Sparseness and Expansion in Sensory Representations

Random compressed coding with neurons

Classical models of efficient coding in neurons assume simple mean responses-"tuning curves"- such as bell-shaped or monotonic functions of a stimulus feature. Real neurons, however, can be more complex: grid cells, for example, exhibit periodic responses that impart the neural population code with high accuracy. But do highly accurate codes require fine-tuning of the response properties? We address this question with the use of a simple model: a population of neurons with random, spatially extended, and irregular tuning curves. Irregularity enhances the local resolution of the code but gives rise to catastrophic, global errors. For optimal smoothness of the tuning curves, when local and global errors balance out, the neural population compresses information about a continuous stimulus into a low-dimensional representation, and the resulting distributed code achieves exponential accuracy. An analysis of recordings from monkey motor cortex points to such "compressed efficient coding." Efficient codes do not require a finely tuned design-they emerge robustly from irregularity or randomness.

Computational functions of precisely balanced neuronal microcircuits in an olfactory memory network

Models of balanced autoassociative memory networks predict that specific inhibition is critical to store information in connectivity. To explore these predictions, we characterized and manipulated different subtypes of fast-spiking interneurons in the posterior telencephalic area Dp (pDp) of adult zebrafish, the homolog of the piriform cortex. Modeling of recurrent networks with assemblies showed that a precise balance of excitation and inhibition is important to prevent not only excessive firing rates ("runaway activity") but also the stochastic occurrence of high pattern correlations ("runaway correlations"). Consistent with model predictions, runaway correlations emerged in pDp when synaptic balance was perturbed by optogenetic manipulations of feedback inhibition but not feedforward inhibition. Runaway correlations were driven by sparse subsets of strongly active neurons rather than by a general broadening of tuning curves. These results are consistent with balanced neuronal assemblies in pDp and reveal novel computational functions of inhibitory microcircuits in an autoassociative network.

Visual experience orthogonalizes visual cortical stimulus responses via population code transformation

Sensory and behavioral experience can alter visual cortical stimulus coding, but the precise form of this plasticity is unclear. We measured orientation tuning in 4,000-neuron populations of mouse V1 before and after training on a visuomotor task. Changes to single-cell tuning curves appeared complex, including development of asymmetries and of multiple peaks. Nevertheless, these complex tuning curve transformations can be explained by a simple equation: a convex transformation suppressing responses to task stimuli specifically in cells responding at intermediate levels. The strength of the transformation varies across trials, suggesting a dynamic circuit mechanism rather than static synaptic plasticity. The transformation results in sparsening and orthogonalization of population codes for task stimuli. It cannot improve the performance of an optimal stimulus decoder, which is already perfect even for naive codes, but it improves the performance of a suboptimal decoder model with inductive bias as might be found in downstream readout circuits.

A biological model of nonlinear dimensionality reduction

Obtaining appropriate low-dimensional representations from high-dimensional sensory inputs in an unsupervised manner is essential for straightforward downstream processing. Although nonlinear dimensionality reduction methods such as t-distributed stochastic neighbor embedding (t-SNE) have been developed, their implementation in simple biological circuits remains unclear. Here, we develop a biologically plausible dimensionality reduction algorithm compatible with t-SNE, which uses a simple three-layer feedforward network mimicking the Drosophila olfactory circuit. The proposed learning rule, described as three-factor Hebbian plasticity, is effective for datasets such as entangled rings and MNIST, comparable to t-SNE. We further show that the algorithm could be working in olfactory circuits in Drosophila by analyzing the multiple experimental data in previous studies. We lastly suggest that the algorithm is also beneficial for association learning between inputs and rewards, allowing the generalization of these associations to other inputs not yet associated with rewards.

Touch-evoked traveling waves establish a translaminar spacetime code

Linking sensory-evoked traveling waves to underlying circuit patterns is critical to understanding the neural basis of sensory perception. To form this link, we performed simultaneous electrophysiology and two-photon calcium imaging through transparent NeuroGrids and mapped touch-evoked traveling waves and underlying microcircuit dynamics. In awake mice, both passive and active whisker touch elicited traveling waves within and across barrels, with a fast early component followed by a late wave that lasted hundreds of milliseconds poststimulus. Notably, late waves were modulated by perceived value and predicted behavioral choice in a two-whisker discrimination task. We found that the late wave feature was (i) modulated by motor feedback, (ii) differentially engaged a sparse ensemble reactivation pattern across layer 2/3, which a balanced-state network model reconciled via feedback-induced inhibitory stabilization, and (iii) aligned to regenerative layer 5 apical dendritic Ca2+ events. Our results reveal that translaminar spacetime patterns organized by cortical feedback support sparse touch-evoked traveling waves.

Cellular and synaptic organization of the Octopus vertical lobe

Understanding memory formation and its influence on behavior is a central challenge in neuroscience. Associative learning networks, including the mushroom body in insects, the cerebellum in mammals, and the vertical lobe (VL) in cephalopods, typically exhibit a 3-layered architecture, characterized by divergence (fan-out) followed by convergence (fan-in), facilitating sparse sensory coding (Babadi and Sompolinsky, 2014; Lin et al., 2014; Litwin-Kumar et al., 2017; Turchetti-Maia et al., 2017). Previously, using volumetric electron microscopy, we showed that the VL uniquely comprises 22 million simple amacrine (SAM) interneurons, each receiving a singular input subject to activity-dependent long-term potentiation, contrasting with typical middle-layer interneurons (Bidel, Meirovitch et al., 2023). We also demonstrated that these SAMs provide excitatory feedforward input to the output cell layer, balanced by approximately 400,000 inhibitory complex amacrines (CAM), which are morphologically diverse and integrate numerous inputs (Bidel, Meirovitch et al., 2023). Here, we leverage the same digital tissue to explore the CAMs' morphological diversity, identifying correlations between structure, postsynaptic site density, and synaptic input proportions, which led to the classification of CAMs into distinct groups. Further analysis of the input layer in the VL revealed a meticulous structural and synaptic compartmentalization, with distinct synaptic bouton types forming three zones that integrate different inputs towards CAMs. Additionally, we identify the potential presence of a neurogenic niche in the VL, hinting at parallels with neurogenic processes in other species and warranting further investigation, particularly in the context of learning and memory. This study deepens our understanding of the VL's cellular and synaptic architecture, revealing both shared and unique features compared to other associative networks, and highlighting the intricate interplay of structural and functional elements in memory formation.

