Efficient Coding Models Research Articles

Efficient Coding in Motor Planning.

A paramount challenge for the brain is to precisely model the world and control behavior within the confines of limited encoding capacities. Efficient coding theory posits a unified framework for understanding how neural systems enhance encoding accuracy by tuning to environmental statistics. While this theory has been thoroughly explored within the perceptual realm, it is less clear how efficient coding applies to the motor system. Here, we probe the core principles of efficient coding theory through center-out reaching tasks. Our results reveal novel sequential effects in motor planning. Specifically, current movements are biased in a direction opposite to recent movements, and movement variance increases with the angular divergence between successive actions. These effects are modulated by the variability within the motor system: a larger repulsive bias is observed when movements are performed with the nondominant hand compared to the dominant hand, and in individuals exhibiting higher motor variance compared to those with lower variance. These behavioral findings align with the predictions of an efficient coding model, suggesting that the motor system rapidly adapts to the context to enhance accuracy in motor planning.

Jointly efficient encoding and decoding in neural populations.

The efficient coding approach proposes that neural systems represent as much sensory information as biological constraints allow. It aims at formalizing encoding as a constrained optimal process. A different approach, that aims at formalizing decoding, proposes that neural systems instantiate a generative model of the sensory world. Here, we put forth a normative framework that characterizes neural systems as jointly optimizing encoding and decoding. It takes the form of a variational autoencoder: sensory stimuli are encoded in the noisy activity of neurons to be interpreted by a flexible decoder; encoding must allow for an accurate stimulus reconstruction from neural activity. Jointly, neural activity is required to represent the statistics of latent features which are mapped by the decoder into distributions over sensory stimuli; decoding correspondingly optimizes the accuracy of the generative model. This framework yields in a family of encoding-decoding models, which result in equally accurate generative models, indexed by a measure of the stimulus-induced deviation of neural activity from the marginal distribution over neural activity. Each member of this family predicts a specific relation between properties of the sensory neurons-such as the arrangement of the tuning curve means (preferred stimuli) and widths (degrees of selectivity) in the population-as a function of the statistics of the sensory world. Our approach thus generalizes the efficient coding approach. Notably, here, the form of the constraint on the optimization derives from the requirement of an accurate generative model, while it is arbitrary in efficient coding models. Moreover, solutions do not require the knowledge of the stimulus distribution, but are learned on the basis of data samples; the constraint further acts as regularizer, allowing the model to generalize beyond the training data. Finally, we characterize the family of models we obtain through alternate measures of performance, such as the error in stimulus reconstruction. We find that a range of models admits comparable performance; in particular, a population of sensory neurons with broad tuning curves as observed experimentally yields both low reconstruction stimulus error and an accurate generative model that generalizes robustly to unseen data.

Constrained brain volume in an efficient coding model explains the fraction of excitatory and inhibitory neurons in sensory cortices.

The number of neurons in mammalian cortex varies by multiple orders of magnitude across different species. In contrast, the ratio of excitatory to inhibitory neurons (E:I ratio) varies in a much smaller range, from 3:1 to 9:1 and remains roughly constant for different sensory areas within a species. Despite this structure being important for understanding the function of neural circuits, the reason for this consistency is not yet understood. While recent models of vision based on the efficient coding hypothesis show that increasing the number of both excitatory and inhibitory cells improves stimulus representation, the two cannot increase simultaneously due to constraints on brain volume. In this work, we implement an efficient coding model of vision under a constraint on the volume (using number of neurons as a surrogate) while varying the E:I ratio. We show that the performance of the model is optimal at biologically observed E:I ratios under several metrics. We argue that this happens due to trade-offs between the computational accuracy and the representation capacity for natural stimuli. Further, we make experimentally testable predictions that 1) the optimal E:I ratio should be higher for species with a higher sparsity in the neural activity and 2) the character of inhibitory synaptic distributions and firing rates should change depending on E:I ratio. Our findings, which are supported by our new preliminary analyses of publicly available data, provide the first quantitative and testable hypothesis based on optimal coding models for the distribution of excitatory and inhibitory neural types in the mammalian sensory cortices.

On the Role of LGN/V1 Spontaneous Activity as an Innate Learning Pattern for Visual Development.

Correlated, spontaneous neural activity is known to play a necessary role in visual development, but the higher-order statistical structure of these coherent, amorphous patterns has only begun to emerge in the past decade. Several computational studies have demonstrated how this endogenous activity can be used to train a developing visual system. Models that generate spontaneous activity analogous to retinal waves have shown that these waves can serve as stimuli for efficient coding models of V1. This general strategy in development has one clear advantage: The same learning algorithm can be used both before and after eye-opening. This same insight can be applied to understanding LGN/V1 spontaneous activity. Although lateral geniculate nucleus (LGN) activity has been less discussed in the literature than retinal waves, here we argue that the waves found in the LGN have a number of properties that fill the role of a training pattern. We make the case that the role of “innate learning” with spontaneous activity is not only possible, but likely in later stages of visual development, and worth pursuing further using an efficient coding paradigm.

