This
gives diverging predictions from current accounts of episodic reconstruction, which can be
tested experimentally.

Perception in the brain, especially the visual processing, what we have studied mainly, has a
hierarchical structure. The role of a cortical area, representing a hierarchical level, is
essentially the re-representation of information in a form to facilitate recognition and
classification of higher level complex objects. To achieve these complex representations the
nervous system utilizes non-linear transformations at all levels. Previous studies have
characterized this process with the full extent of the information at each level. We put the
emphasis on the structure of the information. Easily decodable information is considered to
be a more relevant quantity. We quantify this by linear decodability which can be plausibly
realized by a neuronal layer at the next hierarchical level.

Contribution of firing rate nonlinearity to optimal cortical computations. — Processing of
visual information in the brain is performed in a hierarchical structure. The role of a cortical
area that forms a level of the processing hierarchy can be phrased as the re-representation
of information in a form to facilitate recognition and classification of higher level, or more
complex features. To achieve these complex representations the nervous system utilizes
non-linear transformations at all levels. Previous studies have characterized this process
with the full extent of the information at each level. We put the emphasis on the structure
of the information. Easily decodable information is considered to be a more relevant
quantity. We quantify this by linear decodability of information, since a linear decoder can
be plausibly realized by a neuronal layer at subsequent levels of the hierarchy.
Recently, several studies have shown that the structure and the statistical characteristics of
the nervous system adapt to the statistics of the environment. The subject of our
investigation is the adaptation of the dynamics at the cellular level. We examined this
through the effect of the so-called firing rate nonlinearity on the quality of information that
can be decoded from a population of neurons. A critical feature of sensory neurons is their
mixed sensitivity: a neuron is sensitive to multiple features of the stimulus, which in the case
of simple cells of V1 comprises orientation, phase, spatial frequency and contrast. These
mixed sensitivities pose a critical challenge for decodability: when some of these parameters
are unknown, areas downstream in the processing hierarchy need to integrate over these
features. We point out, however, that when integration occurs, linear decoding becomes
ineffective: orientation cannot be decoded while other parameters are unknown. In our

investigations we have pointed out that in the absence of unknown parameters decoding
from membrane potential is effective and no nonlinearity is required. However, in the
presence of any of these so-called nuisance parameters a nonlinearity is necessary for
efficient decoding. At higher levels of the computational hierarchy the number of nuisance
parameters grows, therefore the importance of nonlinearity becomes even more

Beyond demonstrating the necessity of a non-linearity in the processing we have also shown
quantitatively that the form of the nonlinearity implemented by cortical neurons is optimal
for decoding. Based on the form of firing rate nonlinearity we have derived a prediction for
the optimal firing threshold of V1 neurons that could be contrasted with intracellular
measurements for V1 simple cells. We found a qualitative match between predicted and
measured thresholds. Our results were presented on a poster at an international conference
and in Hungary and at a prestigious international conference in the US. A publication is in
preparation. In the future, we plan to study consistency between shapes of non-linearities
at adjacent hierarchical levels on the basis of our normative linear decoding principle. We
plan to extend our investigations on higher level with more realistic non-local decoding
tasks connected to pattern recognition.

Disentangling learning-dependent and learning-independent processes in human implicit
learning. — Investigating human learning and decision making in dynamical environments in
a general setting could allow one to understand the common principles relating intuitive
physics, natural language understanding and theory of mind. Higher-level representations in
temporal domains could then be measured for each individual.
We contributed to developing and improving methods for inferring human representations.
To gather information in high-dimensional spaces, one requires a large number of data
points during a learning process to identify the model forms individuals use during a
learning task. The generative process of behavioural responses is, however, highly
confounded with learning-independent effects. We developed a method for segregating the
variation in response time measurements that are related to such confounds from the
variation induced by learning. As a result of our analysis, we concluded that the confounds
may impose a much larger effect on the response times than learning itself, rendering
filtering or other form of accounting for confounds essential for inference. We could
demonstrate that using the method developed in this study can increase the predictive
power a learning-based model. Our work was presented at two international conferences
and is now in review at a journal for publication.

“Momentum” Program of the HAS (G. Orbán, 2012-2017)
NAP-B National Programme for Brain Research (G. Orbán, 2015-)
International cooperation
University of Cambridge (Cambridge, UK), M. Lengyel
University of California, Los Angeles (Los Angeles, CA, USA) P. Golshani
Columbia University (New York, NY, USA), A. Losonczy
Central European University (Budapest), J. Fiser
Ernst Strüngmann Institute (Frankfurt, Germany), W. Singer, A. Lazar

1. Orbán G, Berkes P, Fiser J, Lengyel M: Neural variability and sampling-based
probabilistic representations in the visual cortex. NEURON 92:(2) 530-543 (2016)

Conference proceeding
2. Nagy DG, Orbán G: Episodic memory as a prerequisite for online updates of model
structure. In: Proc. 38th Annual Meeting of the Cognitive Science Society, Philadelphia,
Pennsylvania, USA, 10-08-2016 – 13-08-2016. Eds.: Papafragou A, Grodner D, Mirman
D, Trueswell J, Cognitive Science Society, 2016. pp. 2699-2704. (ISBN:978-0-9911967-3-
See also: R-E.12