The ability to flexibly switch our responses to external stimuli according to contextual information is critical for successful interactions with a complex world. Context-dependent computations are necessary across many domains1-3, yet their neural implementations remain poorly understood. Here we developed a novel behavioural task in rats to study context-dependent selection and accumulation of evidence for decision-making4-6. Under assumptions supported by both monkey and rat data, we first show mathematically that this computation can be supported by three dynamical solutions and that all networks performing the task implement a combination of these solutions. These solutions can be identified and tested directly with experimental data. We further show that existing electrophysiological and modelling data are compatible with the full variety of possible combinations of these solutions, suggesting that different individuals could use different combinations. To study variability across individual subjects, we developed automated, high-throughput methods to train rats on our task and trained many subjects using these methods. Consistent with theoretical predictions, neural and behavioural analyses revealed substantial heterogeneity across rats, despite uniformly good task performance. Our theory further predicts a specific link between behavioural and neural signatures, which was robustly supported in the data. In summary, our results provide an experimentally supported theoretical framework to analyse individual variability in biological and artificial systems that perform flexible decision-making tasks, open the door to cellular-resolution studies of individual variability in higher cognition, and provide insights into neural mechanisms of context-dependent computation more generally.

Linearization of the dynamics of recurrent neural networks (RNNs) is often used to study their properties. The same RNN dynamics can be written in terms of the ``activations" (the net inputs to each unit, before its pointwise nonlinearity) or in terms of the ``activities" (the output of each unit, after its pointwise nonlinearity); the two corresponding linearizations are different from each other. This brief and informal technical note describes the relationship between the two linearizations, between the left and right eigenvectors of their dynamics matrices, and shows that some context-dependent effects are readily apparent under linearization of activity dynamics but not linearization of activation dynamics.

The ability to flexibly select and accumulate relevant information to form decisions, while ignoring irrelevant information, is a fundamental component of higher cognition. Yet its neural mechanisms remain unclear. Here we demonstrate that, under assumptions supported by both monkey and rat data, the space of possible network mechanisms to implement this ability is spanned by the combination of three different components, each with specific behavioral and anatomical implications. We further show that existing electrophysiological and modeling data are compatible with the full variety of possible combinations of these components, suggesting that different individuals could use different component combinations. To study variations across subjects, we developed a rat task requiring context-dependent evidence accumulation, and trained many subjects on it. Our task delivers sensory evidence through pulses that have random but precisely known timing, providing high statistical power to characterize each individual’s neural and behavioral responses. Consistent with theoretical predictions, neural and behavioral analysis revealed remarkable heterogeneity across rats, despite uniformly good task performance. The theory further predicts a specific link between behavioral and neural signatures, which was robustly supported in the data. Our results provide a new experimentally-supported theoretical framework to analyze biological and artificial systems performing flexible decision-making tasks, and open the door to the study of individual variability in neural computations underlying higher cognition.

Context-based sensorimotor routing is a hallmark of executive control. Pharmacological inactivations in rats have implicated the midbrain superior colliculus (SC) in this process. But what specific role is this, and what circuit mechanisms support it? Here we report a subset of rat SC neurons that instantiate a specific link between the representations of context and motor choice. Moreover, these neurons encode animals’ choice far earlier than other neurons in the SC or in the frontal cortex, suggesting that their neural dynamics lead choice computation. Optogenetic inactivations revealed that SC activity during context encoding is necessary for choice behavior, even while that choice behavior is robust to inactivations during choice formation. Searches for SC circuit models matching our experimental results identified key circuit predictions while revealing some a priori expected features as unnecessary. Our results reveal circuit mechanisms within the SC that implement response inhibition and context-based vector inversion during executive control.

Linear-nonlinear (LN) models and their extensions have proven successful in describing transformations from stimuli to spiking responses of neurons in early stages of sensory hierarchies. Neural responses at later stages are highly nonlinear and have generally been better characterized in terms of their decoding performance on prespecified tasks. Here we develop a biologically plausible decoding model for classification tasks, that we refer to as neural quadratic discriminant analysis (nQDA). Specifically, we reformulate an optimal quadratic classifier as an LN-LN computation, analogous to "subunit" encoding models that have been used to describe responses in retina and primary visual cortex. We propose a physiological mechanism by which the parameters of the nQDA classifier could be optimized, using a supervised variant of a Hebbian learning rule. As an example of its applicability, we show that nQDA provides a better account than many comparable alternatives for the transformation between neural representations in two high-level brain areas recorded as monkeys performed a visual delayed-match-to-sample task.

Finding sought objects requires the brain to combine visual and target signals to determine when a target is in view. To investigate how the brain implements these computations, we recorded neural responses in inferotemporal cortex (IT) and perirhinal cortex (PRH) as macaque monkeys performed a delayed-match-to-sample target search task. Our data suggest that visual and target signals were combined within or before IT in the ventral visual pathway and then passed onto PRH, where they were reformatted into a more explicit target match signal over ∼10-15 ms. Accounting for these dynamics in PRH did not require proposing dynamic computations within PRH itself but, rather, could be attributed to instantaneous PRH computations performed upon an input representation from IT that changed with time. We found that the dynamics of the IT representation arose from two commonly observed features: individual IT neurons whose response preferences were not simply rescaled with time and variable response latencies across the population. Our results demonstrate that these types of time-varying responses have important consequences for downstream computation and suggest that dynamic representations can arise within a feedforward framework as a consequence of instantaneous computations performed upon time-varying inputs.

