000 Informatik, Informationswissenschaft, allgemeine Werke
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Sparse coding is a popular approach to model natural images but has faced two main challenges: modelling low-level image components (such as edge-like structures and their occlusions) and modelling varying pixel intensities. Traditionally, images are modelled as a sparse linear superposition of dictionary elements, where the probabilistic view of this problem is that the coefficients follow a Laplace or Cauchy prior distribution. We propose a novel model that instead uses a spike-and-slab prior and nonlinear combination of components. With the prior, our model can easily represent exact zeros for e.g. the absence of an image component, such as an edge, and a distribution over non-zero pixel intensities. With the nonlinearity (the nonlinear max combination rule), the idea is to target occlusions; dictionary elements correspond to image components that can occlude each other. There are major consequences of the model assumptions made by both (non)linear approaches, thus the main goal of this paper is to isolate and highlight differences between them. Parameter optimization is analytically and computationally intractable in our model, thus as a main contribution we design an exact Gibbs sampler for efficient inference which we can apply to higher dimensional data using latent variable preselection. Results on natural and artificial occlusion-rich data with controlled forms of sparse structure show that our model can extract a sparse set of edge-like components that closely match the generating process, which we refer to as interpretable components. Furthermore, the sparseness of the solution closely follows the ground-truth number of components/edges in the images. The linear model did not learn such edge-like components with any level of sparsity. This suggests that our model can adaptively well-approximate and characterize the meaningful generation process.
FIAS Scientific Report 2014
(2015)
FIAS Scientific Report 2013
(2014)
FIAS Scientific Report 2012
(2013)
Two generic mechanisms for emergence of direction selectivity coexist in recurrent neural networks
(2013)
Poster presentation: Twenty Second Annual Computational Neuroscience Meeting: CNS*2013. Paris, France. 13-18 July 2013.
In the mammalian visual cortex, the time-averaged response of many neurons is maximal for stimuli moving in a particular direction. Such a direction selective response is not found in LGN, upstream of the visual processing pathway, suggesting that cortical networks play a strong role in the generation of direction selectivity. Here we investigate the mechanisms for the emergence of direction selectivity in the recurrent networks of nonlinear firing rate neurons in layer 4 of V1 receiving the input from LGN. In the model the LGN inputs are characterized by different receptive field positions, and their relative temporal phase shifts are reversed for the stimuli moving in the opposite direction. We propose that two distinct mechanisms result in the neuronal direction selective response in these recurrent networks. The first one is a result of nonlinear feed-forward summation of several time-shifted inputs. The second mechanism is based on the competition between neurons for firing in a winner-take-all regime. Both mechanisms rely on inhibitory interactions in the connectivity matrix of lateral connections, but the second one involves inhibitory loops. Typically, the first mechanism results in lower selectivity values than the second, but the time-course of acquiring direction selective response is faster for the first mechanism. Importantly, the two mechanisms have different input frequency tuning. The first mechanism, based on the nonlinear summation, result in a relatively narrow tuning curve around the preferred frequency of the stimulus in the case of the moving grating. In contrast, the direction selectivity arising from the second mechanism depends only weakly on the input frequency, i.e. has a broader tuning curve. These differences allow us to provide the recipe for identifying in experiment which of the two mechanisms is used by a given direction selective neuron. We then analyze how the statistics of the connections in the random recurrent networks affect the relative contributions from these two mechanisms and determine the distributions of the direction selectivity values. We identify the motifs in the connectivity matrix, which are required for each mechanism and show that the minimal conditions for both mechanisms are met in a very broad set of random recurrent networks with sufficiently strong inhibitory connections. Thus, we propose that these mechanisms coexist in generic recurrent networks with inhibition. Our results may account for the recent experimental observations that direction selectivity is present in dark-reared mice and ferrets [1,2]. It can also explain the emergence of direction selectivity in species lacking a spatially organized direction selectivity map.
