Canonical Neural Computation Research Articles

Perceptual Resolution of Ambiguity: Can Tuned, Divisive Normalization Account for both Interocular Similarity Grouping and Difference Enhancement.

Our visual system usually provides a unique and functional representation of the external world. At times, however, the visual system has more than one compelling interpretation of the same retinal stimulus; in this case, neural populations compete for perceptual dominance to resolve ambiguity. Spatial and temporal context can guide perceptual experience. Recent evidence shows that ambiguous retinal stimuli are sometimes resolved by enhancing either similarity or differences among multiple percepts. Divisive normalization is a canonical neural computation that enables context-dependent sensory processing by attenuating a neuron's response by other neurons. Experiments here show that divisive normalization can account for perceptual representations of either similarity enhancement (so-called grouping) or difference enhancement, offering a unified framework for opposite perceptual outcomes.

Invited Session I: 30 years of normalization in the visual system: Exponentiation and normalization as mechanisms for efficient selection of sensory signals.

The standard formulation of the normalization operation comprises two canonical neural computations, exponentiation and division; a counter-balancing of two forces. Exponentiation favors the strong. Larger responses grow even larger than smaller ones. In the extreme, exponentiation is a winner-take-all computation. Division by the pooled responses of a neural population brings run-away responses back down to an operable range. Division normalizes to the average population activity responses that have grown large through exponentiation. Such simple operations have surprisingly many applications across sensory and cognitive systems of the brain. Here, I will focus on how these operations can facilitate selection of sensory signals for prioritized processing, and thereby explain perceptual benefits of spatial attention.

In vivo extracellular recordings of thalamic and cortical visual responses reveal V1 connectivity rules

The brain's connectome provides the scaffold for canonical neural computations. However, a comparison of connectivity studies in the mouse primary visual cortex (V1) reveals that the average number and strength of connections between specific neuron types can vary. Can variability in V1 connectivity measurements coexist with canonical neural computations? We developed a theory-driven approach to deduce V1 network connectivity from visual responses in mouse V1 and visual thalamus (dLGN). Our method revealed that the same recorded visual responses were captured by multiple connectivity configurations. Remarkably, the magnitude and selectivity of connectivity weights followed a specific order across most of the inferred connectivity configurations. We argue that this order stems from the specific shapes of the recorded contrast response functions and contrast invariance of orientation tuning. Remarkably, despite variability across connectivity studies, connectivity weights computed from individual published connectivity reports followed the order we identified with our method, suggesting that the relations between the weights, rather than their magnitudes, represent a connectivity motif supporting canonical V1 computations.

Contextual Modulation of Feedforward Inputs to Primary Visual Cortex.

Throughout the brain, parallel processing streams compose the building blocks of complex neural functions. One of the most salient models for studying the functional specialization of parallel visual streams in the primate brain is the lateral geniculate nucleus (LGN) of the dorsal thalamus, through which the parvocellular and magnocellular channels, On-center and Off-center channels, and ipsilateral and contralateral eye channels are maintained and provide the foundation for cortical processing. We examined three aspects of neural processing in these streams: (1) the relationship between extraclassical surround suppression, a widespread visual computation thought to represent a canonical neural computation, and the parallel channels of the LGN; (2) the magnitude of binocular interaction in the parallel streams; and (3) the magnitude of suppression elicited by perceptual competition (binocular rivalry) in each stream. Our results show that surround suppression is almost exclusive to Off channel cells; further, we found evidence for two different components of monocular surround suppression—an early-stage suppression exhibited by all magnocellular cells, and a late-stage suppression exhibited only by Off cells in both the parvocellular and magnocellular pathways. This finding indicates that stream-specific circuits contribute to surround suppression in the primate LGN and suggests a distinct role for suppression in the Off channel to the cortex. We also examined the responses of LGN neurons in alert macaque monkeys to determine whether neurons that supply the cortex with visual information are influenced by stimulation of both eyes. Our results demonstrate that LGN neurons are not influenced by stimulation of the non-dominant eye. This was the case when dichoptic stimuli were presented to classical receptive fields of neurons, extraclassical receptive fields of neurons, and when stimuli were appropriate to produce the perception of binocular rivalry.

