SUMMARY Ongoing technological advances will lead to recordings with progressively increasing numbers of neurons, while trial counts may only increase modestly. The analysis of such large-scale data increasingly relies on extracting collective neural population geometry. These combined recording and analysis trends raise the fundamental need for a predictive theory of experimental design that can tell us how accurately we will be able to infer such geometry in future larger scale recordings with more neurons and trials, by extrapolating from past smaller recordings. We derive such a theory for the simplest and most widely used method for extracting population geometry: principal component analysis. Our theory can predict how the dimensionality of neural data will grow with more neurons and trials and how accurate and reliable neuronal correlations and individual neural modes of the population geometry will be. Importantly, we find a blessing of dimensionality in which recording more neurons allows population geometry to be inferred accurately with fewer trials. The need for fewer trials in larger recordings will allow for the design of new experiments with more diverse trial types. Moreover, we derive scaling laws for the performance of neural prediction, setting the stage for the derivation of scaling laws for foundation models in neuroscience. We successfully test our theory across diverse species and recording modalities.

Abstract For the brain to compute, electrical signals must propagate over the membranes of individual neurons, connecting synaptic inputs to synaptic outputs 1 . Complex neuronal morphologies coupled with the spatial organization of synaptic inputs and outputs enable diverse voltage transformations that underlie cell-type specific computations 2,3 . However, measuring these transformations in vivo has remained challenging, leaving a crucial gap in our mechanistic understanding of single neuron computation. Here, we develop ASAP7y, a genetically encoded voltage indicator with unprecedented subthreshold sensitivity and expanded excitation compatibility in both mice and flies. We leveraged ASAP7y combined with two-photon random-access microscopy to record sensory stimulus-evoked voltage dynamics with millisecond, subcellular, and subthreshold resolution along the neurites of individual neurons in Drosophila . We found remarkable heterogeneity in voltage propagation across cell-types, delineating a fundamental axis of electrical diversity. Leveraging a nanoscale EM reconstruction of the visual system 4 , we modeled the electrotonic properties of single neurons spanning 717 cell types, revealing how morphology shapes voltage transformations. Finally, we demonstrate that confined voltage propagation creates substrates for local computation, producing subcellular domains with distinct feature selectivity across multiple cell types. These results provide mechanistic insight into how critical single neuron computations arise and reveal parallel processing in single neurons.

Abrupt learning, long performance plateaus followed by rapid convergence, is a common phenomenon in recurrent neural networks (RNNs) trained on working-memory tasks. In such cases, the networks develop transient slow regions in state space that extend the effective timescales of computation. However, the mechanisms driving sudden performance improvements and their causal role remain unclear, largely because we lack an analytical dynamical-systems framework. To address this gap, we introduce the ghost mechanism, a general process by which finite-dimensional continuous-time dynamical systems exhibit transient slowdown near the remnant of a saddle-node bifurcation. By reducing the high-dimensional dynamics near ghost points, we derive a one-dimensional canonical form that analytically captures learning as a process controlled by a single scale parameter. Using this model, we study a form of abrupt learning emerging from ghost points and identify a critical learning rate that scales as an inverse power law with the timescale of the learned computation. Beyond this rate, learning collapses through two interacting modes: (i) vanishing gradients and (ii) oscillatory gradients near minima. These features can lock the system into high confidence but incorrect predictions when parameter updates trigger a no-learning zone, a region of parameter space where gradients vanish. We validate these predictions in low-rank RNNs, where ghost points precede abrupt transitions and further demonstrate their generality in full-rank RNNs trained on canonical working-memory tasks. Our theory offers two approaches to address these learning difficulties: Increasing trainable ranks stabilizes learning trajectories, while reducing output confidence mitigates entrapment in no-learning zones. Overall, the ghost mechanism reveals how the computational demands of a task constrain the optimization landscape, demonstrating that well-known learning difficulties in RNNs partly arise from the dynamical systems they must learn to implement.

