The team focused on the olfactory system because it offers an unusually clean experimental window into memory. Odors are high-dimensional chemical stimuli, yet the brain rapidly compresses them into compact internal representations. When an animal learns that a particular odor predicts a reward or a punishment, the neural code for that odor changes. The researchers set out to determine exactly how those changes unfold at the level of entire populations rather than single cells.

Using large-scale recordings from mice as the animals learned to associate specific odors with outcomes, the investigators tracked activity in key nodes of the olfactory memory circuit, including the piriform cortex and connected structures. Dimensionality reduction techniques revealed that odor representations occupy smooth, low-dimensional manifolds embedded in the high-dimensional space of population activity. Learning did not simply add noise or scatter the responses; instead, it systematically reorganized the geometry of these manifolds.

Specifically, as animals became better at discriminating rewarded from unrewarded odors, the manifolds corresponding to different odor categories moved apart, increasing the margin between them. This geometric separation mirrors the objective functions used in machine learning classifiers, which seek to maximize the distance between classes. In other words, the biological network appeared to solve an optimization problem: reshape its internal representation space so that behaviorally relevant distinctions become as easy as possible to read out.

The study also examined how this optimization is implemented mechanistically. Plasticity at synapses within the olfactory cortical network provides the natural substrate for manifold reshaping. By adjusting connection strengths in a way that depends on task demands, the circuit can rotate, stretch, and translate the manifolds on which odor memories reside. Computational models in the paper demonstrated that a simple learning rule acting on recurrent connections is sufficient to reproduce the observed geometric changes and the accompanying improvements in behavioral performance.

One of the most striking findings is that manifold reorganization predicted behavior on a trial-by-trial basis. In sessions where the geometric separation between odor categories was larger, animals performed the discrimination task with greater accuracy. This tight coupling between representational geometry and action strengthens the argument that the manifold is not an epiphenomenon of recording analysis but a functional unit of memory itself, something the brain actively constructs and maintains.

The work also addresses a long-standing puzzle in memory research: why memories remain stable even as individual neurons change their firing properties. If a memory were stored in the activity of particular cells, drift in those cells should degrade the memory. But if the memory is stored in the shape and position of a manifold, the system can tolerate turnover and drift at the single-cell level as long as the global geometry is preserved. The olfactory network appears to exploit exactly this robustness, stabilizing the manifold while individual neurons come and go from the active ensemble.

These results resonate with a broader theoretical movement in neuroscience that treats population activity through the lens of geometry and dynamics. Rather than decoding the activity of single neurons, this framework asks how entire trajectories and subspaces of activity support computation. The new findings provide some of the clearest evidence yet that learning sculpts these subspaces deliberately, and that the rules governing this sculpting can be described with the same mathematical language used in machine learning.

The implications reach beyond olfaction. Manifold optimization may be a general principle of representational learning in the brain, applying to motor skills, decision-making, and perhaps even higher cognitive functions. If so, therapeutic strategies for disorders of memory and perception might one day aim not at individual synapses but at restoring healthy manifold geometry in malfunctioning circuits. The study also suggests that artificial neural networks, which already borrow heavily from brain-inspired principles, could benefit from architectures that explicitly optimize manifold structure the way biological networks appear to do.

Future experiments will aim to identify the precise plasticity mechanisms and neuromodulatory signals that guide manifold optimization, and to test whether similar geometric learning rules operate in other sensory and memory systems. For now, the study offers a compelling synthesis: memory is not a static snapshot written into cells, but a dynamically optimized shape in the brain’s representational space, continuously refined by experience until the world’s important distinctions stand out in sharp relief.

The piriform cortex, the largest olfactory cortical area, occupies a distinctive position among sensory cortices. Unlike primary visual or auditory regions, it receives direct input from the olfactory bulb without an intervening thalamic relay, and its recurrent collateral connections are extraordinarily dense. Pyramidal cells in this structure broadcast axonal branches widely across the network, meaning that any learning rule acting at these recurrent synapses has access to an almost associative memory-like architecture. This anatomical arrangement has long suggested that the piriform cortex functions as a pattern completion and pattern separation device, and the manifold optimization account fits naturally within that tradition, extending it from single-cell response changes to the collective geometry of ensembles.

The statistical structure of odor space itself provides important context for why the olfactory system might be particularly suited to geometric reorganization. Natural odorants are mixtures of many volatile molecules, and the relationships between odorants are smooth: chemically similar molecules tend to smell alike, and perceptual similarity decays gradually with molecular distance. The early stages of the olfactory pathway, from receptors in the nose through the glomerular map of the olfactory bulb, already impose a dimensionality reduction on this chemical space. What the new findings add is evidence that later, experience-dependent stages continue this compression but do so adaptively, stretching the dimensions that matter for current behavioral goals while letting irrelevant dimensions collapse.