Fast updating feedback from piriform cortex to the olfactory bulb relays multimodal identity and reward contingency signals during rule-reversal

While animals readily adjust their behavior to adapt to relevant changes in the environment, the neural pathways enabling these changes remain largely unknown. Here, using multiphoton imaging, we investigate whether feedback from the piriform cortex to the olfactory bulb supports such behavioral flexibility. To this end, we engage head-fixed male mice in a multimodal rule-reversal task guided by olfactory and auditory cues. Both odor and, surprisingly, the sound cues trigger responses in the cortical bulbar feedback axons which precede the behavioral report. Responses to the same sensory cue are strongly modulated upon changes in stimulus-reward contingency (rule-reversals). The re-shaping of individual bouton responses occurs within seconds of the rule-reversal events and is correlated with changes in behavior. Optogenetic perturbation of cortical feedback within the bulb disrupts the behavioral performance. Our results indicate that the piriform-to-olfactory bulb feedback axons carry stimulus identity and reward contingency signals which are rapidly re-formatted according to changes in the behavioral context.

Geometry and dynamics of representations in a precisely balanced memory network related to olfactory cortex

Biological memory networks are thought to store information by experience-dependent changes in the synaptic connectivity between assemblies of neurons. Recent models suggest that these assemblies contain both excitatory and inhibitory neurons (E/I assemblies), resulting in co-tuning and precise balance of excitation and inhibition. To understand computational consequences of E/I assemblies under biologically realistic constraints we built a spiking network model based on experimental data from telencephalic area Dp of adult zebrafish, a precisely balanced recurrent network homologous to piriform cortex. We found that E/I assemblies stabilized firing rate distributions compared to networks with excitatory assemblies and global inhibition. Unlike classical memory models, networks with E/I assemblies did not show discrete attractor dynamics. Rather, responses to learned inputs were locally constrained onto manifolds that 'focused' activity into neuronal subspaces. The covariance structure of these manifolds supported pattern classification when information was retrieved from selected neuronal subsets. Networks with E/I assemblies therefore transformed the geometry of neuronal coding space, resulting in continuous representations that reflected both relatedness of inputs and an individual's experience. Such continuous representations enable fast pattern classification, can support continual learning, and may provide a basis for higher-order learning and cognitive computations.

Cerebellar-driven cortical dynamics can enable task acquisition, switching and consolidation

The brain must maintain a stable world model while rapidly adapting to the environment, but the underlying mechanisms are not known. Here, we posit that cortico-cerebellar loops play a key role in this process. We introduce a computational model of cerebellar networks that learn to drive cortical networks with task-outcome predictions. First, using sensorimotor tasks, we show that cerebellar feedback in the presence of stable cortical networks is sufficient for rapid task acquisition and switching. Next, we demonstrate that, when trained in working memory tasks, the cerebellum can also underlie the maintenance of cognitive-specific dynamics in the cortex, explaining a range of optogenetic and behavioural observations. Finally, using our model, we introduce a systems consolidation theory in which task information is gradually transferred from the cerebellum to the cortex. In summary, our findings suggest that cortico-cerebellar loops are an important component of task acquisition, switching, and consolidation in the brain.

Semi-orthogonal subspaces for value mediate a binding and generalization trade-off

When choosing between options, we must associate their values with the actions needed to select them. We hypothesize that the brain solves this binding problem through neural population subspaces. Here, in macaques performing a choice task, we show that neural populations in five reward-sensitive regions encode the values of offers presented on the left and right in distinct subspaces. This encoding is sufficient to bind offer values to their locations while preserving abstract value information. After offer presentation, all areas encode the value of the first and second offers in orthogonal subspaces; this orthogonalization also affords binding. Our binding-by-subspace hypothesis makes two new predictions confirmed by the data. First, behavioral errors should correlate with spatial, but not temporal, neural misbinding. Second, behavioral errors should increase when offers have low or high values, compared to medium values, even when controlling for value difference. Together, these results support the idea that the brain uses semi-orthogonal subspaces to bind features.

Bilateral Alignment of Receptive Fields in the Olfactory Cortex

Each olfactory cortical hemisphere receives ipsilateral odor information directly from the olfactory bulb and contralateral information indirectly from the other cortical hemisphere. Since neural projections to the olfactory cortex (OC) are disordered and nontopographic, spatial information cannot be used to align projections from the two sides like in the visual cortex. Therefore, how bilateral information is integrated in individual cortical neurons is unknown. We have found, in mice, that the odor responses of individual neurons to selective stimulation of each of the two nostrils are significantly correlated, such that odor identity decoding optimized with information arriving from one nostril transfers very well to the other side. Nevertheless, these aligned responses are asymmetric enough to allow decoding of stimulus laterality. Computational analysis shows that such matched odor tuning is incompatible with purely random connections but is explained readily by Hebbian plasticity structuring bilateral connectivity. Our data reveal that despite the distributed and fragmented sensory representation in the OC, odor information across the two hemispheres is highly coordinated.

The representational geometry for naturalistic textures in macaque V1 and V2

Our understanding of visual cortical processing has relied primarily on studying the selectivity of individual neurons in different areas. A complementary approach is to study how the representational geometry of neuronal populations differs across areas. Though the geometry is derived from individual neuronal selectivity, it can reveal encoding strategies difficult to infer from single neuron responses. In addition, recent theoretical work has begun to relate distinct functional objectives to different representational geometries. To understand how the representational geometry changes across stages of processing, we measured neuronal population responses in primary visual cortex (V1) and area V2 of macaque monkeys to an ensemble of synthetic, naturalistic textures. Responses were lower dimensional in V2 than V1, and there was a better alignment of V2 population responses to different textures. The representational geometry in V2 afforded better discriminability between out-of-sample textures. We performed complementary analyses of standard convolutional network models, which did not replicate the representational geometry of cortex. We conclude that there is a shift in the representational geometry between V1 and V2, with the V2 representation exhibiting features of a low-dimensional, systematic encoding of different textures and of different instantiations of each texture. Our results suggest that comparisons of representational geometry can reveal important transformations that occur across successive stages of visual processing.

