A vast space of compact strategies for effective decisions.

Inference-based decision-making, which underlies a broad range of behavioral tasks, is typically studied using a small number of handcrafted models. We instead enumerate a complete ensemble of strategies that could be used to effectively, but not necessarily optimally, solve a dynamic foraging task. Each strategy is expressed as a behavioral "program" that uses a limited number of internal states to specify actions conditioned on past observations. We show that the ensemble of strategies is enormous-comprising a quarter million programs with up to five internal states-but can nevertheless be understood in terms of algorithmic "mutations" that alter the structure of individual programs. We devise embedding algorithms that reveal how mutations away from a Bayesian-like strategy can diversify behavior while preserving performance, and we construct a compositional description to link low-dimensional changes in algorithmic structure with high-dimensional changes in behavior. Together, this work provides an alternative approach for understanding individual variability in behavior across animals and tasks.

A neural circuit architecture for rapid learning in goal-directed navigation.

Anchoring goals to spatial representations enables flexible navigation but is challenging in novel environments when both representations must be acquired simultaneously. We propose a framework for how Drosophila uses internal representations of head direction (HD) to build goal representations upon selective thermal reinforcement. We show that flies use stochastically generated fixations and directed saccades to express heading preferences in an operant visual learning paradigm and that HD neurons are required to modify these preferences based on reinforcement. We used a symmetric visual setting to expose how flies' HD and goal representations co-evolve and how the reliability of these interacting representations impacts behavior. Finally, we describe how rapid learning of new goal headings may rest on a behavioral policy whose parameters are flexible but whose form is genetically encoded in circuit architecture. Such evolutionarily structured architectures, which enable rapidly adaptive behavior driven by internal representations, may be relevant across species.

Dynamics of cortical contrast adaptation predict perception of signals in noise.

Neurons throughout the sensory pathway adapt their responses depending on the statistical structure of the sensory environment. Contrast gain control is a form of adaptation in the auditory cortex, but it is unclear whether the dynamics of gain control reflect efficient adaptation, and whether they shape behavioral perception. Here, we trained mice to detect a target presented in background noise shortly after a change in the contrast of the background. The observed changes in cortical gain and behavioral detection followed the dynamics of a normative model of efficient contrast gain control; specifically, target detection and sensitivity improved slowly in low contrast, but degraded rapidly in high contrast. Auditory cortex was required for this task, and cortical responses were not only similarly affected by contrast but predicted variability in behavioral performance. Combined, our results demonstrate that dynamic gain adaptation supports efficient coding in auditory cortex and predicts the perception of sounds in noise.

Environmental dynamics shape perceptual decision bias.

To interpret the sensory environment, the brain combines ambiguous sensory measurements with knowledge that reflects context-specific prior experience. But environmental contexts can change abruptly and unpredictably, resulting in uncertainty about the current context. Here we address two questions: how should context-specific prior knowledge optimally guide the interpretation of sensory stimuli in changing environments, and do human decision-making strategies resemble this optimum? We probe these questions with a task in which subjects report the orientation of ambiguous visual stimuli that were drawn from three dynamically switching distributions, representing different environmental contexts. We derive predictions for an ideal Bayesian observer that leverages knowledge about the statistical structure of the task to maximize decision accuracy, including knowledge about the dynamics of the environment. We show that its decisions are biased by the dynamically changing task context. The magnitude of this decision bias depends on the observer's continually evolving belief about the current context. The model therefore not only predicts that decision bias will grow as the context is indicated more reliably, but also as the stability of the environment increases, and as the number of trials since the last context switch grows. Analysis of human choice data validates all three predictions, suggesting that the brain leverages knowledge of the statistical structure of environmental change when interpreting ambiguous sensory signals.

Disorder and the Neural Representation of Complex Odors.

Animals smelling in the real world use a small number of receptors to sense a vast number of natural molecular mixtures, and proceed to learn arbitrary associations between odors and valences. Here, we propose how the architecture of olfactory circuits leverages disorder, diffuse sensing and redundancy in representation to meet these immense complementary challenges. First, the diffuse and disordered binding of receptors to many molecules compresses a vast but sparsely-structured odor space into a small receptor space, yielding an odor code that preserves similarity in a precise sense. Introducing any order/structure in the sensing degrades similarity preservation. Next, lateral interactions further reduce the correlation present in the low-dimensional receptor code. Finally, expansive disordered projections from the periphery to the central brain reconfigure the densely packed information into a high-dimensional representation, which contains multiple redundant subsets from which downstream neurons can learn flexible associations and valences. Moreover, introducing any order in the expansive projections degrades the ability to recall the learned associations in the presence of noise. We test our theory empirically using data from Drosophila. Our theory suggests that the neural processing of sparse but high-dimensional olfactory information differs from the other senses in its fundamental use of disorder.

A connectome of the Drosophila central complex reveals network motifs suitable for flexible navigation and context-dependent action selection.

