An agglomerative clustering algorithm merges the most similar pair of clusters at every iteration. The function that evaluates similarity is traditionally hand- designed, but there has been recent interest in supervised or semisupervised settings in which ground-truth clustered data is available for training. Here we show how to train a similarity function by regarding it as the action-value function of a reinforcement learning problem. We apply this general method to segment images by clustering superpixels, an application that we call Learning to Agglomerate Superpixel Hierarchies (LASH). When applied to a challenging dataset of brain images from serial electron microscopy, LASH dramatically improved segmentation accuracy when clustering supervoxels generated by state of the boundary detection algorithms. The naive strategy of directly training only supervoxel similarities and applying single linkage clustering produced less improvement.

An agglomerative clustering algorithm merges the most similar pair of clusters at every iteration. The function that evaluates similarity is traditionally handdesigned, but there has been recent interest in supervised or semisupervised settings in which ground-truth clustered data is available for training. Here we show how to train a similarity function by regarding it as the action-value function of a reinforcement learning problem. We apply this general method to segment images by clustering superpixels, an application that we call Learning to Agglomerate Superpixel Hierarchies (LASH). When applied to a challenging dataset of brain images from serial electron microscopy, LASH dramatically improved segmentation accuracy when clustering supervoxels generated by state of the boundary detection algorithms. The naive strategy of directly training only supervoxel similarities and applying single linkage clustering produced less improvement.

Manifold attractors are a key framework for understanding how continuous variables, such as position or head direction, are encoded in the brain. In this framework, the variable is represented along a continuum of persistent neuronal states which forms a manifold attactor. Neural networks with symmetric synaptic connectivity that can implement manifold attractors have become the dominant model in this framework. In addition to a symmetric connectome, these networks imply homogeneity of individual-neuron tuning curves and symmetry of the representational space; these features are largely inconsistent with neurobiological data. Here, we developed a theory for computations based on manifold attractors in trained neural networks and show how these manifolds can cope with diverse neuronal responses, imperfections in the geometry of the manifold and a high level of synaptic heterogeneity. In such heterogeneous trained networks, a continuous representational space emerges from a small set of stimuli used for training. Furthermore, we find that the network response to external inputs depends on the geometry of the representation and on the level of synaptic heterogeneity in an analytically tractable and interpretable way. Finally, we show that a too complex geometry of the neuronal representation impairs the attractiveness of the manifold and may lead to its destabilization. Our framework reveals that continuous features can be represented in the recurrent dynamics of heterogeneous networks without assuming unrealistic symmetry. It suggests that the representational space of putative manifold attractors in the brain dictates the dynamics in their vicinity.

We present a dynamic nonlinear generative model for visual motion based on a latent representation of binary-gated Gaussian variables. Trained on sequences of images, the model learns to represent different movement directions in different variables. We use an online approximate-inference scheme that can be mapped to the dynamics of networks of neurons. Probed with drifting grating stimuli and moving bars of light, neurons in the model show patterns of responses analogous to those of direction-selective simple cells in primary visual cortex. Most model neurons also show speed tuning and respond equally well to a range of motion directions and speeds aligned to the constraint line of their respective preferred speed. We show how these computations are enabled by a specific pattern of recurrent connections learned by the model.

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.

Cortical neurons form specific circuits, but the functional structure of this microarchitecture and its relation to behaviour are poorly understood. Two-photon calcium imaging can monitor activity of spatially defined neuronal ensembles in the mammalian cortex. Here we applied this technique to the motor cortex of mice performing a choice behaviour. Head-fixed mice were trained to lick in response to one of two odours, and to withhold licking for the other odour. Mice routinely showed significant learning within the first behavioural session and across sessions. Microstimulation and trans-synaptic tracing identified two non-overlapping candidate tongue motor cortical areas. Inactivating either area impaired voluntary licking. Imaging in layer 2/3 showed neurons with diverse response types in both areas. Activity in approximately half of the imaged neurons distinguished trial types associated with different actions. Many neurons showed modulation coinciding with or preceding the action, consistent with their involvement in motor control. Neurons with different response types were spatially intermingled. Nearby neurons (within approximately 150 mum) showed pronounced coincident activity. These temporal correlations increased with learning within and across behavioural sessions, specifically for neuron pairs with similar response types. We propose that correlated activity in specific ensembles of functionally related neurons is a signature of learning-related circuit plasticity. Our findings reveal a fine-scale and dynamic organization of the frontal cortex that probably underlies flexible behaviour.