Barcode activity in a recurrent network model of the hippocampus enables efficient memory binding

Forming an episodic memory requires binding together disparate elements that co-occur in a single experience. One model of this process is that neurons representing different components of a memory bind to an "index" - a subset of neurons unique to that memory. Evidence for this model has recently been found in chickadees, which use hippocampal memory to store and recall locations of cached food. Chickadee hippocampus produces sparse, high-dimensional patterns ("barcodes") that uniquely specify each caching event. Unexpectedly, the same neurons that participate in barcodes also exhibit conventional place tuning. It is unknown how barcode activity is generated, and what role it plays in memory formation and retrieval. It is also unclear how a memory index (e.g. barcodes) could function in the same neural population that represents memory content (e.g. place). Here, we design a biologically plausible model that generates barcodes and uses them to bind experiential content. Our model generates barcodes from place inputs through the chaotic dynamics of a recurrent neural network and uses Hebbian plasticity to store barcodes as attractor states. The model matches experimental observations that memory indices (barcodes) and content signals (place tuning) are randomly intermixed in the activity of single neurons. We demonstrate that barcodes reduce memory interference between correlated experiences. We also show that place tuning plays a complementary role to barcodes, enabling flexible, contextually-appropriate memory retrieval. Finally, our model is compatible with previous models of the hippocampus as generating a predictive map. Distinct predictive and indexing functions of the network are achieved via an adjustment of global recurrent gain. Our results suggest how the hippocampus may use barcodes to resolve fundamental tensions between memory specificity (pattern separation) and flexible recall (pattern completion) in general memory systems.

A cerebellar granule cell-climbing fiber computation to learn to track long time intervals

In classical cerebellar learning, Purkinje cells (PkCs) associate climbing fiber (CF) error signals with predictive granule cells (GrCs) that were active just prior (∼150 ms). The cerebellum also contributes to behaviors characterized by longer timescales. To investigate how GrC-CF-PkC circuits might learn seconds-long predictions, we imaged simultaneous GrC-CF activity over days of forelimb operant conditioning for delayed water reward. As mice learned reward timing, numerous GrCs developed anticipatory activity ramping at different rates until reward delivery, followed by widespread time-locked CF spiking. Relearning longer delays further lengthened GrC activations. We computed CF-dependent GrC→PkC plasticity rules, demonstrating that reward-evoked CF spikes sufficed to grade many GrC synapses by anticipatory timing. We predicted and confirmed that PkCs could thereby continuously ramp across seconds-long intervals from movement to reward. Learning thus leads to new GrC temporal bases linking predictors to remote CF reward signals-a strategy well suited for learning to track the long intervals common in cognitive domains.

Selective consolidation of learning and memory via recall-gated plasticity

In a variety of species and behavioral contexts, learning and memory formation recruits two neural systems, with initial plasticity in one system being consolidated into the other over time. Moreover, consolidation is known to be selective; that is, some experiences are more likely to be consolidated into long-term memory than others. Here, we propose and analyze a model that captures common computational principles underlying such phenomena. The key component of this model is a mechanism by which a long-term learning and memory system prioritizes the storage of synaptic changes that are consistent with prior updates to the short-term system. This mechanism, which we refer to as recall-gated consolidation, has the effect of shielding long-term memory from spurious synaptic changes, enabling it to focus on reliable signals in the environment. We describe neural circuit implementations of this model for different types of learning problems, including supervised learning, reinforcement learning, and autoassociative memory storage. These implementations involve synaptic plasticity rules modulated by factors such as prediction accuracy, decision confidence, or familiarity. We then develop an analytical theory of the learning and memory performance of the model, in comparison to alternatives relying only on synapse-local consolidation mechanisms. We find that recall-gated consolidation provides significant advantages, substantially amplifying the signal-to-noise ratio with which memories can be stored in noisy environments. We show that recall-gated consolidation gives rise to a number of phenomena that are present in behavioral learning paradigms, including spaced learning effects, task-dependent rates of consolidation, and differing neural representations in short- and long-term pathways.

Common principles for odour coding across vertebrates and invertebrates

The olfactory system is an ideal and tractable system for exploring how the brain transforms sensory inputs into behaviour. The basic tasks of any olfactory system include odour detection, discrimination and categorization. The challenge for the olfactory system is to transform the high-dimensional space of olfactory stimuli into the much smaller space of perceived objects and valence that endows odours with meaning. Our current understanding of how neural circuits address this challenge has come primarily from observations of the mechanisms of the brain for processing other sensory modalities, such as vision and hearing, in which optimized deep hierarchical circuits are used to extract sensory features that vary along continuous physical dimensions. The olfactory system, by contrast, contends with an ill-defined, high-dimensional stimulus space and discrete stimuli using a circuit architecture that is shallow and parallelized. Here, we present recent observations in vertebrate and invertebrate systems that relate the statistical structure and state-dependent modulation of olfactory codes to mechanisms of perception and odour-guided behaviour.

Computational role of structure in neural activity and connectivity

One major challenge of neuroscience is identifying structure in seemingly disorganized neural activity. Different types of structure have different computational implications that can help neuroscientists understand the functional role of a particular brain area. Here, we outline a unified approach to characterize structure by inspecting the representational geometry and the modularity properties of the recorded activity and show that a similar approach can also reveal structure in connectivity. We start by setting up a general framework for determining geometry and modularity in activity and connectivity and relating these properties with computations performed by the network. We then use this framework to review the types of structure found in recent studies of model networks performing three classes of computations.

Peripheral preprocessing in Drosophila facilitates odor classification

The mammalian brain implements sophisticated sensory processing algorithms along multilayered ("deep") neural networks. Strategies that insects use to meet similar computational demands, while relying on smaller nervous systems with shallow architectures, remain elusive. Using Drosophila as a model, we uncover the algorithmic role of odor preprocessing by a shallow network of compartmentalized olfactory receptor neurons. Each compartment operates as a ratiometric unit for specific odor-mixtures. This computation arises from a simple mechanism: electrical coupling between two differently sized neurons. We demonstrate that downstream synaptic connectivity is shaped to optimally leverage amplification of a hedonic value signal in the periphery. Furthermore, peripheral preprocessing is shown to markedly improve novel odor classification in a higher brain center. Together, our work highlights a far-reaching functional role of the sensory periphery for downstream processing. By elucidating the implementation of powerful computations by a shallow network, we provide insights into general principles of efficient sensory processing algorithms.