Divisive normalization unifies disparate response signatures throughout the human visual hierarchy

Neural processing is hypothesized to apply the same mathematical operations in a variety of contexts, implementing so-called canonical neural computations. Divisive normalization (DN) is considered a prime candidate for a canonical computation. Here, we propose a population receptive field (pRF) model based on DN and evaluate it using ultra-high-field functional MRI (fMRI). The DN model parsimoniously captures seemingly disparate response signatures with a single computation, superseding existing pRF models in both performance and biological plausibility. We observe systematic variations in specific DN model parameters across the visual hierarchy and show how they relate to differences in response modulation and visuospatial information integration. The DN model delivers a unifying framework for visuospatial responses throughout the human visual hierarchy and provides insights into its underlying information-encoding computations. These findings extend the role of DN as a canonical computation to neuronal populations throughout the human visual hierarchy.

A minimal synaptic model for direction selective neurons in Drosophila.

Visual motion estimation is a canonical neural computation. In Drosophila, recent advances have identified anatomic and functional circuitry underlying direction-selective computations. Models with varying levels of abstraction have been proposed to explain specific experimental results but have rarely been compared across experiments. Here we use the wealth of available anatomical and physiological data to construct a minimal, biophysically inspired synaptic model for Drosophila’s first-order direction-selective T4 cells. We show how this model relates mathematically to classical models of motion detection, including the Hassenstein-Reichardt correlator model. We used numerical simulation to test how well this synaptic model could reproduce measurements of T4 cells across many datasets and stimulus modalities. These comparisons include responses to sinusoid gratings, to apparent motion stimuli, to stochastic stimuli, and to natural scenes. Without fine-tuning this model, it sufficed to reproduce many, but not all, response properties of T4 cells. Since this model is flexible and based on straightforward biophysical properties, it provides an extensible framework for developing a mechanistic understanding of T4 neural response properties. Moreover, it can be used to assess the sufficiency of simple biophysical mechanisms to describe features of the direction-selective computation and identify where our understanding must be improved.

Adaptation in models of visual object recognition

Convolutional neural network (CNN) models of the ventral stream provide an unprecedented opportunity to relate neural mechanisms to sensory representations and even perception. Current CNNs lack the temporal dynamics of biological vision such as adaptation to previous stimulation. Perceptually, adaptation has been widely studied in the form of aftereffects (Webster, 2015), while in single neurons adaptation is often equated to repetition suppression (Vogels, 2016). Whereas the two are often thought to be associated, they remain to be integrated in a truly general framework. One proposed mechanism underlying repetition suppression is a reduced excitability depending on previous neural activity, called response fatigue. Here, we implemented fatigue in each unit of a CNN (Krizhevsky et al., 2012) and asked whether it could account for more complex phenomena of neural and visual adaptation. Specifically, we assigned a latent fatigue variable to each unit that increased after high, but decreased after lower activation. The activation of a unit was then obtained by subtracting its fatigue from its input activity (before the linear rectifier). The resulting CNN units showed repetition suppression matching neural adaptation on several hallmark properties: stimulus-specificity, increased adaptation in higher layers, adaptation degree proportional with the number of repetitions (Vinken et al., 2017), and decreased adaptation with longer interstimulus intervals (Sawamura et al., 2006). Furthermore, the response patterns could account for the perceptual effects we tested: from afterimages in the first layer to a face gender aftereffect in later layers (Webster et al., 2004). Thus, when considered in a CNN, a simple mechanism of response fatigue operating at the level of single neurons can account for complex adaptation effects. In addition to providing a general model for adaptation, these results demonstrate the strength of using deep neural networks to connect low-level canonical neural properties or computations to high-level neural and perceptual phenomena.

Intact perceptual bias in autism contradicts the decreased normalization model

One recent, promising account of Autism Spectrum Disorders (ASD) situates the cause of the disorder in an atypicality in basic neural information processing, more specifically in how activity of one neuron is modulated by neighboring neurons. The canonical neural computation that implements such contextual influence is called divisive (or suppressive) normalization. The account proposes that this normalization is reduced in ASD. We tested one fundamental prediction of this model for low-level perception, namely that individuals with ASD would show reduced cross-orientation suppression (leading to an illusory tilt perception). 11 young adults with an ASD diagnosis and 12 age-, gender-, and IQ-matched control participants performed a psychophysical orientation perception task with compound grating stimuli. Illusory tilt perception did not differ significantly between groups, indicating typical divisive normalization in individuals with ASD. In fact, all individuals with ASD showed a considerable orientation bias. There was also no correlation between illusory tilt perception and autistic traits as measured by the Social Responsiveness Scale. These results provide clear evidence against the decreased divisive normalization model of ASD in low-level perception, where divisive normalization is best characterized. We evaluate the broader existing evidence for this model and propose ways to salvage and refine the model.

