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 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.

In natural environments, animals must efficiently allocate their choices across multiple concurrently available resources when foraging, a complex decision-making process not fully captured by existing models. To understand how rodents learn to navigate this challenge we developed a novel paradigm in which untrained, water-restricted mice were free to sample from six options rewarded at a range of deterministic intervals and positioned around the walls of a large ( 2m) arena. Mice exhibited rapid learning, matching their choices to integrated reward ratios across six options within the first session. A reinforcement learning model with separate states for staying or leaving an option and a dynamic, global learning rate was able to accurately reproduce mouse learning and decision-making. Fiber photometry recordings revealed that dopamine in the nucleus accumbens core (NAcC), but not dorsomedial striatum (DMS), more closely reflected the global learning rate than local error-based updating. Altogether, our results provide insight into the neural substrate of a learning algorithm that allows mice to rapidly exploit multiple options when foraging in large spatial environments.

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.

To survive, animals must be able quickly infer the state of their surroundings. For example, to successfully escape an approaching predator, prey must quickly estimate the direction of approach from incoming sensory stimuli. Such rapid inferences are particularly challenging because the animal has only a brief window of time to gather sensory stimuli, and yet the accuracy of inference is critical for survival. Due to evolutionary pressures, nervous systems have likely evolved effective computational strategies that enable accurate inferences under strong time limitations. Traditionally, the relationship between the speed and accuracy of inference has been described by the "speed-accuracy tradeoff" (SAT), which quantifies how the average performance of an ideal observer improves as the observer has more time to collect incoming stimuli. While this trial-averaged description can reasonably account for individual inferences made over long timescales, it does not capture individual inferences on short timescales, when trial-to-trial variability gives rise to diverse patterns of error dynamics. We show that an ideal observer can exploit this single-trial structure by adaptively tracking the dynamics of its belief about the state of the environment, which enables it make more rapid inferences and more reliably track its own error but also causes it to violate the SAT. We show that these features can be used to improve overall performance during rapid escape. The resulting behavior qualitatively reproduces features of escape behavior in the fruit fly Drosophila melanogaster, whose escapes have presumably been highly optimized by natural selection.

To survive, animals must be able quickly infer the state of their surroundings. For example, to successfully escape an approaching predator, prey must quickly estimate the direction of approach from incoming sensory stimuli and guide their behavior accordingly. Such rapid inferences are particularly challenging because the animal has only a brief window of time to gather sensory stimuli, and yet the accuracy of inference is critical for survival. Due to evolutionary pressures, nervous systems have likely evolved effective computational strategies that enable accurate inferences under strong time limitations. Traditionally, the relationship between the speed and accuracy of inference has been described by the “speed-accuracy tradeoff” (SAT), which quantifies how the average performance of an ideal observer improves as the observer has more time to collect incoming stimuli. While this trial-averaged description can reasonably account for individual inferences made over long timescales, it does not capture individual inferences on short timescales, when trial-to-trial variability gives rise to diverse patterns of error dynamics. We show that an ideal observer can exploit this single-trial structure by adaptively tracking the dynamics of its belief about the state of the environment, which enables it to speed its own inferences and more reliably track its own error, but also causes it to violate the SAT. We show that these features can be used to improve overall performance during rapid escape. The resulting behavior qualitatively reproduces features of escape behavior in the fruit fly Drosophila melanogaster, whose escapes have presumably been highly optimized by natural selection.

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.

To flexibly navigate, many animals rely on internal spatial representations that persist when the animal is standing still in darkness, and update accurately by integrating the animal's movements in the absence of localizing sensory cues. Theories of mammalian head direction cells have proposed that these dynamics can be realized in a special class of networks that maintain a localized bump of activity via structured recurrent connectivity, and that shift this bump of activity via angular velocity input. Although there are many different variants of these so-called ring attractor networks, they all rely on large numbers of neurons to generate representations that persist in the absence of input and accurately integrate angular velocity input. Surprisingly, in the fly, Drosophila melanogaster, a head direction representation is maintained by a much smaller number of neurons whose dynamics and connectivity resemble those of a ring attractor network. These findings challenge our understanding of ring attractors and their putative implementation in neural circuits. Here, we analyzed failures of angular velocity integration that emerge in small attractor networks with only a few computational units. Motivated by the peak performance of the fly head direction system in darkness, we mathematically derived conditions under which small networks, even with as few as 4 neurons, achieve the performance of much larger networks. The resulting description reveals that by appropriately tuning the network connectivity, the network can maintain persistent representations over the continuum of head directions, and it can accurately integrate angular velocity inputs. We then analytically determined how performance degrades as the connectivity deviates from this optimally-tuned setting, and we find a trade-off between network size and the tuning precision needed to achieve persistence and accurate integration. This work shows how even small networks can accurately track an animal's movements to guide navigation, and it informs our understanding of the functional capabilities of discrete systems more broadly.

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.

Uncertainty is a fundamental aspect of the natural environment, requiring the brain to infer and integrate noisy signals to guide behavior effectively. Sampling-based inference has been proposed as a mechanism for dealing with uncertainty, particularly in early sensory processing. However, it is unclear how to reconcile sampling-based methods with operational principles of higher-order brain areas, such as attractor dynamics of persistent neural representations. In this study, we present a spiking neural network model for the head-direction (HD) system that combines sampling-based inference with attractor dynamics. To achieve this, we derive the required spiking neural network dynamics and interactions to perform sampling from a large family of probability distributions - including variables encoded with Poisson noise. We then propose a method that allows the network to update its estimate of the current head direction by integrating angular velocity samples - derived from noisy inputs - with a pull towards a circular manifold, thereby maintaining consistent attractor dynamics. This model makes specific, testable predictions about the HD system that can be examined in future neurophysiological experiments: it predicts correlated subthreshold voltage fluctuations; distinctive short- and long-term firing correlations among neurons; and characteristic statistics of the movement of the neural activity "bump" representing the head direction. Overall, our approach extends previous theories on probabilistic sampling with spiking neurons, offers a novel perspective on the computations responsible for orientation and navigation, and supports the hypothesis that sampling-based methods can be combined with attractor dynamics to provide a viable framework for studying neural dynamics across the brain.Competing Interest StatementThe authors have declared no competing interest.

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 . 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.