Each training step for a variational autoencoder (VAE) requires us to sample from the approximate posterior, so we usually choose simple (e.g. factorised) approximate posteriors in which sampling is an efficient computation that fully exploits GPU parallelism. However, such simple approximate posteriors are often insufficient, as they eliminate statistical dependencies in the posterior. While it is possible to use normalizing flow approximate posteriors for continuous latents, some problems have discrete latents and strong statistical dependencies. The most natural approach to model these dependencies is an autoregressive distribution, but sampling from such distributions is inherently sequential and thus slow. We develop a fast, parallel sampling procedure for autoregressive distributions based on fixed-point iterations which enables efficient and accurate variational inference in discrete state-space latent variable dynamical systems. To optimize the variational bound, we considered two ways to evaluate probabilities: inserting the relaxed samples directly into the pmf for the discrete distribution, or converting to continuous logistic latent variables and interpreting the K-step fixed-point iterations as a normalizing flow. We found that converting to continuous latent variables gave considerable additional scope for mismatch between the true and approximate posteriors, which resulted in biased inferences, we thus used the former approach. Using our fast sampling procedure, we were able to realize the benefits of correlated posteriors, including accurate uncertainty estimates for one cell, and accurate connectivity estimates for multiple cells, in an order of magnitude less time.

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.

To control reaching, the nervous system must generate large changes in muscle activation to drive the limb toward the target, and must also make smaller adjustments for precise and accurate behavior. Motor cortex controls the arm through projections to diverse targets across the central nervous system, but it has been challenging to identify the roles of cortical projections to specific targets. Here, we selectively disrupt cortico-cerebellar communication in the mouse by optogenetically stimulating the pontine nuclei in a cued reaching task. This perturbation did not typically block movement initiation, but degraded the precision, accuracy, duration, or success rate of the movement. Correspondingly, cerebellar and cortical activity during movement were largely preserved, but differences in hand velocity between control and stimulation conditions predicted from neural activity were correlated with observed velocity differences. These results suggest that while the total output of motor cortex drives reaching, the cortico-cerebellar loop makes small adjustments that contribute to the successful execution of this dexterous movement.

In their classic experiments, Olds and Milner showed that rats learn to lever press to receive an electric stimulus in specific brain regions. This led to the identification of mammalian reward centers. Our interest in defining the neuronal substrates of reward perception in the fruit fly Drosophila melanogaster prompted us to develop a simpler experimental approach wherein flies could implement behavior that induces self-stimulation of specific neurons in their brains. The high-throughput assay employs optogenetic activation of neurons when the fly occupies a specific area of a behavioral chamber, and the flies' preferential occupation of this area reflects their choosing to experience optogenetic stimulation. Flies in which neuropeptide F (NPF) neurons are activated display preference for the illuminated side of the chamber. We show that optogenetic activation of NPF neuron is rewarding in olfactory conditioning experiments and that the preference for NPF neuron activation is dependent on NPF signaling. Finally, we identify a small subset of NPF-expressing neurons located in the dorsomedial posterior brain that are sufficient to elicit preference in our assay. This assay provides the means for carrying out unbiased screens to map reward neurons in flies.

Sensory cues that precede reward acquire predictive (expected value) and incentive (drive reward-seeking action) properties. Mesolimbic dopamine neurons' responses to sensory cues correlate with both expected value and reward-seeking action. This has led to the proposal that phasic dopamine responses may be sufficient to inform value-based decisions, elicit actions, and/or induce motivational states; however, causal tests are incomplete. Here, we show that direct dopamine neuron stimulation, both calibrated to physiological and greater intensities, at the time of reward can be sufficient to induce and maintain reward seeking (reinforcing) although replacement of a cue with stimulation is insufficient to induce reward seeking or act as an informative cue. Stimulation of descending cortical inputs, one synapse upstream, are sufficient for reinforcement and cues to future reward. Thus, physiological activation of mesolimbic dopamine neurons can be sufficient for reinforcing properties of reward without being sufficient for the predictive and incentive properties of cues.

