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When foraging in dynamic and uncertain environments, animals can benefit from basing their decisions on smart inferences about hidden properties of the world. Typical theoretical approaches to understand the strategies that animals use in such settings combine Bayesian inference and value iteration to derive optimal behavioral policies that maximize total reward given changing beliefs about the environment. However, specifying these beliefs requires infinite numerical precision; with limited resources, this problem can no longer be separated into optimizing inference and optimizing action selections. To understand the space of behavioral policies in this constrained setting, we enumerate and evaluate all possible behavioral programs that can be constructed from just a handful of states. We show that only a small fraction of the top-performing programs can be constructed by approximating Bayesian inference; the remaining programs are structurally or even functionally distinct from Bayesian. To assess structural and functional relationships among all programs, we developed novel tree embedding algorithms; these embeddings, which are capable of extracting different relational structures within the program space, reveal that nearly all good programs are closely connected through single algorithmic “mutations”. We demonstrate how one can use such relational structures to efficiently search for good solutions via an evolutionary algorithm. Moreover, these embeddings reveal that the diversity of non-Bayesian behaviors originates from a handful of key mutations that broaden the functional repertoire within the space of good programs. The fact that this diversity of behaviors does not significantly compromise performance suggests a novel approach for studying how these strategies generalize across 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.

To interpret the sensory environment, the brain combines ambiguous sensory measurements with 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 the statistical structure of the task to maximize decision accuracy and show that its decisions are biased by task context. The magnitude of this decision bias is not a fixed property of the sensory measurement but depends on the observer’s belief about the current context. The model therefore predicts that decision bias will grow with the reliability of the context cue, the stability of the environment, and with the number of trials since the last context switch. Analysis of human choice data validates all three predictions, providing evidence that the brain continuously updates probabilistic representations of the environment to best interpret an uncertain, ever-changing world.SIGNIFICANCEThe brain relies on prior knowledge to make perceptual inferences when sensory information is ambiguous. However, when the environmental context changes, the appropriate prior knowledge often changes with it. Here, we develop a Bayesian observer model to investigate how to make optimal perceptual inferences when sensory information and environmental context are both uncertain. The behavioral signature of this strategy is a context-appropriate decision bias whose strength grows with the reliability of the context cue, the stability of the environment, and with the number of decisions since the most recent change in context. We identified exactly this pattern in the behavior of human subjects performing a dynamic orientation discrimination task. Together, our results suggest that the brain continuously updates probabilistic representations of the environment to make perceptual decisions in the face of uncertainty over both sensory and contextual information.

Many animals rely on a representation of head direction for flexible, goal-directed navigation. In insects, a compass-like head direction representation is maintained in a conserved brain region called the central complex. This head direction representation is updated by self-motion information and by tethering to sensory cues in the surroundings through a plasticity mechanism. However, under natural settings, some of these sensory cues may temporarily disappear—for example, when clouds hide the sun—and prominent landmarks at different distances from the insect may move across the animal’s field of view during translation, creating potential conflicts for a neural compass. We used two-photon calcium imaging in head-fixed Drosophila behaving in virtual reality to monitor the fly’s compass during navigation in immersive naturalistic environments with approachable local landmarks. We found that the fly’s compass remains stable even in these settings by tethering to available global cues, likely preserving the animal’s ability to perform compass-driven behaviors such as maintaining a constant heading.