Abstract Parallel revolutions in intravital microscopy and spatial biology techniques have respectively enabled large-scale recordings of cellular dynamics in live animals and multi-dimensional molecular profiling at single-cell resolution. However, due to the challenges of aligning data from different modalities at cellular resolution, these two transformational approaches have generally been applied on separate biological samples, stymying the ability to link activity patterns and molecular attributes in the same exact cells. To enable routine, multimodal investigations of cells’ in vivo dynamics and molecular content, we created TRU-FACT (Total Registration Under Functional Activity, Connectivity, and Transcriptomics), a broadly applicable experimental and computational pipeline for registering large populations of individual cells across intravital imaging and spatial biology datasets. The pipeline combines three key innovations: an optomechanical tissue handling and alignment method to parallelize specimen planes, a graph-theoretic method to register individual cells based on their geometric relationships to neighboring cells, and a statistical framework that provides for each cell an a posteriori probability of correct registration. We validated TRU-FACT with several preparations for imaging neural Ca 2+ activity in cortical and deep brain areas in head-fixed and freely behaving mice, RNA-barcode-expressing viruses for labeling neural projections, and low- and high-plex spatial transcriptomic methods. In mice performing a skilled reaching task, TRU-FACT alignments revealed the movement-related signaling patterns of intratelencephalic, extratelencephalic, and striatum-, superior colliculus-, and thalamus-projecting motor cortical neurons. Overall, TRU-FACT constitutes a scalable, multimodal discovery platform that is applicable to diverse tissue-types and spatial biology techniques, thereby enabling multiscale analyses of many complex biological systems.

Cognitive dysfunction in conditions such as schizophrenia involves disrupted communication between the prefrontal cortex (PFC) and the mediodorsal thalamus (MD). Parvalbumin interneurons (PVIs) are known to regulate PFC microcircuits and generate synchronized gamma-frequency (∼40 Hz) neural oscillations that are recruited during many executive functions, necessary for cognitive flexibility, and deficient in schizophrenia. While targeting PVI-mediated gamma oscillations holds great therapeutic promise, their nature and specific functions, e.g., for regulating PFC→MD communication, remain elusive. Using dual-color voltage indicators and optogenetics in mice, we reveal that PVIs dynamically synchronize with MD-projecting PFC neurons both locally and contralaterally, creating multiple distinct circuit-specific patterns of distributed gamma synchronization that are recruited in a behaviorally specific manner to support particular aspects of flexible behavior. Thus, gamma oscillations are not unitary phenomena characterized by one microcircuit-wide pattern of synchrony. Rather, they comprise diverse motifs, defined by specific cell types and phase relationships, that are dynamically recruited for specific functions.

Neurons are noisy computational substrates, yet large neural populations achieve reliable computation. What determines the maximal duration that a noisy population can sustain working memory? We study this question with recurrent networks subject to stochastic noise and present three theoretical results. First, networks suppress independent neuronal noise when activity lies on a low-dimensional latent manifold. Second, this structure induces correlated noise across neurons, limiting the downstream information that can be extracted. Third, these effects yield an analytical bound on working memory duration that scales linearly with network size. We test these predictions using large-scale neocortical recordings, and provide a behavioral signature in mice consistent with the theory. Overall, noise suppression constitutes a key functional benefit of low-dimensional neural coding, with which large populations sustain reliable working memory over extended timescales.