Flexible behaviors over long timescales are thought to engage recurrent neural networks in deep brain regions, which are experimentally challenging to study. In insects, recurrent circuit dynamics in a brain region called the central complex (CX) enable directed locomotion, sleep, and context- and experience-dependent spatial navigation. We describe the first complete electron microscopy-based connectome of the Drosophila CX, including all its neurons and circuits at synaptic resolution. We identified new CX neuron types, novel sensory and motor pathways, and network motifs that likely enable the CX to extract the fly's head direction, maintain it with attractor dynamics, and combine it with other sensorimotor information to perform vector-based navigational computations. We also identified numerous pathways that may facilitate the selection of CX-driven behavioral patterns by context and internal state. The CX connectome provides a comprehensive blueprint necessary for a detailed understanding of network dynamics underlying sleep, flexible navigation, and state-dependent action selection.

Structured patterns of activity in pulse-coupled oscillator networks with varied connectivity.

Identifying coordinated activity within complex systems is essential to linking their structure and function. We study collective activity in networks of pulse-coupled oscillators that have variable network connectivity and integrate-and-fire dynamics. Starting from random initial conditions, we see the emergence of three broad classes of behaviors that differ in their collective spiking statistics. In the first class ("temporally-irregular"), all nodes have variable inter-spike intervals, and the resulting firing patterns are irregular. In the second ("temporally-regular"), the network generates a coherent, repeating pattern of activity in which all nodes fire with the same constant inter-spike interval. In the third ("chimeric"), subgroups of coherently-firing nodes coexist with temporally-irregular nodes. Chimera states have previously been observed in networks of oscillators; here, we find that the notions of temporally-regular and chimeric states encompass a much richer set of dynamical patterns than has yet been described. We also find that degree heterogeneity and connection density have a strong effect on the resulting state: in binomial random networks, high degree variance and intermediate connection density tend to produce temporally-irregular dynamics, while low degree variance and high connection density tend to produce temporally-regular dynamics. Chimera states arise with more frequency in networks with intermediate degree variance and either high or low connection densities. Finally, we demonstrate that a normalized compression distance, computed via the Lempel-Ziv complexity of nodal spike trains, can be used to distinguish these three classes of behavior even when the phase relationship between nodes is arbitrary.

Efficient and adaptive sensory codes.

The ability to adapt to changes in stimulus statistics is a hallmark of sensory systems. Here, we developed a theoretical framework that can account for the dynamics of adaptation from an information processing perspective. We use this framework to optimize and analyze adaptive sensory codes, and we show that codes optimized for stationary environments can suffer from prolonged periods of poor performance when the environment changes. To mitigate the adversarial effects of these environmental changes, sensory systems must navigate tradeoffs between the ability to accurately encode incoming stimuli and the ability to rapidly detect and adapt to changes in the distribution of these stimuli. We derive families of codes that balance these objectives, and we demonstrate their close match to experimentally observed neural dynamics during mean and variance adaptation. Our results provide a unifying perspective on adaptation across a range of sensory systems, environments, and sensory tasks.

Efficient coding of natural scene statistics predicts discrimination thresholds for grayscale textures.

Previously, in Hermundstad et al., 2014, we showed that when sampling is limiting, the efficient coding principle leads to a 'variance is salience' hypothesis, and that this hypothesis accounts for visual sensitivity to binary image statistics. Here, using extensive new psychophysical data and image analysis, we show that this hypothesis accounts for visual sensitivity to a large set of grayscale image statistics at a striking level of detail, and also identify the limits of the prediction. We define a 66-dimensional space of local grayscale light-intensity correlations, and measure the relevance of each direction to natural scenes. The 'variance is salience' hypothesis predicts that two-point correlations are most salient, and predicts their relative salience. We tested these predictions in a texture-segregation task using un-natural, synthetic textures. As predicted, correlations beyond second order are not salient, and predicted thresholds for over 300 second-order correlations match psychophysical thresholds closely (median fractional error <0.13).

Generation of stable heading representations in diverse visual scenes.

Many animals rely on an internal heading representation when navigating in varied environments1-10. How this representation is linked to the sensory cues that define different surroundings is unclear. In the fly brain, heading is represented by 'compass' neurons that innervate a ring-shaped structure known as the ellipsoid body3,11,12. Each compass neuron receives inputs from 'ring' neurons that are selective for particular visual features13-16; this combination provides an ideal substrate for the extraction of directional information from a visual scene. Here we combine two-photon calcium imaging and optogenetics in tethered flying flies with circuit modelling, and show how the correlated activity of compass and visual neurons drives plasticity17-22, which flexibly transforms two-dimensional visual cues into a stable heading representation. We also describe how this plasticity enables the fly to convert a partial heading representation, established from orienting within part of a novel setting, into a complete heading representation. Our results provide mechanistic insight into the memory-related computations that are essential for flexible navigation in varied surroundings.

Adaptive coding for dynamic sensory inference.

Behavior relies on the ability of sensory systems to infer properties of the environment from incoming stimuli. The accuracy of inference depends on the fidelity with which behaviorally relevant properties of stimuli are encoded in neural responses. High-fidelity encodings can be metabolically costly, but low-fidelity encodings can cause errors in inference. Here, we discuss general principles that underlie the tradeoff between encoding cost and inference error. We then derive adaptive encoding schemes that dynamically navigate this tradeoff. These optimal encodings tend to increase the fidelity of the neural representation following a change in the stimulus distribution, and reduce fidelity for stimuli that originate from a known distribution. We predict dynamical signatures of such encoding schemes and demonstrate how known phenomena, such as burst coding and firing rate adaptation, can be understood as hallmarks of optimal coding for accurate inference.