The responses of high-level neurons tend to be mixtures of many different types of signals. While this diversity is thought to allow for flexible neural processing, it presents a challenge for understanding how neural responses relate to task performance and to neural computation. To address these challenges, we have developed a new method to parse the responses of individual neurons into weighted sums of intuitive signal components. Our method computes the weights by projecting a neuron's responses onto a predefined orthonormal basis. Once determined, these weights can be combined into measures of signal modulation; however, in their raw form these signal modulation measures are biased by noise. Here we introduce and evaluate two methods for correcting this bias, and we report that an analytically derived approach produces performance that is robust and superior to a bootstrap procedure. Using neural data recorded from inferotemporal cortex and perirhinal cortex as monkeys performed a delayed-match-to-sample target search task, we demonstrate how the method can be used to quantify the amounts of task-relevant signals in heterogeneous neural populations. We also demonstrate how these intuitive quantifications of signal modulation can be related to single-neuron measures of task performance (d').

Finding sought visual targets requires our brains to flexibly combine working memory information about what we are looking for with visual information about what we are looking at. To investigate the neural computations involved in finding visual targets, we recorded neural responses in inferotemporal cortex (IT) and perirhinal cortex (PRH) as macaque monkeys performed a task that required them to find targets in sequences of distractors. We found similar amounts of total task-specific information in both areas; however, information about whether a target was in view was more accessible using a linear read-out or, equivalently, was more untangled in PRH. Consistent with the flow of information from IT to PRH, we also found that task-relevant information arrived earlier in IT. PRH responses were well-described by a functional model in which computations in PRH untangle input from IT by combining neurons with asymmetric tuning correlations for target matches and distractors.

The anterior inferotemporal cortex (IT) is the highest stage along the hierarchy of visual areas that, in primates, processes visual objects. Although several lines of evidence suggest that IT primarily represents visual shape information, some recent studies have argued that neuronal ensembles in IT code the semantic membership of visual objects (i.e., represent conceptual classes such as animate and inanimate objects). In this study, we investigated to what extent semantic, rather than purely visual information, is represented in IT by performing a multivariate analysis of IT responses to a set of visual objects. By relying on a variety of machine-learning approaches (including a cutting-edge clustering algorithm that has been recently developed in the domain of statistical physics), we found that, in most instances, IT representation of visual objects is accounted for by their similarity at the level of shape or, more surprisingly, low-level visual properties. Only in a few cases we observed IT representations of semantic classes that were not explainable by the visual similarity of their members. Overall, these findings reassert the primary function of IT as a conveyor of explicit visual shape information, and reveal that low-level visual properties are represented in IT to a greater extent than previously appreciated. In addition, our work demonstrates how combining a variety of state-of-the-art multivariate approaches, and carefully estimating the contribution of shape similarity to the representation of object categories, can substantially advance our understanding of neuronal coding of visual objects in cortex.

In primates, visual object information is processed through a hierarchy of cortico-cortical stages that culminates with the inferotemporal cortex (IT). Although the nature of visual processing in IT is still poorly understood, several lines of evidence suggest that IT conveys an explicit object representation that can directly serve as a basis for decision, action and memory - e.g., it can support flexible formation of semantic categories in downstream areas, such as prefrontal and perirhinal cortex. However, some recent studies (Kiani et al, 2007; Kriegeskorte et al, 2008) have argued that IT neuronal ensembles may themselves code the semantic membership of visual objects (i.e., represent such abstract conceptual classes such as animate and inanimate objects, animals, etc). In this study, we have applied an array of multi-variate computational approaches to investigate the nature of visual objects' representation in IT. Our results show that IT neuronal ensembles represent a surprisingly broad spectrum of visual features complexity, ranging from low-level visual properties (e.g., brightness), to visual patterns of intermediate complexity (e.g., star-like shapes), to complex objects (e.g., four-leg animals) that appear to be coded so invariantly that their clustering in the IT neuronal space is not easily accountable by any similarity metric we used. On the one hand, these findings show that IT supports recognition of low-level properties of the visual input that are typically though to be extracted by lower-level visual areas. On the other hand, IT appears to convey such an explicit representation of some object classes that coding of semantic membership in IT (at least for a few categories) cannot be excluded. Overall, these results shed new light on IT amazing pluripotency in supporting recognition tasks as diverse as detection of brightness and categorization of complex shapes

We present an experimental investigation of the performance of the Lemke-Howson algorithm, which is the most widely used algorithm for the computation of a Nash equilibrium for bimatrix games. Lemke-Howson algorithm is based upon a simple pivoting strategy, which corresponds to following a path whose endpoint is a Nash equilibrium. We analyze both the basic Lemke-Howson algorithm and a heuristic modification of it, which we designed to cope with the effects of a 'bad' initial choice of the pivot. Our experimental findings show that, on uniformly random games, the heuristics achieves a linear running time, while the basic Lemke-Howson algorithm runs in time roughly proportional to a polynomial of degree seven. To conduct the experiments, we have developed our own implementation of Lemke-Howson algorithm, which turns out to be significantly faster than state-of-the-art software. This allowed us to run the algorithm on a much larger set of data, and on instances of much larger size, compared with previous work.