Signatures of criticality arise in simple neural population models with correlations

Large-scale recordings of neuronal activity make it possible to gain insights into the collective activity of neural ensembles. It has been hypothesized that neural populations might be optimized to operate at a 'thermodynamic critical point', and that this property has implications for information processing. Support for this notion has come from a series of studies which identified statistical signatures of criticality in the ensemble activity of retinal ganglion cells. What are the underlying mechanisms that give rise to these observations? Here we show that signatures of criticality arise even in simple feed-forward models of retinal population activity. In particular, they occur whenever neural population data exhibits correlations, and is randomly sub-sampled during data analysis. These results show that signatures of criticality are not necessarily indicative of an optimized coding strategy, and challenge the utility of analysis approaches based on equilibrium thermodynamics for understanding partially observed biological systems.Comment: 36 pages, LaTeX; added journal reference on page 1, added link to code repositor

The computational magic of the ventral stream

I argue that the sample complexity of (biological, feedforward) object recognition is mostly due to geometric image transformations and conjecture that a main goal of the ventral stream – V1, V2, V4 and IT – is to learn-and-discount image transformations.

In the first part of the paper I describe a class of simple and biologically plausible memory-based modules that learn transformations from unsupervised visual experience. The main theorems show that these modules provide (for every object) a signature which is invariant to local affine transformations and approximately invariant for other transformations. I also prove that,
in a broad class of hierarchical architectures, signatures remain invariant from layer to layer. The identification of these memory-based modules with complex (and simple) cells in visual areas leads to a theory of invariant recognition for the ventral stream.

In the second part, I outline a theory about hierarchical architectures that can learn invariance to transformations. I show that the memory complexity of learning affine transformations is drastically reduced in a hierarchical architecture that factorizes transformations in terms of the subgroup of translations and the subgroups of rotations and scalings. I then show how translations are automatically selected as the only learnable transformations during development by enforcing small apertures – eg small receptive fields – in the first layer.

In a third part I show that the transformations represented in each area can be optimized in terms of storage and robustness, as a consequence determining the tuning of the neurons in the area, rather independently (under normal conditions) of the statistics of natural images. I describe a model of learning that can be proved to have this property, linking in an elegant way the spectral properties of the signatures with the tuning of receptive fields in different areas. A surprising implication of these theoretical results is that the computational goals and some of the tuning properties of cells in the ventral stream may follow from symmetry properties (in the sense of physics) of the visual world through a process of unsupervised correlational learning, based on Hebbian synapses. In particular, simple and complex cells do not directly care about oriented bars: their tuning is a side effect of their role in translation invariance. Across the whole ventral stream the preferred features reported for neurons in different areas are only a symptom of the invariances computed and represented.

The results of each of the three parts stand on their own independently of each other. Together this theory-in-fieri makes several broad predictions, some of which are:

-invariance to small transformations in early areas (eg translations in V1) may underly stability of visual perception (suggested by Stu Geman);

-each cell’s tuning properties are shaped by visual experience of image transformations during developmental and adult plasticity;

-simple cells are likely to be the same population as complex cells, arising from different convergence of the Hebbian learning rule. The input to complex “complex” cells are dendritic branches with simple cell properties;

-class-specific transformations are learned and represented at the top of the ventral stream hierarchy; thus class-specific modules such as faces, places and possibly body areas should exist in IT;

-the type of transformations that are learned from visual experience depend on the size of the receptive fields and thus on the area (layer in the models) – assuming that the size increases with layers;

-the mix of transformations learned in each area influences the tuning properties of the cells oriented bars in V1+V2, radial and spiral patterns in V4 up to class specific tuning in AIT (eg face tuned cells);

-features must be discriminative and invariant: invariance to transformations is the primary determinant of the tuning of cortical neurons rather than statistics of natural images.

The theory is broadly consistent with the current version of HMAX. It explains it and extend it in terms of unsupervised learning, a broader class of transformation invariance and higher level modules. The goal of this paper is to sketch a comprehensive theory with little regard for mathematical niceties. If the theory turns out to be useful there will be scope for deep mathematics, ranging from group representation tools to wavelet theory to dynamics of learning

The Computational Magic of the Ventral Stream: Towards a Theory

I conjecture that the sample complexity of object recognition is mostly due to geometric image transformations and that a main goal of the ventral stream – V1, V2, V4 and IT – is to learn-and-discount image transformations. The most surprising implication of the theory emerging from these assumptions is that the computational goals and detailed properties of cells in the ventral stream follow from symmetry properties of the visual world through a process of unsupervised correlational learning.

From the assumption of a hierarchy of areas with receptive fields of increasing size the theory predicts that the size of the receptive fields determines which transformations are learned during development and then factored out during normal processing; that the transformation represented in each area determines the tuning of the neurons in the aerea, independently of the statistics of natural images; and that class-specific transformations are learned and represented at the top of the ventral stream hierarchy.