A Translaminar Spacetime Code Supports Touch-Evoked Traveling Waves

Linking sensory-evoked traveling waves to underlying circuit patterns is critical to understanding the neural basis of sensory perception. To form this link, we performed simultaneous electrophysiology and two-photon calcium imaging through transparent NeuroGrids and mapped touch-evoked cortical traveling waves and their underlying microcircuit dynamics. In awake mice, both passive and active whisker touch elicited traveling waves within and across barrels, with a fast early component followed by a variable late wave that lasted hundreds of milliseconds post-stimulus. Strikingly, late-wave dynamics were modulated by stimulus value and correlated with task performance. Mechanistically, the late wave component was i) modulated by motor feedback, ii) complemented by a sparse ensemble pattern across layer 2/3, which a balanced-state network model reconciled via inhibitory stabilization, and iii) aligned to regenerative Layer-5 apical dendritic Ca 2+ events. Our results reveal a translaminar spacetime pattern organized by cortical feedback in the sensory cortex that supports touch-evoked traveling waves.

GRAPHICAL ABSTRACT AND HIGHLIGHTS

Whisker touch evokes both early- and late-traveling waves in the barrel cortex over 100's of millisecondsReward reinforcement modulates wave dynamics Late wave emergence coincides with network sparsity in L23 and time-locked L5 dendritic Ca 2+ spikes Experimental and computational results link motor feedback to distinct translaminar spacetime patterns.

Sensory encoding and memory in the mushroom body: signals, noise, and variability

To survive in changing environments, animals need to learn to associate specific sensory stimuli with positive or negative valence. How do they form stimulus-specific memories to distinguish between positively/negatively associated stimuli and other irrelevant stimuli? Solving this task is one of the functions of the mushroom body, the associative memory center in insect brains. Here we summarize recent work on sensory encoding and memory in the Drosophila mushroom body, highlighting general principles such as pattern separation, sparse coding, noise and variability, coincidence detection, and spatially localized neuromodulation, and placing the mushroom body in comparative perspective with mammalian memory systems.

Specific connectivity optimizes learning in thalamocortical loops

Thalamocortical loops have a central role in cognition and motor control, but precisely how they contribute to these processes is unclear. Recent studies showing evidence of plasticity in thalamocortical synapses indicate a role for the thalamus in shaping cortical dynamics through learning. Since signals undergo a compression from the cortex to the thalamus, we hypothesized that the computational role of the thalamus depends critically on the structure of corticothalamic connectivity. To test this, we identified the optimal corticothalamic structure that promotes biologically plausible learning in thalamocortical synapses. We found that corticothalamic projections specialized to communicate an efference copy of the cortical output benefit motor control, while communicating the modes of highest variance is optimal for working memory tasks. We analyzed neural recordings from mice performing grasping and delayed discrimination tasks and found corticothalamic communication consistent with these predictions. These results suggest that the thalamus orchestrates cortical dynamics in a functionally precise manner through structured connectivity.

Distinct information conveyed to the olfactory bulb by feedforward input from the nose and feedback from the cortex

Sensory systems are organized hierarchically, but feedback projections frequently disrupt this order. In the olfactory bulb (OB), cortical feedback projections numerically match sensory inputs. To unravel information carried by these two streams, we imaged the activity of olfactory sensory neurons (OSNs) and cortical axons in the mouse OB using calcium indicators, multiphoton microscopy, and diverse olfactory stimuli. Here, we show that odorant mixtures of increasing complexity evoke progressively denser OSN activity, yet cortical feedback activity is of similar sparsity for all stimuli. Also, representations of complex mixtures are similar in OSNs but are decorrelated in cortical axons. While OSN responses to increasing odorant concentrations exhibit a sigmoidal relationship, cortical axonal responses are complex and nonmonotonic, which can be explained by a model with activity-dependent feedback inhibition in the cortex. Our study indicates that early-stage olfactory circuits have access to local feedforward signals and global, efficiently formatted information about odor scenes through cortical feedback.

Representational maps in the brain: concepts, approaches, and applications

Neural systems have evolved to process sensory stimuli in a way that allows for efficient and adaptive behavior in a complex environment. Recent technological advances enable us to investigate sensory processing in animal models by simultaneously recording the activity of large populations of neurons with single-cell resolution, yielding high-dimensional datasets. In this review, we discuss concepts and approaches for assessing the population-level representation of sensory stimuli in the form of a representational map. In such a map, not only are the identities of stimuli distinctly represented, but their relational similarity is also mapped onto the space of neuronal activity. We highlight example studies in which the structure of representational maps in the brain are estimated from recordings in humans as well as animals and compare their methodological approaches. Finally, we integrate these aspects and provide an outlook for how the concept of representational maps could be applied to various fields in basic and clinical neuroscience.

Cortical field maps across human sensory cortex

Cortical processing pathways for sensory information in the mammalian brain tend to be organized into topographical representations that encode various fundamental sensory dimensions. Numerous laboratories have now shown how these representations are organized into numerous cortical field maps (CMFs) across visual and auditory cortex, with each CFM supporting a specialized computation or set of computations that underlie the associated perceptual behaviors. An individual CFM is defined by two orthogonal topographical gradients that reflect two essential aspects of feature space for that sense. Multiple adjacent CFMs are then organized across visual and auditory cortex into macrostructural patterns termed cloverleaf clusters. CFMs within cloverleaf clusters are thought to share properties such as receptive field distribution, cortical magnification, and processing specialization. Recent measurements point to the likely existence of CFMs in the other senses, as well, with topographical representations of at least one sensory dimension demonstrated in somatosensory, gustatory, and possibly olfactory cortical pathways. Here we discuss the evidence for CFM and cloverleaf cluster organization across human sensory cortex as well as approaches used to identify such organizational patterns. Knowledge of how these topographical representations are organized across cortex provides us with insight into how our conscious perceptions are created from our basic sensory inputs. In addition, studying how these representations change during development, trauma, and disease serves as an important tool for developing improvements in clinical therapies and rehabilitation for sensory deficits.