Autistic adults show preserved normalisation of sensory responses in gaze processing

Progress in our understanding of autism spectrum disorder (ASD) has recently been sought by characterising how systematic differences in canonical neural computations employed across the sensory cortex might contribute to clinical symptoms in diverse sensory, cognitive, and social domains. A key proposal is that ASD is characterised by reduced divisive normalisation of sensory responses. This provides a bridge between genetic and molecular evidence for an increased ratio of cortical excitation to inhibition in ASD and the functional characteristics of sensory coding that are relevant for understanding perception and behaviour. Here we tested this hypothesis in the context of gaze processing (i.e., the perception of other people's direction of gaze), a domain with direct relevance to the core diagnostic features of ASD. We show that reduced divisive normalisation in gaze processing is associated with specific predictions regarding the psychophysical effects of sensory adaptation to gaze direction, and test these predictions in adults with ASD. We report compelling evidence that both divisive normalisation and sensory adaptation occur robustly in adults with ASD in the context of gaze processing. These results have important theoretical implications for defining the types of divisive computations that are likely to be intact or compromised in this condition (e.g., relating to local vs distal control of cortical gain). These results are also a strong testament to the typical sensory coding of gaze direction in ASD, despite the atypical responses to others' gaze that are a hallmark feature of this diagnosis.

The Patient Repository for EEG Data + Computational Tools (PRED+CT).

Electroencephalographic (EEG) recordings are thought to reflect the network-wide operations of canonical neural computations, making them a uniquely insightful measure of brain function. As evidence of these virtues, numerous candidate biomarkers of different psychiatric and neurological diseases have been advanced. Presumably, we would only need to apply powerful machine-learning methods to validate these ideas and provide novel clinical tools. Yet, the reality of this advancement is more complex: the scale of data required for robust and reliable identification of a clinical biomarker transcends the ability of any single laboratory. To surmount this logistical hurdle, collective action and transparent methods are required. Here we introduce the Patient Repository of EEG Data + Computational Tools (PRED+CT: predictsite.com). The ultimate goal of this project is to host a multitude of available tasks, patient datasets, and analytic tools, facilitating large-scale data mining. We hope that successful completion of this aim will lead to the development of novel EEG biomarkers for differentiating populations of neurological and psychiatric disorders.

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.

A mechanistic perspective on canonical neural computation

Although it has been argued that mechanistic explanation is compatible with abstraction (i.e., that there are abstract mechanistic models), there are still doubts about whether mechanism can account for the explanatory power of significant abstract models in computational neuroscience. Chirimuuta has recently claimed that models describing canonical neural computations (CNCs) must be evaluated using a non-mechanistic framework. I defend two claims regarding these models. First, I argue that their prevailing neurocognitive interpretation is mechanistic. Additionally, a criterion recently proposed by Levy and Bechtel to legitimize mechanistic abstract models, and also a criterion proposed by Chirimuuta herself aimed to distinguish between causal and non-causal explanation, can be employed to show why these models are explanatory only under this interpretation (as opposed to a purely mathematical or non-causal interpretation). Second, I argue that mechanism is able to account for the special epistemic achievement implied by CNC models. Canonical neural components contribute to an integrated understanding of different cognitive functions. They make it possible for us to explain these functions by describing different mechanisms constituted by common basic components arranged in different ways.

The unity of neuroscience: a flat view

This paper offers a novel view of unity in neuroscience. I set out by discussing problems with the classical account of unity-by-reduction, due to Oppenheim and Putnam. That view relies on a strong notion of levels, which has substantial problems. A more recent alternative, the mechanistic “mosaic” view due to Craver, does not have such problems. But I argue that the mosaic ideal of unity is too minimal, and we should, if possible, aspire for more. Relying on a number of recent works in theoretical neuroscience—network motifs, canonical neural computations (CNCs) and design-principles—I then present my alternative: a “flat” view of unity, i.e. one that is not based on levels. Instead, it treats unity as attained via the identification of recurrent explanatory patterns, under which a range of neuroscientific phenomena are subsumed. I develop this view by recourse to a causal conception of explanation, and distinguish it from Kitcher’s view of explanatory unification and related ideas. Such a view of unity is suitably ambitious, I suggest, and has empirical plausibility. It is fit to serve as an appropriate working hypothesis for 21st century neuroscience.