Some of the main predictions of this theory-in-fieri are:
1. the type of transformation that are learned from visual experience depend on the size (measured in terms of wavelength) and thus on the area (layer in the models) – assuming that the aperture size increases with layers;
2. the mix of transformations learned determine the properties of the receptive fields – oriented bars in V1+V2, radial and spiral patterns in V4 up to class specific tuning in AIT (eg face tuned cells);
3. invariance to small translations in V1 may underly stability of visual perception
4. class-specific modules – such as faces, places and possibly body areas – should exist in IT to process images of object classes

Invariance of visual operations at the level of receptive fields

Receptive field profiles registered by cell recordings have shown that mammalian vision has developed receptive fields tuned to different sizes and orientations in the image domain as well as to different image velocities in space-time. This article presents a theoretical model by which families of idealized receptive field profiles can be derived mathematically from a small set of basic assumptions that correspond to structural properties of the environment. The article also presents a theory for how basic invariance properties to variations in scale, viewing direction and relative motion can be obtained from the output of such receptive fields, using complementary selection mechanisms that operate over the output of families of receptive fields tuned to different parameters. Thereby, the theory shows how basic invariance properties of a visual system can be obtained already at the level of receptive fields, and we can explain the different shapes of receptive field profiles found in biological vision from a requirement that the visual system should be invariant to the natural types of image transformations that occur in its environment.Comment: 40 pages, 17 figure

The computational magic of the ventral stream: sketch of a theory (and why some deep architectures work).

This paper explores the theoretical consequences of a simple assumption: the computational goal of the feedforward path in the ventral stream -- from V1, V2, V4 and to IT -- is to discount image transformations, after learning them during development

Contextual modulation of primary visual cortex by auditory signals

Early visual cortex receives non-feedforward input from lateral and top-down connections (Muckli & Petro 2013 Curr. Opin. Neurobiol. 23, 195–201. (doi:10.1016/j.conb.2013.01.020)), including long-range projections from auditory areas. Early visual cortex can code for high-level auditory information, with neural patterns representing natural sound stimulation (Vetter et al. 2014 Curr. Biol. 24, 1256–1262. (doi:10.1016/j.cub.2014.04.020)). We discuss a number of questions arising from these findings. What is the adaptive function of bimodal representations in visual cortex? What type of information projects from auditory to visual cortex? What are the anatomical constraints of auditory information in V1, for example, periphery versus fovea, superficial versus deep cortical layers? Is there a putative neural mechanism we can infer from human neuroimaging data and recent theoretical accounts of cortex? We also present data showing we can read out high-level auditory information from the activation patterns of early visual cortex even when visual cortex receives simple visual stimulation, suggesting independent channels for visual and auditory signals in V1. We speculate which cellular mechanisms allow V1 to be contextually modulated by auditory input to facilitate perception, cognition and behaviour. Beyond cortical feedback that facilitates perception, we argue that there is also feedback serving counterfactual processing during imagery, dreaming and mind wandering, which is not relevant for immediate perception but for behaviour and cognition over a longer time frame. This article is part of the themed issue ‘Auditory and visual scene analysis’

Representation Learning in Sensory Cortex: a theory

We review and apply a computational theory of the feedforward path of the ventral stream in visual cortex based on the hypothesis that its main function is the encoding of invariant representations of images. A key justification of the theory is provided by a theorem linking invariant representations to small sample complexity for recognition – that is, invariant representations allows learning from very few labeled examples. The theory characterizes how an algorithm that can be implemented by a set of ”simple” and ”complex” cells – a ”HW module” – provides invariant and selective representations. The invariance can be learned in an unsupervised way from observed transformations. Theorems show that invariance implies several properties of the ventral stream organization, including the eccentricity dependent lattice of units in the retina and in V1, and the tuning of its neurons. The theory requires two stages of processing: the first, consisting of retinotopic visual areas such as V1, V2 and V4 with generic neuronal tuning, leads to representations that are invariant to translation and scaling; the second, consisting of modules in IT, with class- and object-specific tuning, provides a representation for recognition with approximate invariance to class specific transformations, such as pose (of a body, of a face) and expression. In the theory the ventral stream main function is the unsupervised learning of ”good” representations that reduce the sample complexity of the final supervised learning stage.This work was supported by the Center for Brains, Minds and Machines (CBMM), funded by NSF STC award CCF - 1231216

The Spatial Structure of Stimuli Shapes the Timescale of Correlations in Population Spiking Activity

Throughout the central nervous system, the timescale over which pairs of neural spike trains are correlated is shaped by stimulus structure and behavioral context. Such shaping is thought to underlie important changes in the neural code, but the neural circuitry responsible is largely unknown. In this study, we investigate a stimulus-induced shaping of pairwise spike train correlations in the electrosensory system of weakly electric fish. Simultaneous single unit recordings of principal electrosensory cells show that an increase in the spatial extent of stimuli increases correlations at short (~10 ms) timescales while simultaneously reducing correlations at long (~100 ms) timescales. A spiking network model of the first two stages of electrosensory processing replicates this correlation shaping, under the assumptions that spatially broad stimuli both saturate feedforward afferent input and recruit an open-loop inhibitory feedback pathway. Our model predictions are experimentally verified using both the natural heterogeneity of the electrosensory system and pharmacological blockade of descending feedback projections. For weak stimuli, linear response analysis of the spiking network shows that the reduction of long timescale correlation for spatially broad stimuli is similar to correlation cancellation mechanisms previously suggested to be operative in mammalian cortex. The mechanism for correlation shaping supports population-level filtering of irrelevant distractor stimuli, thereby enhancing the population response to relevant prey and conspecific communication inputs. © 2012 Litwin-Kumar et al