Simple and complex cells revisited: toward a selectivity-invariance model of object recognition

This paper presents a theoretical perspective on modeling ventral stream processing by revisiting the computational abstraction of simple and complex cells. In parallel to David Marr's vision theory, we organize the new perspective into three levels. At the computational level, we abstract simple and complex cells into space partitioning and composition in a topological space based on the redundancy exploitation hypothesis of Horace Barlow. At the algorithmic level, we present a hierarchical extension of sparse coding by exploiting the manifold constraint in high-dimensional space (i.e., the blessing of dimensionality). The resulting over-parameterized models for object recognition differ from existing hierarchical models by disentangling the objectives of selectivity and invariance computation. It is possible to interpret our hierarchical construction as a computational implementation of cortically local subspace untangling for object recognition and face representation, which are closely related to exemplar-based and axis-based coding in the medial temporal lobe. At the implementation level, we briefly discuss two possible implementations based on asymmetric sparse autoencoders and divergent spiking neural networks.

Reducing Catastrophic Forgetting With Associative Learning: A Lesson From Fruit Flies

Catastrophic forgetting remains an outstanding challenge in continual learning. Recently, methods inspired by the brain, such as continual representation learning and memory replay, have been used to combat catastrophic forgetting. Associative learning (retaining associations between inputs and outputs, even after good representations are learned) plays an important function in the brain; however, its role in continual learning has not been carefully studied. Here, we identified a two-layer neural circuit in the fruit fly olfactory system that performs continual associative learning between odors and their associated valences. In the first layer, inputs (odors) are encoded using sparse, high-dimensional representations, which reduces memory interference by activating nonoverlapping populations of neurons for different odors. In the second layer, only the synapses between odor-activated neurons and the odor's associated output neuron are modified during learning; the rest of the weights are frozen to prevent unrelated memories from being overwritten. We prove theoretically that these two perceptron-like layers help reduce catastrophic forgetting compared to the original perceptron algorithm, under continual learning. We then show empirically on benchmark data sets that this simple and lightweight architecture outperforms other popular neural-inspired algorithms when also using a two-layer feedforward architecture. Overall, fruit flies evolved an efficient continual associative learning algorithm, and circuit mechanisms from neuroscience can be translated to improve machine computation.

Recent data on the cerebellum require new models and theories

The cerebellum has been a popular topic for theoretical studies because its structure was thought to be simple. Since David Marr and James Albus related its function to motor skill learning and proposed the Marr-Albus cerebellar learning model, this theory has guided and inspired cerebellar research. In this review, we summarize the theoretical progress that has been made within this framework of error-based supervised learning. We discuss the experimental progress that demonstrates more complicated molecular and cellular mechanisms in the cerebellum as well as new cell types and recurrent connections. We also cover its involvement in diverse non-motor functions and evidence of other forms of learning. Finally, we highlight the need to explain these new experimental findings into an integrated cerebellar model that can unify its diverse computational functions.

Dimension of Activity in Random Neural Networks

Neural networks are high-dimensional nonlinear dynamical systems that process information through the coordinated activity of many connected units. Understanding how biological and machine-learning networks function and learn requires knowledge of the structure of this coordinated activity, information contained, for example, in cross covariances between units. Self-consistent dynamical mean field theory (DMFT) has elucidated several features of random neural networks-in particular, that they can generate chaotic activity-however, a calculation of cross covariances using this approach has not been provided. Here, we calculate cross covariances self-consistently via a two-site cavity DMFT. We use this theory to probe spatiotemporal features of activity coordination in a classic random-network model with independent and identically distributed (i.i.d.) couplings, showing an extensive but fractionally low effective dimension of activity and a long population-level timescale. Our formulas apply to a wide range of single-unit dynamics and generalize to non-i.i.d. couplings. As an example of the latter, we analyze the case of partially symmetric couplings.

Task-dependent optimal representations for cerebellar learning

The cerebellar granule cell layer has inspired numerous theoretical models of neural representations that support learned behaviors, beginning with the work of Marr and Albus. In these models, granule cells form a sparse, combinatorial encoding of diverse sensorimotor inputs. Such sparse representations are optimal for learning to discriminate random stimuli. However, recent observations of dense, low-dimensional activity across granule cells have called into question the role of sparse coding in these neurons. Here, we generalize theories of cerebellar learning to determine the optimal granule cell representation for tasks beyond random stimulus discrimination, including continuous input-output transformations as required for smooth motor control. We show that for such tasks, the optimal granule cell representation is substantially denser than predicted by classical theories. Our results provide a general theory of learning in cerebellum-like systems and suggest that optimal cerebellar representations are task-dependent.

Identification of interacting neural populations: methods and statistical considerations

As improved recording technologies have created new opportunities for neurophysiological investigation, emphasis has shifted from individual neurons to multiple populations that form circuits, and it has become important to provide evidence of cross-population coordinated activity. We review various methods for doing so, placing them in six major categories while avoiding technical descriptions and instead focusing on high-level motivations and concerns. Our aim is to indicate what the methods can achieve and the circumstances under which they are likely to succeed. Toward this end, we include a discussion of four cross-cutting issues: the definition of neural populations, trial-to-trial variability and Poisson-like noise, time-varying dynamics, and causality.

Optimal routing to cerebellum-like structures

The vast expansion from mossy fibers to cerebellar granule cells (GrC) produces a neural representation that supports functions including associative and internal model learning. This motif is shared by other cerebellum-like structures and has inspired numerous theoretical models. Less attention has been paid to structures immediately presynaptic to GrC layers, whose architecture can be described as a 'bottleneck' and whose function is not understood. We therefore develop a theory of cerebellum-like structures in conjunction with their afferent pathways that predicts the role of the pontine relay to cerebellum and the glomerular organization of the insect antennal lobe. We highlight a new computational distinction between clustered and distributed neuronal representations that is reflected in the anatomy of these two brain structures. Our theory also reconciles recent observations of correlated GrC activity with theories of nonlinear mixing. More generally, it shows that structured compression followed by random expansion is an efficient architecture for flexible computation.

Neuroscience: Hacking development to understand sensory discrimination

Fine sensory discrimination abilities are enabled by specific neural circuit architectures. A new study reveals how manipulating particular network parameters in the fly's memory centre, the mushroom body, alters sensory coding and discrimination.