Neural signatures of dynamic stimulus selection in Drosophila.

Many animals orient using visual cues, but how a single cue is selected from among many is poorly understood. Here we show that Drosophila ring neurons-central brain neurons implicated in navigation-display visual stimulus selection. Using in vivo two-color two-photon imaging with genetically encoded calcium indicators, we demonstrate that individual ring neurons inherit simple-cell-like receptive fields from their upstream partners. Stimuli in the contralateral visual field suppressed responses to ipsilateral stimuli in both populations. Suppression strength depended on when and where the contralateral stimulus was presented, an effect stronger in ring neurons than in their upstream inputs. This history-dependent effect on the temporal structure of visual responses, which was well modeled by a simple biphasic filter, may determine how visual references are selected for the fly's internal compass. Our approach highlights how two-color calcium imaging can help identify and localize the origins of sensory transformations across synaptically connected neural populations.

Variance predicts salience in central sensory processing.

Information processing in the sensory periphery is shaped by natural stimulus statistics. In the periphery, a transmission bottleneck constrains performance; thus efficient coding implies that natural signal components with a predictably wider range should be compressed. In a different regime--when sampling limitations constrain performance--efficient coding implies that more resources should be allocated to informative features that are more variable. We propose that this regime is relevant for sensory cortex when it extracts complex features from limited numbers of sensory samples. To test this prediction, we use central visual processing as a model: we show that visual sensitivity for local multi-point spatial correlations, described by dozens of independently-measured parameters, can be quantitatively predicted from the structure of natural images. This suggests that efficient coding applies centrally, where it extends to higher-order sensory features and operates in a regime in which sensitivity increases with feature variability.

Structurally-constrained relationships between cognitive states in the human brain.

The anatomical connectivity of the human brain supports diverse patterns of correlated neural activity that are thought to underlie cognitive function. In a manner sensitive to underlying structural brain architecture, we examine the extent to which such patterns of correlated activity systematically vary across cognitive states. Anatomical white matter connectivity is compared with functional correlations in neural activity measured via blood oxygen level dependent (BOLD) signals. Functional connectivity is separately measured at rest, during an attention task, and during a memory task. We assess these structural and functional measures within previously-identified resting-state functional networks, denoted task-positive and task-negative networks, that have been independently shown to be strongly anticorrelated at rest but also involve regions of the brain that routinely increase and decrease in activity during task-driven processes. We find that the density of anatomical connections within and between task-positive and task-negative networks is differentially related to strong, task-dependent correlations in neural activity. The space mapped out by the observed structure-function relationships is used to define a quantitative measure of separation between resting, attention, and memory states. We find that the degree of separation between states is related to both general measures of behavioral performance and relative differences in task-specific measures of attention versus memory performance. These findings suggest that the observed separation between cognitive states reflects underlying organizational principles of human brain structure and function.

Structural foundations of resting-state and task-based functional connectivity in the human brain.

Magnetic resonance imaging enables the noninvasive mapping of both anatomical white matter connectivity and dynamic patterns of neural activity in the human brain. We examine the relationship between the structural properties of white matter streamlines (structural connectivity) and the functional properties of correlations in neural activity (functional connectivity) within 84 healthy human subjects both at rest and during the performance of attention- and memory-demanding tasks. We show that structural properties, including the length, number, and spatial location of white matter streamlines, are indicative of and can be inferred from the strength of resting-state and task-based functional correlations between brain regions. These results, which are both representative of the entire set of subjects and consistently observed within individual subjects, uncover robust links between structural and functional connectivity in the human brain.

Learning, memory, and the role of neural network architecture.

The performance of information processing systems, from artificial neural networks to natural neuronal ensembles, depends heavily on the underlying system architecture. In this study, we compare the performance of parallel and layered network architectures during sequential tasks that require both acquisition and retention of information, thereby identifying tradeoffs between learning and memory processes. During the task of supervised, sequential function approximation, networks produce and adapt representations of external information. Performance is evaluated by statistically analyzing the error in these representations while varying the initial network state, the structure of the external information, and the time given to learn the information. We link performance to complexity in network architecture by characterizing local error landscape curvature. We find that variations in error landscape structure give rise to tradeoffs in performance; these include the ability of the network to maximize accuracy versus minimize inaccuracy and produce specific versus generalizable representations of information. Parallel networks generate smooth error landscapes with deep, narrow minima, enabling them to find highly specific representations given sufficient time. While accurate, however, these representations are difficult to generalize. In contrast, layered networks generate rough error landscapes with a variety of local minima, allowing them to quickly find coarse representations. Although less accurate, these representations are easily adaptable. The presence of measurable performance tradeoffs in both layered and parallel networks has implications for understanding the behavior of a wide variety of natural and artificial learning systems.