The Spatiotemporal Power Spectrum of Natural Human Vision

When engaging in natural tasks, the human visual system processes a highly dynamic visual data stream. The retina, performing the very first steps in this processing, is thought to be adapted to take advantage of low-level signal regularities, such as the autocorrelation function or power spectrum, to produce a more efficient encoding of the data (Atick & Redlich, 1992). Previous work examined the joint spatio-temporal power spectrum of handheld camera videos and Hollywood movies, showing that power falls as an inverse power-law function of spatial and temporal frequency, with an inseparable relationship (Dong & Attick, 1995). However these data are far from a true characterization of a day in the life of the retina due to body, head and eye motion. In addition, the distribution of natural tasks will influence the statistics of this signal. Here, we aim to characterize these statistics of natural vision using a custom device that consists of a head-mounted eye tracker coupled with high frame-rate world cameras and orientation sensors. Using video data captured from this setup, we analyze the joint spatiotemporal power spectrum for three conditions: 1) a static camera viewing a natural task being performed, 2) a head mounted camera worn by a subject engaged in a natural task, and 3) videos simulating the dynamic retinal image, created by overlaying the subject's eye motions on the head-mounted camera video stream. Results suggest that compared to a static camera, body and head motion have the effect of boosting high temporal frequencies. Eye motion enhances this effect, particularly for mid to high spatial frequencies, causing this portion to deviate from the power law and become nearly flat. These data will be important for developing efficient coding models relevant to natural vision.

Examination of efficient coding model for auditory nerves during infant development

Examination of efficient coding model for auditory nerves during infant development

VARIETIES OF DIFFERENCE-MAKERS: CONSIDERATIONS ON CHIRIMUUTA’S APPROACH TO NON-CAUSAL EXPLANATION IN NEUROSCIENCE

Abstract Causal approaches to explanation often assume that a model explains by describing features that make a difference regarding the phenomenon. Chirimuuta claims that this idea can be also used to understand non-causal explanation in computational neuroscience. She argues that mathematical principles that figure in efficient coding explanations are non-causal difference-makers. Although these principles cannot be causally altered, efficient coding models can be used to show how would the phenomenon change if the principles were modified in counterpossible situations. The problem is that efficient coding models also involve difference-makers that, prima facie, cannot be characterized as non-causal in this sense. Mathematical principles always involve variables which have counterfactual (instead of counterpossible) relations between them. However, we cannot simply assume that these difference-makers are causal. They can also be found in paradigmatic non-causal explanations and therefore they must be characterized as non-causal in some sense. I argue that, despite appearances, Chirimuuta's view can be applied to these cases. The mentioned counterfactual relations presuppose the counterpossible conditionals that describe the modification of a relevant mathematical principle. If these conditionals are the hallmark of non-causal relations, then Chirimuuta’s criterion has the desired implication that variables in mathematical principles are non-causal difference-makers.

An efficient coding approach to the debate on grounded cognition

The debate between the amodal and the grounded views of cognition seems to be stuck. Their only substantial disagreement is about the vehicle or format of concepts. Amodal theorists reject the grounded claim that concepts are couched in the same modality-specific format as representations in sensory systems. The problem is that there is no clear characterization of (modal or amodal) format or its neural correlate. In order to make the disagreement empirically meaningful and move forward in the discussion we need a neurocognitive criterion for representational format. I argue that efficient coding models in computational neuroscience can be used to characterize modal codes: These are codes which satisfy special informational demands imposed by sensory tasks. Additionally, I examine recent studies on neural coding and argue that although they do not provide conclusive evidence for either the grounded or the amodal views, they can be used to determine what predictions these approaches can make and what experimental and theoretical developments would be required to settle the debate.

Toward a unified theory of efficient, predictive, and sparse coding

A central goal in theoretical neuroscience is to predict the response properties of sensory neurons from first principles. To this end, "efficient coding" posits that sensory neurons encode maximal information about their inputs given internal constraints. There exist, however, many variants of efficient coding (e.g., redundancy reduction, different formulations of predictive coding, robust coding, sparse coding, etc.), differing in their regimes of applicability, in the relevance of signals to be encoded, and in the choice of constraints. It is unclear how these types of efficient coding relate or what is expected when different coding objectives are combined. Here we present a unified framework that encompasses previously proposed efficient coding models and extends to unique regimes. We show that optimizing neural responses to encode predictive information can lead them to either correlate or decorrelate their inputs, depending on the stimulus statistics; in contrast, at low noise, efficiently encoding the past always predicts decorrelation. Later, we investigate coding of naturalistic movies and show that qualitatively different types of visual motion tuning and levels of response sparsity are predicted, depending on whether the objective is to recover the past or predict the future. Our approach promises a way to explain the observed diversity of sensory neural responses, as due to multiple functional goals and constraints fulfilled by different cell types and/or circuits.