Olfactory memories can be very good-your mother's baking-or very bad-your father's cooking. We go through life forming these different associations with the smells we encounter. But what makes one association pleasant and another repulsive? Work in deep areas of the Drosophila brain has revealed the beginnings of an answer, as reported in this issue of Neuron by Owald et al. (2015).

Two simple models, vaulting over stiff legs and rebounding over compliant legs, are employed to describe the mechanics of legged locomotion. It is agreed that compliant legs are necessary for describing running and that legs are compliant while walking. Despite this agreement, stiff legs continue to be employed to model walking. Here, we show that leg compliance is necessary to model walking and, in the process, identify the principles that underpin two important features of legged locomotion: First, at the same speed, step length, and stance duration, multiple gaits that differ in the number of leg contraction cycles are possible. Among them, humans and other animals choose a gait with M-shaped vertical ground reaction forces because it is energetically favored. Second, the transition from walking to running occurs because of the inability to redirect the vertical component of the velocity during the double stance phase. Additionally, we also examine the limits of double spring-loaded pendulum (DSLIP) as a quantitative model for locomotion, and conclude that DSLIP is limited as a model for walking. However, insights gleaned from the analytical treatment of DSLIP are general and will inform the construction of more accurate models of walking.

Leptin is an adipose tissue hormone that maintains homeostatic control of adipose tissue mass by regulating the activity of specific neural populations controlling appetite and metabolism1. Leptin regulates food intake by inhibiting orexigenic agouti-related protein (AGRP) neurons and activating anorexigenic pro-opiomelanocortin (POMC) neurons2. However, while AGRP neurons regulate food intake on a rapid time scale, acute activation of POMC neurons has only a minimal effect3–5. This has raised the possibility that there is a heretofore unidentified leptin-regulated neural population that suppresses appetite on a rapid time scale. Here, we report the discovery of a novel population of leptin-target neurons expressing basonuclin 2 (Bnc2) that acutely suppress appetite by directly inhibiting AGRP neurons. Opposite to the effect of AGRP activation, BNC2 neuronal activation elicited a place preference indicative of positive valence in hungry but not fed mice. The activity of BNC2 neurons is finely tuned by leptin, sensory food cues, and nutritional status. Finally, deleting leptin receptors in BNC2 neurons caused marked hyperphagia and obesity, similar to that observed in a leptin receptor knockout in AGRP neurons. These data indicate that BNC2-expressing neurons are a key component of the neural circuit that maintains energy balance, thus filling an important gap in our understanding of the regulation of food intake and leptin action.

Obesity is associated with increased blood pressure (BP), which in turn increases the risk of cardiovascular diseases. We found that the increase in leptin levels seen in diet-induced obesity (DIO) drives an increase in BP in rodents, an effect that was not seen in animals deficient in leptin or leptin receptors (LepR). Furthermore, humans with loss-of-function mutations in leptin and the LepR have low BP despite severe obesity. Leptin's effects on BP are mediated by neuronal circuits in the dorsomedial hypothalamus (DMH), as blocking leptin with a specific antibody, antagonist, or inhibition of the activity of LepR-expressing neurons in the DMH caused a rapid reduction of BP in DIO mice, independent of changes in weight. Re-expression of LepRs in the DMH of DIO LepR-deficient mice caused an increase in BP. These studies demonstrate that leptin couples changes in weight to changes in BP in mammalian species.