Shallow networks run deep: Peripheral preprocessing facilitates odor classification

The mammalian brain implements sophisticated sensory processing algorithms along multilayered ('deep') neural-networks. Strategies that insects use to meet similar computational demands, while relying on smaller nervous systems with shallow architectures, remain elusive. Using Drosophila as a model, we uncover the algorithmic role of odor preprocessing by a shallow network of compartmentalized olfactory receptor neurons. Each compartment operates as a ratiometric unit for specific odor-mixtures. This computation arises from a simple mechanism: electrical coupling between two differently-sized neurons. We demonstrate that downstream synaptic connectivity is shaped to optimally leverage amplification of a hedonic value signal in the periphery. Furthermore, peripheral preprocessing is shown to markedly improve novel odor classification in a higher brain center. Together, our work highlights a far-reaching functional role of the sensory periphery for downstream processing. By elucidating the implementation of powerful computations by a shallow network, we provide insights into general principles of efficient sensory processing algorithms.

Input density tunes Kenyon cell sensory responses in the Drosophila mushroom body

The ability to discriminate sensory stimuli with overlapping features is thought to arise in brain structures called expansion layers, where neurons carrying information about sensory features make combinatorial connections onto a much larger set of cells. For 50 years, expansion coding has been a prime topic of theoretical neuroscience, which seeks to explain how quantitative parameters of the expansion circuit influence sensory sensitivity, discrimination, and generalization. Here, we investigate the developmental events that produce the quantitative parameters of the arthropod expansion layer, called the mushroom body. Using Drosophila melanogaster as a model, we employ genetic and chemical tools to engineer changes to circuit development. These allow us to produce living animals with hypothesis-driven variations on natural expansion layer wiring parameters. We then test the functional and behavioral consequences. By altering the number of expansion layer neurons (Kenyon cells) and their dendritic complexity, we find that input density, but not cell number, tunes neuronal odor selectivity. Simple odor discrimination behavior is maintained when the Kenyon cell number is reduced and augmented by Kenyon cell number expansion. Animals with increased input density to each Kenyon cell show increased overlap in Kenyon cell odor responses and become worse at odor discrimination tasks.

Connectomics of the Octopus vulgaris vertical lobe provides insight into conserved and novel principles of a memory acquisition network

Here, we present the first analysis of the connectome of a small volume of the Octopus vulgaris vertical lobe (VL), a brain structure mediating the acquisition of long-term memory in this behaviorally advanced mollusk. Serial section electron microscopy revealed new types of interneurons, cellular components of extensive modulatory systems, and multiple synaptic motifs. The sensory input to the VL is conveyed via~1.8 × 106 axons that sparsely innervate two parallel and interconnected feedforward networks formed by the two types of amacrine interneurons (AM), simple AMs (SAMs) and complex AMs (CAMs). SAMs make up 89.3% of the~25 × 106VL cells, each receiving a synaptic input from only a single input neuron on its non-bifurcating primary neurite, suggesting that each input neuron is represented in only~12 ± 3.4SAMs. This synaptic site is likely a 'memory site' as it is endowed with LTP. The CAMs, a newly described AM type, comprise 1.6% of the VL cells. Their bifurcating neurites integrate multiple inputs from the input axons and SAMs. While the SAM network appears to feedforward sparse 'memorizable' sensory representations to the VL output layer, the CAMs appear to monitor global activity and feedforward a balancing inhibition for 'sharpening' the stimulus-specific VL output. While sharing morphological and wiring features with circuits supporting associative learning in other animals, the VL has evolved a unique circuit that enables associative learning based on feedforward information flow.

Evolution of neural activity in circuits bridging sensory and abstract knowledge

The ability to associate sensory stimuli with abstract classes is critical for survival. How are these associations implemented in brain circuits? And what governs how neural activity evolves during abstract knowledge acquisition? To investigate these questions, we consider a circuit model that learns to map sensory input to abstract classes via gradient-descent synaptic plasticity. We focus on typical neuroscience tasks (simple, and context-dependent, categorization), and study how both synaptic connectivity and neural activity evolve during learning. To make contact with the current generation of experiments, we analyze activity via standard measures such as selectivity, correlations, and tuning symmetry. We find that the model is able to recapitulate experimental observations, including seemingly disparate ones. We determine how, in the model, the behaviour of these measures depends on details of the circuit and the task. These dependencies make experimentally testable predictions about the circuitry supporting abstract knowledge acquisition in the brain.

Cocaine regulates sensory filtering in cortical pyramidal neurons

Exposure to cocaine leads to robust changes in the structure and function of neurons within the mesocorticolimbic pathway. However, little is known about how cocaine influences the processing of information within the sensory cortex. We address this by using patch-clamp and juxtacellular voltage recordings and two-photon Ca2+ imaging in vivo to investigate the influence of acute cocaine exposure on layer 2/3 (L2/3) pyramidal neurons within the primary somatosensory cortex (S1). Here, cocaine dampens membrane potential state transitions and decreases spontaneous somatic action potentials and Ca2+ transients. In contrast to the uniform decrease in background spontaneous activity, cocaine has a heterogeneous influence on sensory encoding, increasing tactile-evoked responses in dendrites that do not typically encode sensory information and decreasing responses in those dendrites that are more reliable sensory encoders. Combined, these findings suggest that cocaine acts as a filter that suppresses background noise to selectively modulate incoming sensory information.

Restructuring of olfactory representations in the fly brain around odor relationships in natural sources

A core challenge of olfactory neuroscience is to understand how neural representations of odor are generated and progressively transformed across different layers of the olfactory circuit into formats that support perception and behavior. The encoding of odor by odorant receptors in the input layer of the olfactory system reflects, at least in part, the chemical relationships between odor compounds. Neural representations of odor in higher order associative olfactory areas, generated by random feedforward networks, are expected to largely preserve these input odor relationships1-3. We evaluated these ideas by examining how odors are represented at different stages of processing in the olfactory circuit of the vinegar fly D. melanogaster. We found that representations of odor in the mushroom body (MB), a third-order associative olfactory area in the fly brain, are indeed structured and invariant across flies. However, the structure of MB representational space diverged significantly from what is expected in a randomly connected network. In addition, odor relationships encoded in the MB were better correlated with a metric of the similarity of their distribution across natural sources compared to their similarity with respect to chemical features, and the converse was true for odor relationships encoded in primary olfactory receptor neurons (ORNs). Comparison of odor coding at primary, secondary, and tertiary layers of the circuit revealed that odors were significantly regrouped with respect to their representational similarity across successive stages of olfactory processing, with the largest changes occurring in the MB. The non-linear reorganization of odor relationships in the MB indicates that unappreciated structure exists in the fly olfactory circuit, and this structure may facilitate the generalization of odors with respect to their co-occurence in natural sources.

