On the Sparse Structure of Natural Sounds and Natural Images: Similarities, Differences, and Implications for Neural Coding.

Sparse coding models of natural images and sounds have been able to predict several response properties of neurons in the visual and auditory systems. While the success of these models suggests that the structure they capture is universal across domains to some degree, it is not yet clear which aspects of this structure are universal and which vary across sensory modalities. To address this, we fit complete and highly overcomplete sparse coding models to natural images and spectrograms of speech and report on differences in the statistics learned by these models. We find several types of sparse features in natural images, which all appear in similar, approximately Laplace distributions, whereas the many types of sparse features in speech exhibit a broad range of sparse distributions, many of which are highly asymmetric. Moreover, individual sparse coding units tend to exhibit higher lifetime sparseness for overcomplete models trained on images compared to those trained on speech. Conversely, population sparseness tends to be greater for these networks trained on speech compared with sparse coding models of natural images. To illustrate the relevance of these findings to neural coding, we studied how they impact a biologically plausible sparse coding network's representations in each sensory modality. In particular, a sparse coding network with synaptically local plasticity rules learns different sparse features from speech data than are found by more conventional sparse coding algorithms, but the learned features are qualitatively the same for these models when trained on natural images.

Sparse coding models can exhibit decreasing sparseness while learning sparse codes for natural images.

The sparse coding hypothesis has enjoyed much success in predicting response properties of simple cells in primary visual cortex (V1) based solely on the statistics of natural scenes. In typical sparse coding models, model neuron activities and receptive fields are optimized to accurately represent input stimuli using the least amount of neural activity. As these networks develop to represent a given class of stimulus, the receptive fields are refined so that they capture the most important stimulus features. Intuitively, this is expected to result in sparser network activity over time. Recent experiments, however, show that stimulus-evoked activity in ferret V1 becomes less sparse during development, presenting an apparent challenge to the sparse coding hypothesis. Here we demonstrate that some sparse coding models, such as those employing homeostatic mechanisms on neural firing rates, can exhibit decreasing sparseness during learning, while still achieving good agreement with mature V1 receptive field shapes and a reasonably sparse mature network state. We conclude that observed developmental trends do not rule out sparseness as a principle of neural coding per se: a mature network can perform sparse coding even if sparseness decreases somewhat during development. To make comparisons between model and physiological receptive fields, we introduce a new nonparametric method for comparing receptive field shapes using image registration techniques.

Sparse codes for speech predict spectrotemporal receptive fields in the inferior colliculus.

We have developed a sparse mathematical representation of speech that minimizes the number of active model neurons needed to represent typical speech sounds. The model learns several well-known acoustic features of speech such as harmonic stacks, formants, onsets and terminations, but we also find more exotic structures in the spectrogram representation of sound such as localized checkerboard patterns and frequency-modulated excitatory subregions flanked by suppressive sidebands. Moreover, several of these novel features resemble neuronal receptive fields reported in the Inferior Colliculus (IC), as well as auditory thalamus and cortex, and our model neurons exhibit the same tradeoff in spectrotemporal resolution as has been observed in IC. To our knowledge, this is the first demonstration that receptive fields of neurons in the ascending mammalian auditory pathway beyond the auditory nerve can be predicted based on coding principles and the statistical properties of recorded sounds.

Dead leaves and the dirty ground: low-level image statistics in transmissive and occlusive imaging environments.

The opacity of typical objects in the world results in occlusion, an important property of natural scenes that makes inference of the full three-dimensional structure of the world challenging. The relationship between occlusion and low-level image statistics has been hotly debated in the literature, and extensive simulations have been used to determine whether occlusion is responsible for the ubiquitously observed power-law power spectra of natural images. To deepen our understanding of this problem, we have analytically computed the two- and four-point functions of a generalized "dead leaves" model of natural images with parameterized object transparency. Surprisingly, transparency alters these functions only by a multiplicative constant, so long as object diameters follow a power-law distribution. For other object size distributions, transparency more substantially affects the low-level image statistics. We propose that the universality of power-law power spectra for both natural scenes and radiological medical images, formed by the transmission of x-rays through partially transparent tissue, stems from power-law object size distributions, independent of object opacity.

A sparse coding model with synaptically local plasticity and spiking neurons can account for the diverse shapes of V1 simple cell receptive fields.

Sparse coding algorithms trained on natural images can accurately predict the features that excite visual cortical neurons, but it is not known whether such codes can be learned using biologically realistic plasticity rules. We have developed a biophysically motivated spiking network, relying solely on synaptically local information, that can predict the full diversity of V1 simple cell receptive field shapes when trained on natural images. This represents the first demonstration that sparse coding principles, operating within the constraints imposed by cortical architecture, can successfully reproduce these receptive fields. We further prove, mathematically, that sparseness and decorrelation are the key ingredients that allow for synaptically local plasticity rules to optimize a cooperative, linear generative image model formed by the neural representation. Finally, we discuss several interesting emergent properties of our network, with the intent of bridging the gap between theoretical and experimental studies of visual cortex.

How should prey animals respond to uncertain threats?

A prey animal surveying its environment must decide whether there is a dangerous predator present or not. If there is, it may flee. Flight has an associated cost, so the animal should not flee if there is no danger. However, the prey animal cannot know the state of its environment with certainty, and is thus bound to make some errors. We formulate a probabilistic automaton model of a prey animal's life and use it to compute the optimal escape decision strategy, subject to the animal's uncertainty. The uncertainty is a major factor in determining the decision strategy: only in the presence of uncertainty do economic factors (like mating opportunities lost due to flight) influence the decision. We performed computer simulations and found that in silico populations of animals subject to predation evolve to display the strategies predicted by our model, confirming our choice of objective function for our analytic calculations. To the best of our knowledge, this is the first theoretical study of escape decisions to incorporate the effects of uncertainty, and to demonstrate the correctness of the objective function used in the model.