Training-Based Gradient LBP Feature Models for Multiresolution Texture Classification.

Local binary pattern (LBP) is a simple, yet efficient coding model for extracting texture features. To improve texture classification, this paper designs a median sampling regulation, defines a group of gradient LBP (gLBP) descriptors, proposes a training-based feature model mapping method, and then develops a texture classification frame using the multiresolution feature fusion of four gLBP descriptors. Cooperated by median sampling, four descriptors encode a pixel respectively by central gradient, radial gradient, magnitude gradient and tangent gradient to generate initial gLBP patterns. The feature mapping models of gLBP descriptors are constructed by the maximal relative-variation rate (mr2) of rotation-invariant patterns, and then prestored as mapping lookup files. By mapping, initial patterns can be transformed into low-dimensional ones. And then it generates multiresolution texture features via the joint and concatenation of gLBP descriptors on different sampling parameters. A trained nearest neighbor classifier with chi-square distance is applied to classify textures by feature histograms. The experimental results of simulation on five public texture databases show that the proposed method is reliable and efficient in texture classification. In comparison with nine other similar approaches, including two state-of-the-art ones, the proposed method runs faster than most of them and also outperforms all of them in terms of classification accuracy and noise robustness. It achieves higher accuracy and has also better robustness to the Salt&Pepper and Gaussian noise added artificially into texture images.

Pluralistic Mechanism

An argument recently proposed by Chirimuuta (2014) seems to motivate the rejection of the claims that every neurocognitive phenomenon can have a mechanistic explanation and that every neurocognitive explanation is mechanistic. In this paper, I focus on efficient coding models involving the so-called “canonical neural computations” and argue that although they imply some form of pluralism, they are compatible with two mechanistic generalizations: all neurocognitive explanations are (at least in part) mechanistic; and all neurocognitive phenomena that have an explanation have (at least) a purely mechanistic explanation.

Biologically realistic excitatory and inhibitory cell properties emerge from a sparse coding network

Neurons in the primary visual cortex exhibit a baffling array of tuning properties, often unaccountable by the classical linear feedforward model. Specifically, excitatory neurons display a number of nonlinear effects collectively known as non-classical receptive field (nCRF) effects [1], and inhibitory neurons have diverse orientation tuning properties [2]. Furthermore, excitatory cells outnumber inhibitory cells by a ratio of 9:1 [3], yet the excitatory and inhibitory drives are balanced. Efficient coding models of early vision have been shown to be able to explain key features of linear filtering properties [4] and some single cell nonlinear effects [5]. However, population statistics of nonlinear properties have not been studied in these models. In addition, inhibitory cells were not typically modeled. Here we demonstrate that many of the aforementioned excitatory cell and inhibitory cell properties emerge naturally from a network that implements sparse coding. To be specific, several nCRF effects including surround suppression, contrast invariant orientation tuning, and cross orientation suppression emerge in the excitatory cell population as a result of sparse coding strategy; the excitatory to inhibitory cell ratio could be understood largely as a result of the overcompletness of representation; moreover, a subpopulation of inhibitory interneurons exhibit orientation tuning due to sparse recurrent connections with the principal cells; another subpopulation displays untuned properties due to low rank connectivity patterns. We also demonstrate that the network exhibits balanced excitation and inhibition, as a result of the receptive field structure. We simulated a population of 2048 excitatory neurons with graded response described by the dynamics of locally competitive algorithm (LCA; [6]), which converges to the sparse coding representation at steady state. Inhibitory interneurons were described by linear units. The low rank and sparse recurrent connectivity pattern was a result of low rank plus sparse decomposition [7] of the LCA connectivity matrix. Non-classical receptive field effects were studied by presenting bar and drifting grating stimuli to the simulated network. Receptive fields of the inhibitory cells were mapped by sparse dots patterns.

Sparse Coding on the Spot: Spontaneous Retinal Waves Suffice for Orientation Selectivity

Ohshiro, Hussain, and Weliky (2011) recently showed that ferrets reared with exposure to flickering spot stimuli, in the absence of oriented visual experience, develop oriented receptive fields. They interpreted this as refutation of efficient coding models, which require oriented input in order to develop oriented receptive fields. Here we show that these data are compatible with the efficient coding hypothesis if the influence of spontaneous retinal waves is considered. We demonstrate that independent component analysis learns predominantly oriented receptive fields when trained on a mixture of spot stimuli and spontaneous retinal waves. Further, we show that the efficient coding hypothesis provides a compelling explanation for the contrast between the lack of receptive field changes seen in animals reared with spot stimuli and the significant cortical reorganisation observed in stripe-reared animals.