Hacking brain development to test models of sensory coding

Animals can discriminate myriad sensory stimuli but can also generalize from learned experience. You can probably distinguish the favorite teas of your colleagues while still recognizing that all tea pales in comparison to coffee. Tradeoffs between detection, discrimination, and generalization are inherent at every layer of sensory processing. During development, specific quantitative parameters are wired into perceptual circuits and set the playing field on which plasticity mechanisms play out. A primary goal of systems neuroscience is to understand how material properties of a circuit define the logical operations-computations--that it makes, and what good these computations are for survival. A cardinal method in biology-and the mechanism of evolution--is to change a unit or variable within a system and ask how this affects organismal function. Here, we make use of our knowledge of developmental wiring mechanisms to modify hard-wired circuit parameters in the Drosophila melanogaster mushroom body and assess the functional and behavioral consequences. By altering the number of expansion layer neurons (Kenyon cells) and their dendritic complexity, we find that input number, but not cell number, tunes odor selectivity. Simple odor discrimination performance is maintained when Kenyon cell number is reduced and augmented by Kenyon cell expansion.

Signal denoising through topographic modularity of neural circuits

Information from the sensory periphery is conveyed to the cortex via structured projection pathways that spatially segregate stimulus features, providing a robust and efficient encoding strategy. Beyond sensory encoding, this prominent anatomical feature extends throughout the neocortex. However, the extent to which it influences cortical processing is unclear. In this study, we combine cortical circuit modeling with network theory to demonstrate that the sharpness of topographic projections acts as a bifurcation parameter, controlling the macroscopic dynamics and representational precision across a modular network. By shifting the balance of excitation and inhibition, topographic modularity gradually increases task performance and improves the signal-to-noise ratio across the system. We demonstrate that in biologically constrained networks, such a denoising behavior is contingent on recurrent inhibition. We show that this is a robust and generic structural feature that enables a broad range of behaviorally relevant operating regimes, and provide an in-depth theoretical analysis unraveling the dynamical principles underlying the mechanism.

Structured cerebellar connectivity supports resilient pattern separation

The cerebellum is thought to help detect and correct errors between intended and executed commands1,2 and is critical for social behaviours, cognition and emotion3-6. Computations for motor control must be performed quickly to correct errors in real time and should be sensitive to small differences between patterns for fine error correction while being resilient to noise7. Influential theories of cerebellar information processing have largely assumed random network connectivity, which increases the encoding capacity of the network's first layer8-13. However, maximizing encoding capacity reduces the resilience to noise7. To understand how neuronal circuits address this fundamental trade-off, we mapped the feedforward connectivity in the mouse cerebellar cortex using automated large-scale transmission electron microscopy and convolutional neural network-based image segmentation. We found that both the input and output layers of the circuit exhibit redundant and selective connectivity motifs, which contrast with prevailing models. Numerical simulations suggest that these redundant, non-random connectivity motifs increase the resilience to noise at a negligible cost to the overall encoding capacity. This work reveals how neuronal network structure can support a trade-off between encoding capacity and redundancy, unveiling principles of biological network architecture with implications for the design of artificial neural networks.

Cerebellum as a kernel machine: A novel perspective on expansion recoding in granule cell layer

Sensorimotor information provided by mossy fibers (MF) is mapped to high-dimensional space by a huge number of granule cells (GrC) in the cerebellar cortex's input layer. Significant studies have demonstrated the computational advantages and primary contributor of this expansion recoding. Here, we propose a novel perspective on the expansion recoding where each GrC serve as a kernel basis function, thereby the cerebellum can operate like a kernel machine that implicitly use high dimensional (even infinite) feature spaces. We highlight that the generation of kernel basis function is indeed biologically plausible scenario, considering that the key idea of kernel machine is to memorize important input patterns. We present potential regimes for developing kernels under constrained resources and discuss the advantages and disadvantages of each regime using various simulation settings.

Long-range functional loops in the mouse olfactory system and their roles in computing odor identity

Elucidating the neural circuits supporting odor identification remains an open challenge. Here, we analyze the contribution of the two output cell types of the mouse olfactory bulb (mitral and tufted cells) to decode odor identity and concentration and its dependence on top-down feedback from their respective major cortical targets: piriform cortex versus anterior olfactory nucleus. We find that tufted cells substantially outperform mitral cells in decoding both odor identity and intensity. Cortical feedback selectively regulates the activity of its dominant bulb projection cell type and implements different computations. Piriform feedback specifically restructures mitral responses, whereas feedback from the anterior olfactory nucleus preferentially controls the gain of tufted representations without altering their odor tuning. Our results identify distinct functional loops involving the mitral and tufted cells and their cortical targets. We suggest that in addition to the canonical mitral-to-piriform pathway, tufted cells and their target regions are ideally positioned to compute odor identity.

A cerebellum inspired spiking neural network as a multi-model for pattern classification and robotic trajectory prediction

Spiking neural networks were introduced to understand spatiotemporal information processing in neurons and have found their application in pattern encoding, data discrimination, and classification. Bioinspired network architectures are considered for event-driven tasks, and scientists have looked at different theories based on the architecture and functioning. Motor tasks, for example, have networks inspired by cerebellar architecture where the granular layer recodes sparse representations of the mossy fiber (MF) inputs and has more roles in motor learning. Using abstractions from cerebellar connections and learning rules of deep learning network (DLN), patterns were discriminated within datasets, and the same algorithm was used for trajectory optimization. In the current work, a cerebellum-inspired spiking neural network with dynamics of cerebellar neurons and learning mechanisms attributed to the granular layer, Purkinje cell (PC) layer, and cerebellar nuclei interconnected by excitatory and inhibitory synapses was implemented. The model’s pattern discrimination capability was tested for two tasks on standard machine learning (ML) datasets and on following a trajectory of a low-cost sensor-free robotic articulator. Tuned for supervised learning, the pattern classification capability of the cerebellum-inspired network algorithm has produced more generalized models than data-specific precision models on smaller training datasets. The model showed an accuracy of 72%, which was comparable to standard ML algorithms, such as MLP (78%), Dl4jMlpClassifier (64%), RBFNetwork (71.4%), and libSVM-linear (85.7%). The cerebellar model increased the network’s capability and decreased storage, augmenting faster computations. Additionally, the network model could also implicitly reconstruct the trajectory of a 6-degree of freedom (DOF) robotic arm with a low error rate by reconstructing the kinematic parameters. The variability between the actual and predicted trajectory points was noted to be ± 3 cm (while moving to a position in a cuboid space of 25 × 30 × 40 cm). Although a few known learning rules were implemented among known types of plasticity in the cerebellum, the network model showed a generalized processing capability for a range of signals, modulating the data through the interconnected neural populations. In addition to potential use on sensor-free or feed-forward based controllers for robotic arms and as a generalized pattern classification algorithm, this model adds implications to motor learning theory.