Divisive Normalization Predicts Adaptation-Induced Response Changes in Macaque Inferior Temporal Cortex.

Stimulus repetition alters neural responses to the repeated stimulus. This so-called adaptation phenomenon has been commonly observed at multiple spatial and temporal scales and in different brain areas, and has been hypothesized to affect the neural representation of the sensory input. Yet, the neural mechanisms underlying adaptation still remain unclear, especially in higher-order cortical areas. Here we employ a divisive normalization model of neural responses to predict adaptation-induced changes in responses of single neurons in the macaque inferior temporal (IT) cortex. According to this model, the response of a neuron is determined by an interplay between its direct excitatory and divisive normalizing inputs, with each input being subject to adaptation. To test the model, we recorded the responses of single IT cortex neurons to complex visual stimuli while separately adapting the two putative types of input to those neurons. We compared the changes in responses of these neurons following such adaptation with predictions derived from the divisive normalization model. As predicted by the model, we show that adaptation in the IT cortex can, depending on the relative strength of each putative type of input to a neuron, suppress or enhance the neural response to a complex stimulus. More generally, our data suggest that adaptation serves to selectively enhance processing of the stimuli that differ from recently experienced ones, even when these occur within a configuration of multiple stimuli. Stimulus repetition alters neural responses to the repeated stimulus. This so-called adaptation phenomenon has been robustly demonstrated in brains of different species and is considered to be a form of short-term plasticity inherent to the processing of sensory stimuli. Nevertheless, the functional role and underlying mechanisms of adaptation remain unclear. Here we demonstrate that divisive normalization, a canonical neural computation operating throughout the brain, predicts the adaptation-induced changes in response of single neurons to complex stimulus configurations in the macaque inferotemporal cortex. Our findings embed adaptation effects of inferotemporal neurons into the context of a broader neural network perspective that includes divisive normalization. Additionally, our findings have implications for understanding of the function of adaptation in higher-order sensory cortices.

Language Processing as Cue Integration: Grounding the Psychology of Language in Perception and Neurophysiology.

I argue that cue integration, a psychophysiological mechanism from vision and multisensory perception, offers a computational linking hypothesis between psycholinguistic theory and neurobiological models of language. I propose that this mechanism, which incorporates probabilistic estimates of a cue's reliability, might function in language processing from the perception of a phoneme to the comprehension of a phrase structure. I briefly consider the implications of the cue integration hypothesis for an integrated theory of language that includes acquisition, production, dialogue and bilingualism, while grounding the hypothesis in canonical neural computation.

Normalization in human somatosensory cortex.

Functional magnetic resonance imaging (fMRI) was used to measure activity in human somatosensory cortex and to test for cross-digit suppression. Subjects received stimulation (vibration of varying amplitudes) to the right thumb (target) with or without concurrent stimulation of the right middle finger (mask). Subjects were less sensitive to target stimulation (psychophysical detection thresholds were higher) when target and mask digits were stimulated concurrently compared with when the target was stimulated in isolation. fMRI voxels in a region of the left postcentral gyrus each responded when either digit was stimulated. A regression model (called a forward model) was used to separate the fMRI measurements from these voxels into two hypothetical channels, each of which responded selectively to only one of the two digits. For the channel tuned to the target digit, responses in the left postcentral gyrus increased with target stimulus amplitude but were suppressed by concurrent stimulation to the mask digit, evident as a shift in the gain of the response functions. For the channel tuned to the mask digit, a constant baseline response was evoked for all target amplitudes when the mask was absent and responses decreased with increasing target amplitude when the mask was concurrently presented. A computational model based on divisive normalization provided a good fit to the measurements for both mask-absent and target + mask stimulation. We conclude that the normalization model can explain cross-digit suppression in human somatosensory cortex, supporting the hypothesis that normalization is a canonical neural computation.