Classical work on olfactory learning in rodents emphasized changes in single-neuron selectivity, with individual piriform neurons broadening or sharpening their tuning after conditioning. Those observations were sometimes difficult to reconcile, because different cells appeared to change in inconsistent directions. The manifold perspective resolves this apparent inconsistency: heterogeneous single-cell changes can produce a coherent geometric shift if they collectively move or reshape the ensemble’s low-dimensional subspace. A neuron increasing its responses to one odor while a neighbor decreases its responses may look contradictory at the single-cell level, yet both changes can contribute to expanding the distance between odor-category manifolds, exactly what improved discrimination requires.

The distinction between representational drift and manifold stability also connects to an active debate about how the brain balances flexibility and permanence. Longitudinal recordings in several systems have documented that the identities of neurons participating in a code can change over days and weeks, even when behavioral performance is fully preserved. Explanations of this drift have ranged from passive turnover to active consolidation processes. The finding that geometric structure is preserved while its cellular substrate rotates suggests that the relevant invariant for memory is relational rather than compositional: what matters is how representations sit relative to one another, not which particular neurons carry them. This reframing gives theorists a concrete target for models of memory maintenance over long timescales.

Connections to machine learning deepen the significance of the results. Classification algorithms such as support vector machines explicitly maximize margins between categories, and deep networks trained with error-driven rules are known to linearize their internal representations as performance improves, spreading class clusters apart in hidden-layer activity spaces. The apparent convergence between these engineered objectives and the geometry observed in olfactory cortex suggests that margin maximization may be a general computational principle that biological networks arrived at independently. It also raises the question of whether the brain’s learning rules approximate gradient-based optimization over a representational objective, or whether local synaptic plasticity merely produces margin expansion as an emergent byproduct. The computational models in the study, which reproduce the geometric changes with simple recurrent plasticity, favor the latter possibility, indicating that no explicit global error signal is required.

Methodologically, the study illustrates the growing power of combining large-scale electrophysiology or imaging with tools from applied mathematics. Dimensionality reduction methods, including approaches that preserve local neighborhood structure and those that track low-dimensional trajectories over time, allow researchers to ask quantitative questions about representational geometry that were previously unanswerable. Trial-by-trial alignment between geometric measures and behavior exemplifies a broader trend: rather than treating population analyses as descriptive, investigators now use them to generate predictions that can be tested against the animal’s choices on individual trials, tightening the link between neural data and computation.

Several questions remain open. Whether manifold optimization operates during passive exposure to odors or requires explicit reinforcement is unresolved, as is the role of top-down signals from prefrontal or hippocampal structures that inform the olfactory cortex about task context. The timescale of geometric consolidation, and whether reshaped manifolds persist during sleep-related replay, would clarify how learning is stabilized. Answering these questions will require the same combination of longitudinal population recording, behavioral quantification, and geometric analysis demonstrated here, applied across circuits and species. The study thus serves both as an empirical advance for olfactory neuroscience and as a methodological template for testing whether representational optimization is a universal grammar of learned neural computation.

Subject of Research: Representational learning through geometric optimization of neural manifolds in the olfactory memory network

Article Title: Representational learning by optimization of neural manifolds in an olfactory memory network

Article References: Hu, B., Temiz, N. Z., Chou, C.-N., Rupprecht, P., Meissner-Bernard, C., Titze, B., Chung, S., & Friedrich, R. W. (2026). Representational learning by optimization of neural manifolds in an olfactory memory network. Nature Neuroscience. https://doi.org/10.1038/s41593-026-02429-3

Image Credits: AI Generated

DOI: 10.1038/s41593-026-02429-3

Keywords: neuroscience, olfaction, neural manifolds, memory, representational learning, piriform cortex, neural plasticity, population coding, dimensionality reduction, behavioral learning, machine learning, Nature Neuroscience

The intellectual foundation of the new work lies in the concept of neural manifolds. When neuroscientists record from many neurons at once, they find that the activity of the population does not explore all of the dimensions theoretically available to it. Instead, the patterns of co-activation are confined to a lower-dimensional subspace, a manifold whose axes reflect the correlated structure of the circuit. Pioneering experiments by Sadtler and colleagues in 2014, using brain-computer interfaces in monkeys, demonstrated that animals could readily learn to control a cursor when the mapping between neural activity and cursor movement stayed within the intrinsic manifold of their motor cortex. When the mapping was altered to require activity patterns outside that manifold, performance collapsed and learning proceeded far more slowly. Subsequent work by Oby and colleagues in 2019 and by Golub and colleagues in 2018 extended this principle, showing that the boundaries of the manifold impose real, measurable constraints on what a brain can learn to do.

Those experiments, however, were performed with invasive recordings in animal models. Whether the same geometric principle governs learning in the intact, behaving human brain remained an open question, and a technically daunting one. Human learning is typically studied with functional magnetic resonance imaging, which measures blood-oxygen-level-dependent signals across the cortex rather than the firing of individual neurons. Busch and colleagues tackled the challenge by extracting the latent structure of whole-brain activity from imaging data, characterizing the manifold of human brain activity at a population level and then asking how that structure changes, or fails to change, as people learn new tasks. Their central result is elegantly asymmetric: learning proceeds smoothly when the required new activity patterns remain within the existing manifold, but is sharply limited when the task demands patterns that lie beyond it.