Adult-born dentate granule cells promote hippocampal population sparsity

The dentate gyrus (DG) gates neocortical information flow to the hippocampus. Intriguingly, the DG also produces adult-born dentate granule cells (abDGCs) throughout the lifespan, but their contribution to downstream firing dynamics remains unclear. Here, we show that abDGCs promote sparser hippocampal population spiking during mnemonic processing of novel stimuli. By combining triple-(DG-CA3-CA1) ensemble recordings and optogenetic interventions in behaving mice, we show that abDGCs constitute a subset of high-firing-rate neurons with enhanced activity responses to novelty and strong modulation by theta oscillations. Selectively activating abDGCs in their 4-7-week post-birth period increases sparsity of hippocampal population patterns, whereas suppressing abDGCs reduces this sparsity, increases principal cell firing rates and impairs novel object recognition with reduced dimensionality of the network firing structure, without affecting single-neuron spatial representations. We propose that adult-born granule cells transiently support sparser hippocampal population activity structure for higher-dimensional responses relevant to effective mnemonic information processing.

Precise and stable edge orientation signaling by human first-order tactile neurons

Fast-adapting type 1 (FA-1) and slow-adapting type 1 (SA-1) first-order neurons in the human tactile system have distal axons that branch in the skin and form many transduction sites, yielding receptive fields with many highly sensitive zones or 'subfields.' We previously demonstrated that this arrangement allows FA-1 and SA-1 neurons to signal the geometric features of touched objects, specifically the orientation of raised edges scanned with the fingertips. Here, we show that such signaling operates for fine edge orientation differences (5-20°) and is stable across a broad range of scanning speeds (15-180 mm/s); that is, under conditions relevant for real-world hand use. We found that both FA-1 and SA-1 neurons weakly signal fine edge orientation differences via the intensity of their spiking responses and only when considering a single scanning speed. Both neuron types showed much stronger edge orientation signaling in the sequential structure of the evoked spike trains, and FA-1 neurons performed better than SA-1 neurons. Represented in the spatial domain, the sequential structure was strikingly invariant across scanning speeds, especially those naturally used in tactile spatial discrimination tasks. This speed invariance suggests that neurons' responses are structured via sequential stimulation of their subfields and thus links this capacity to their terminal organization in the skin. Indeed, the spatial precision of elicited action potentials rationally matched spatial acuity of subfield arrangements, which corresponds to a spatial period similar to the dimensions of individual fingertip ridges.

High-throughput sequencing of single neuron projections reveals spatial organization in the olfactory cortex

In most sensory modalities, neuronal connectivity reflects behaviorally relevant stimulus features, such as spatial location, orientation, and sound frequency. By contrast, the prevailing view in the olfactory cortex, based on the reconstruction of dozens of neurons, is that connectivity is random. Here, we used high-throughput sequencing-based neuroanatomical techniques to analyze the projections of 5,309 mouse olfactory bulb and 30,433 piriform cortex output neurons at single-cell resolution. Surprisingly, statistical analysis of this much larger dataset revealed that the olfactory cortex connectivity is spatially structured. Single olfactory bulb neurons targeting a particular location along the anterior-posterior axis of piriform cortex also project to matched, functionally distinct, extra-piriform targets. Moreover, single neurons from the targeted piriform locus also project to the same matched extra-piriform targets, forming triadic circuit motifs. Thus, as in other sensory modalities, olfactory information is routed at early stages of processing to functionally diverse targets in a coordinated manner.

A neural theory for counting memories

Keeping track of the number of times different stimuli have been experienced is a critical computation for behavior. Here, we propose a theoretical two-layer neural circuit that stores counts of stimulus occurrence frequencies. This circuit implements a data structure, called a count sketch, that is commonly used in computer science to maintain item frequencies in streaming data. Our first model implements a count sketch using Hebbian synapses and outputs stimulus-specific frequencies. Our second model uses anti-Hebbian plasticity and only tracks frequencies within four count categories ("1-2-3-many"), which trades-off the number of categories that need to be distinguished with the potential ethological value of those categories. We show how both models can robustly track stimulus occurrence frequencies, thus expanding the traditional novelty-familiarity memory axis from binary to discrete with more than two possible values. Finally, we show that an implementation of the "1-2-3-many" count sketch exists in the insect mushroom body.

Structured sampling of olfactory input by the fly mushroom body

Associative memory formation and recall in the fruit fly Drosophila melanogaster is subserved by the mushroom body (MB). Upon arrival in the MB, sensory information undergoes a profound transformation from broadly tuned and stereotyped odorant responses in the olfactory projection neuron (PN) layer to narrowly tuned and nonstereotyped responses in the Kenyon cells (KCs). Theory and experiment suggest that this transformation is implemented by random connectivity between KCs and PNs. However, this hypothesis has been challenging to test, given the difficulty of mapping synaptic connections between large numbers of brain-spanning neurons. Here, we used a recent whole-brain electron microscopy volume of the adult fruit fly to map PN-to-KC connectivity at synaptic resolution. The PN-KC connectome revealed unexpected structure, with preponderantly food-responsive PN types converging at above-chance levels on downstream KCs. Axons of the overconvergent PN types tended to arborize near one another in the MB main calyx, making local KC dendrites more likely to receive input from those types. Overconvergent PN types preferentially co-arborize and connect with dendrites of αβ and α'β' KC subtypes. Computational simulation of the observed network showed degraded discrimination performance compared with a random network, except when all signal flowed through the overconvergent, primarily food-responsive PN types. Additional theory and experiment will be needed to fully characterize the impact of the observed non-random network structure on associative memory formation and recall.

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.