The mammalian hippocampus, comprised of serially connected subfields, participates in diverse behavioral and cognitive functions. It has been postulated that parallel circuitry embedded within hippocampal subfields may underlie such functional diversity. We sought to identify, delineate, and manipulate this putatively parallel architecture in the dorsal subiculum, the primary output subfield of the dorsal hippocampus. Population and single-cell RNA-seq revealed that the subiculum can be divided into two spatially adjacent subregions associated with prominent differences in pyramidal cell gene expression. Pyramidal cells occupying these two regions differed in their long-range inputs, local wiring, projection targets, and electrophysiological properties. Leveraging gene-expression differences across these regions, we use genetically restricted neuronal silencing to show that these regions differentially contribute to spatial working memory. This work provides a coherent molecular-, cellular-, circuit-, and behavioral-level demonstration that the hippocampus embeds structurally and functionally dissociable streams within its serial architecture.

Mouse visual cortex is subdivided into multiple distinct, hierarchically organized areas that are interconnected through feedforward (FF) and feedback (FB) pathways. The principal synaptic targets of FF and FB axons that reciprocally interconnect primary visual cortex (V1) with the higher lateromedial extrastriate area (LM) are pyramidal cells (Pyr) and parvalbumin (PV)-expressing GABAergic interneurons. Recordings in slices of mouse visual cortex have shown that layer 2/3 Pyr cells receive excitatory monosynaptic FF and FB inputs, which are opposed by disynaptic inhibition. Most notably, inhibition is stronger in the FF than FB pathway, suggesting pathway-specific organization of feedforward inhibition (FFI). To explore the hypothesis that this difference is due to diverse pathway-specific strengths of the inputs to PV neurons we have performed subcellular Channelrhodopsin-2-assisted circuit mapping in slices of mouse visual cortex. Whole-cell patch-clamp recordings were obtained from retrobead-labeled FFV1→LM- and FBLM→V1-projecting Pyr cells, as well as from tdTomato-expressing PV neurons. The results show that the FFV1→LM pathway provides on average 3.7-fold stronger depolarizing input to layer 2/3 inhibitory PV neurons than to neighboring excitatory Pyr cells. In the FBLM→V1 pathway, depolarizing inputs to layer 2/3 PV neurons and Pyr cells were balanced. Balanced inputs were also found in the FFV1→LM pathway to layer 5 PV neurons and Pyr cells, whereas FBLM→V1 inputs to layer 5 were biased toward Pyr cells. The findings indicate that FFI in FFV1→LM and FBLM→V1 circuits are organized in a pathway- and lamina-specific fashion.

The superficial layers of the superior colliculus (sSC) receive retinal input and project to thalamic regions - the dorsal lateral geniculate (dLGN) and lateral posterior (LP; or pulvinar) nuclei -that convey visual information to cortex. A critical step towards understanding the functional impact of sSC neurons on these parallel thalamo-cortical pathways is determining whether different classes of sSC neurons, which are known to respond to different features of visual stimuli, innervate overlapping or distinct thalamic targets. Here, we identified a transgenic mouse line that labels sSC neurons that project to dLGN but not LP. We utilized selective expression of fluorophores and channelrhodopsin in this and previously characterized mouse lines to demonstrate that distinct cell types give rise to sSC projections to dLGN and LP. We further show that the glutamatergic sSC cell type that projects to dLGN also provides input to the sSC cell type that projects to LP. These results clarify the cellular origin of parallel sSC-thalamo-cortical pathways and reveal an interaction between these pathways via local connections within the sSC.

Activity in the motor cortex predicts movements, seconds before they are initiated. This preparatory activity has been observed across cortical layers, including in descending pyramidal tract neurons in layer 5. A key question is how preparatory activity is maintained without causing movement, and is ultimately converted to a motor command to trigger appropriate movements. Here, using single-cell transcriptional profiling and axonal reconstructions, we identify two types of pyramidal tract neuron. Both types project to several targets in the basal ganglia and brainstem. One type projects to thalamic regions that connect back to motor cortex; populations of these neurons produced early preparatory activity that persisted until the movement was initiated. The second type projects to motor centres in the medulla and mainly produced late preparatory activity and motor commands. These results indicate that two types of motor cortex output neurons have specialized roles in motor control.