The technical machinery behind this conclusion deserves attention, because it represents a methodological bridge between two levels of analysis that have long been difficult to reconcile. Dimensionality reduction techniques, such as principal component analysis and related latent variable methods, allow researchers to compress the activity of thousands of voxels into a small number of dominant activity patterns. The geometry of these patterns, their relative positions, orientations and curvatures in the reduced space, constitutes a fingerprint of the brain’s intrinsic organization. By tracking how task-related activity trajectories move through this space during training, the researchers could quantify precisely how far a learner had to push their neural activity away from its habitual configuration. Distance within the manifold predicted rapid improvement; distance beyond the manifold predicted stagnation. The geometry was not a passive byproduct of learning. It was the variable that best explained the pace of learning itself.

This asymmetry carries profound implications for how neuroscientists think about plasticity. The traditional view of learning emphasizes synaptic modification: connections strengthen or weaken, and behavior changes accordingly. The manifold framework does not contradict that view, but it adds a crucial layer of constraint. Synaptic plasticity may be abundant and readily available, yet if the circuit’s correlated structure funnels activity along a limited set of axes, then only certain behavioral changes are cheap to produce. Changing the manifold itself, reorganizing the fundamental correlations that define it, appears to be a far more expensive operation for the brain. In effect, the brain possesses two distinct currencies of adaptation: cheap movements within its existing neural geometry, and costly renovations of that geometry. Busch and colleagues provide the strongest human evidence yet that the exchange rate between these currencies governs what we can learn and how fast.

The findings also resonate with an older literature on muscle synergies and motor primitives. Work by Berger, Gentner, Edmunds, Pai and d’Avella in 2013 showed that the motor system composes movements from a small repertoire of coordinated activation patterns rather than controlling every muscle independently. If behavior is built from a finite set of building blocks, then learning new behaviors is easiest when the desired behavior can be assembled from blocks already in stock. The manifold results generalize this intuition from muscles to cortex: the brain’s activity repertoire constrains the behaviors it can readily acquire. Interestingly, the conceptual reach of neural geometry now extends beyond neuroscience altogether. Research in artificial intelligence, notably the work of Elhage and colleagues on features and representations inside neural networks, has revealed that artificial deep networks also organize their computations along low-dimensional manifolds, and that the geometry of these representations shapes what the networks can learn. Brains and machines, it seems, confront the same geometric trade-offs.

For the growing field of brain-computer interfaces, the implications are immediate and practical. A user learning to control a robotic limb or a communication prosthesis is, in geometric terms, being asked to steer their neural activity into configurations that map onto device commands. The new results suggest that interface designers should work with the brain’s intrinsic geometry rather than against it, aligning decoder mappings with the existing manifold to shorten training times and boost performance. Conversely, when a therapeutic goal requires the brain to adopt genuinely novel activity patterns, clinicians may need to design training protocols that gradually reshape the manifold itself, perhaps through carefully staged practice that pulls the geometry outward over time. Similar reasoning applies to neurorehabilitation after stroke, where recovery may depend on whether the damaged cortex can re-express lost skills within its surviving manifold or must construct new geometric structure from the ground up.

The study also sharpens a question that has lingered since the first manifold experiments: what determines the geometry in the first place? Candidates include the statistics of a lifetime of experience, the anatomical wiring of cortical circuits, developmental programs and genetic constraints. If intrinsic geometry is largely fixed by anatomy and history, then the fastest route to enhanced learning may be to choose training tasks that sit comfortably within a person’s existing manifold, a principle that could personalize education and skill training. If, on the other hand, geometry is malleable with the right kind of experience, then identifying the activities that expand manifolds becomes a central goal for learning science. Busch and colleagues’ human imaging paradigm provides a tool for testing these possibilities, because it allows researchers to measure manifold structure repeatedly as individuals accumulate different kinds of experience.

Writing in Nature Neuroscience, Batista emphasizes the elegance of the asymmetry at the heart of the new findings: the same geometric framework that explains effortless learning also explains its limits, unifying what previously looked like separate phenomena under a single principle. The work transforms a philosophical question, why some skills come easily and others do not, into a quantitative one, measurable in the coordinates of brain activity. As imaging methods and latent variable models continue to improve, researchers may soon be able to read out an individual’s neural geometry and predict, before the first practice session, which skills that person will master quickly and which will demand a renovation of the brain’s deepest structure. Learning, on this view, is not a climb up an abstract ladder of difficulty. It is a journey through a landscape whose contours were drawn long before the journey began, and knowing the map may be the first step toward redrawing it.

Subject of Research: How the intrinsic geometry of human brain activity constrains and guides learning

Article Title: Neural geometry guides learning

Article References: Batista, A. P. (2026). Neural geometry guides learning. Nature Neuroscience. https://doi.org/10.1038/s41593-026-02442-6

Image Credits: AI Generated

DOI: 10.1038/s41593-026-02442-6

Keywords: neural manifolds, neural geometry, motor learning, functional MRI, brain-computer interfaces, neural dimensionality, cortical plasticity, skill acquisition, latent variable models, human neuroscience, Neural, geometry