FIAS Scientific Report
(2011)
FIAS Scientific Report 2011
(2012)
FIAS Scientific Report 2010
(2011)
In the year 2010 the Frankfurt Institute for Advanced Studies has successfully continued to follow its agenda to pursue theoretical research in the natural sciences. As stipulated in its charter, FIAS closely collaborates with extramural research institutions, like the Max Planck Institute for Brain Research in Frankfurt and the GSI Helmholtz Center for Heavy Ion Research, Darmstadt and with research groups at the science departments of Goethe University. The institute also engages in the training of young researchers and the education of doctoral students. This Annual Report documents how these goals have been pursued in the year 2010. Notable events in the scientific life of the Institute will be presented, e.g., teaching activities in the framework of the Frankfurt International Graduate School for Science (FIGSS), colloquium schedules, conferences organized by FIAS, and a full bibliography of publications by authors affiliated with FIAS. The main part of the Report consists of short one-page summaries describing the scientific progress reached in individual research projects in the year 2010...
FIAS Scientific Report 2009
(2010)
In this Annual Report we present some of the ongoing activities of FIAS and of the associated graduate
school, the “Frankfurt International Graduate School for Science” (FIGSS) in the year 2009. The main part of the Report consists of a collection of short reports describing the research projects of scientists working at or associated with FIAS.
This thesis will first introduce in more detail the Bayesian theory and its use in integrating multiple information sources. I will briefly talk about models and their relation to the dynamics of an environment, and how to combine multiple alternative models. Following that I will discuss the experimental findings on multisensory integration in humans and animals. I start with psychophysical results on various forms of tasks and setups, that show that the brain uses and combines information from multiple cues. Specifically, the discussion will focus on the finding that humans integrate this information in a way that is close to the theoretical optimal performance. Special emphasis will be put on results about the developmental aspects of cue integration, highlighting experiments that could show that children do not perform similar to the Bayesian predictions. This section also includes a short summary of experiments on how subjects handle multiple alternative environmental dynamics. I will also talk about neurobiological findings of cells receiving input from multiple receptors both in dedicated brain areas but also primary sensory areas. I will proceed with an overview of existing theories and computational models of multisensory integration. This will be followed by a discussion on reinforcement learning (RL). First I will talk about the original theory including the two different main approaches model-free and model-based reinforcement learning. The important variables will be introduced as well as different algorithmic implementations. Secondly, a short review on the mapping of those theories onto brain and behaviour will be given. I mention the most in uential papers that showed correlations between the activity in certain brain regions with RL variables, most prominently between dopaminergic neurons and temporal difference errors. I will try to motivate, why I think that this theory can help to explain the development of near-optimal cue integration in humans. The next main chapter will introduce our model that learns to solve the task of audio-visual orienting. Many of the results in this section have been published in [Weisswange et al. 2009b,Weisswange et al. 2011]. The model agent starts without any knowledge of the environment and acts based on predictions of rewards, which will be adapted according to the reward signaling the quality of the performed action. I will show that after training this model performs similarly to the prediction of a Bayesian observer. The model can also deal with more complex environments in which it has to deal with multiple possible underlying generating models (perform causal inference). In these experiments I use di#erent formulations of Bayesian observers for comparison with our model, and find that it is most similar to the fully optimal observer doing model averaging. Additional experiments using various alterations to the environment show the ability of the model to react to changes in the input statistics without explicitly representing probability distributions. I will close the chapter with a discussion on the benefits and shortcomings of the model. The thesis continues whith a report on an application of the learning algorithm introduced before to two real world cue integration tasks on a robotic head. For these tasks our system outperforms a commonly used approximation to Bayesian inference, reliability weighted averaging. The approximation is handy because of its computational simplicity, because it relies on certain assumptions that are usually controlled for in a laboratory setting, but these are often not true for real world data. This chapter is based on the paper [Karaoguz et al. 2011]. Our second modeling approach tries to address the neuronal substrates of the learning process for cue integration. I again use a reward based training scheme, but this time implemented as a modulation of synaptic plasticity mechanisms in a recurrent network of binary threshold neurons. I start the chapter with an additional introduction section to discuss recurrent networks and especially the various forms of neuronal plasticity that I will use in the model. The performance on a task similar to that of chapter 3 will be presented together with an analysis of the in uence of different plasticity mechanisms on it. Again benefits and shortcomings and the general potential of the method will be discussed. I will close the thesis with a general conclusion and some ideas about possible future work.