Minimal models and canonical neural computations: the distinctness of computational explanation in neuroscience

In a recent paper, Kaplan (Synthese 183:339–373, 2011) takes up the task of extending Craver’s (Explaining the brain, 2007) mechanistic account of explanation in neuroscience to the new territory of computational neuroscience. He presents the model to mechanism mapping (3M) criterion as a condition for a model’s explanatory adequacy. This mechanistic approach is intended to replace earlier accounts which posited a level of computational analysis conceived as distinct and autonomous from underlying mechanistic details. In this paper I discuss work in computational neuroscience that creates difficulties for the mechanist project. Carandini and Heeger (Nat Rev Neurosci 13:51–62, 2012) propose that many neural response properties can be understood in terms of canonical neural computations. These are “standard computational modules that apply the same fundamental operations in a variety of contexts.” Importantly, these computations can have numerous biophysical realisations, and so straightforward examination of the mechanisms underlying these computations carries little explanatory weight. Through a comparison between this modelling approach and minimal models in other branches of science, I argue that computational neuroscience frequently employs a distinct explanatory style, namely, efficient coding explanation. Such explanations cannot be assimilated into the mechanistic framework but do bear interesting similarities with evolutionary and optimality explanations elsewhere in biology.

Neural computation with efficient population codes

Brain function depends on populations of neurons that perform computations on perceptually and behaviorally relevant variables. One of the main goals of neuroscience is to understand how the responses of populations of neurons and the connectivity patterns between groups of neurons allow brains to perform a wide range of neural computations. The Neural Engineering Framework (NEF) is a promising approach to designing neural models that perform many neural computations [1,2]. The central thesis behind the NEF is that populations of neurons represent, and perform computations on, low-dimensional time-dependent variables. By characterizing how neurons in a population encode a variable, and how the variable can be decoded from the distributed representation, functioning neural circuits are constructed that allow a comparison with experimental data at a range of levels from single neuron responses to connectivity patterns to perceptual and behavioral performance. The particular models that result from this approach depend on how the neural encoding and decoding processes are characterized. This is where emerging principles of neural computation constrain models of neural encoding and decoding. We describe how efficient codes are used to design neural circuit models that perform a wide variety of computations. The fundamental characteristic of the efficient code is that the neural representation is adapted to the statistics of the environment. Here, we take an efficient code to be one where the preferred stimuli are drawn from the prior distribution and the neural tuning curves are proportional to the likelihood function [3-6]. We show that in an efficient code, a general center-of-mass decoder can extract Bayesian estimates of encoded variables or functions of encoded variables, which allows for the construction of networks that perform many computations [3,4]. Networks constructed using the method we describe have several nice functional properties and match many experimental observations. First, neural tuning properties match the statistics of the variables they process. Second, in this framework, normalization is an essential computation at each stage of processing. This is consistent with normalization being described as a canonical neural computation [7]. Also, computation in networks of neurons using efficient coding is robust to neuronal loss and uses local connection rules. Finally, the networks we describe are flexible and can incorporate changes to environmental statistics or goals using gain modulation or changes in tuning curve widths. The overall result is to show the importance of several emerging principles of neural computation in an already successful modeling framework.

Normalization is a general neural mechanism for context-dependent decision making

Understanding the neural code is critical to linking brain and behavior. In sensory systems, divisive normalization seems to be a canonical neural computation, observed in areas ranging from retina to cortex and mediating processes including contrast adaptation, surround suppression, visual attention, and multisensory integration. Recent electrophysiological studies have extended these insights beyond the sensory domain, demonstrating an analogous algorithm for the value signals that guide decision making, but the effects of normalization on choice behavior are unknown. Here, we show that choice models using normalization generate significant (and classically irrational) choice phenomena driven by either the value or number of alternative options. In value-guided choice experiments, both monkey and human choosers show novel context-dependent behavior consistent with normalization. These findings suggest that the neural mechanism of value coding critically influences stochastic choice behavior and provide a generalizable quantitative framework for examining context effects in decision making.

Erratum: Normalization as a canonical neural computation

Nature Reviews Neuroscience 13, 51–62 (2012) On page 52 of this article, in the legend for figure 1, the text “lower concentrations are shown by lighter colours” should have read “lower concentrations are shown by darker colours”. This has been corrected in the online version.