The mammalian brain's long-term memory circuits integrate information from prior and new experiences. The medial prefrontal cortex (mPFC) has a crucial role in this process and can reliably store information for weeks to months in rodents and over years in humans. To maintain information over these extended timescales, the neural encoding of remote memories involves persistent synaptic, transcriptional, and epigenetic changes that outlast the more transient forms of molecular activation that occur in the initial minutes to hours of memory storage. However, whether these persistent effects include long-lasting changes to chromatin structure and whether chromatin states mainly reflect prior episodes of neural activation or retune transcriptional responses to future bouts of activation remain unknown. Here we show that mPFC neurons engaged during the initial formation of memory undergo progressive changes in chromatin accessibility over the first four weeks of memory storage, evincing long-lasting modifications to the genetic programs activated during subsequent memory retrieval. Our experiments involved genetic trapping and single-cell multiomic sequencing analyses of mouse mPFC engram neurons activated during contextual fear conditioning. In the absence of subsequent memory recall, memory storage-related changes to chromatin structure were modestly reflected in gene expression patterns at 7 and 28 days after fear conditioning. However, upon memory recall, the genetically trapped engram neurons executed distinct transcriptional programs from those of other neurons of the same genetic types, suggesting that chromatin rearrangements arising during remote memory storage alter the transcriptional control logic by which engram neurons respond to new experiences. These metaplastic changes to transcriptional programs preferentially affect gene-regulatory and post-transcriptional control mechanisms, show substantial enrichment for transcription factor motifs related to neural development and cell-state regulation, and downregulate the neuron's transcriptional responses to future excitation. Thus, rather than merely preserving a molecular record of prior learning, chromatin architectural changes in engram neurons occur over timescales of weeks and appear, in part, to repurpose conserved regulatory machinery to dampen the extent to which these neurons will engage in further information storage. Based on these findings, we propose that chromatin structural changes provide a slow-timescale component of neural computation that reduces interference between the representations of different memories.

Remembering object locations is crucial for survival, yet how the anterior cingulate cortex (ACC) encodes spatial features across repeated experiences has not been fully characterized. Using longitudinal calcium imaging in freely moving mice, we tracked excitatory ACC neurons while animals explored objects across multiple days. We demonstrate that the ACC employs a highly dynamic coding strategy: while the overall proportion of object-responsive neurons remains constant across sessions, the specific identities of these cells fluctuate, showing a continuous turnover alongside a small, stable core. This dynamic coding is modulated by behavior, with high-exploring mice exhibiting greater cellular stability. Crucially, population-level analyses reveal that stable spatial representations emerge from collective dynamics rather than fixed single-cell identities. Population decoding demonstrates that information becomes linearly separable and highly efficient at a coarser ensemble scale. Thus, the ACC achieves representational stability through emergent network organization despite persistent single-cell dynamics.

Exogenous opioids that activate μ-opioid receptors (MORs) in nociceptive circuits mediate transient pain relief lasting minutes to hours but have more limited utility for treating chronic pain. By comparison, electrical or magnetic stimulation of the motor cortex can induce pain relief lasting weeks, for which the underlying mechanisms have remained unclear. Here we report an unconventional role for endogenous opioidergic signaling in the rapid induction of long-lasting analgesia from motor cortical stimulation, which triggers opioid-peptide-dependent neural plasticity in the rostral ventromedial medulla (RVM), a key node in the brain's descending pain control pathways. To dissect the circuit and cellular bases for these effects, we created a miniaturized, millimeter-sized device allowing focal, non-invasive transcranial magnetic stimulation (TMS) of the mouse motor cortex. In mice with chronic neuropathic pain, reflexive and affective pain behaviors diminished for 1-2 weeks after one session of TMS treatment. Chemogenetic and optogenetic manipulations showed that motor cortical layer 5 pyramidal neurons with axonal projections to the RVM mediated TMS-induced pain relief. High-density electrophysiological recordings revealed that TMS treatment shifted the balance of RVM activity between pain-ON and pain-OFF neurons to a state promoting greater suppression of pain. Genetic and neuropharmacological manipulations revealed that NMDA-receptor-dependent signaling and MOR activation by endogenous opioid peptides in the RVM jointly mediate the long-lasting analgesia induced by a transient bout of TMS. Strikingly, enkephalinase inhibition in the RVM during TMS treatment enhanced the amplitude and duration of analgesia, showing that transiently boosting endogenous opioidergic signaling during TMS increases analgesia-conferring plasticity. In accord, re-analyses of data from human subjects with chronic pain support the idea that opioid administration amplifies analgesia from motor cortical TMS. Overall, our results showcase miniaturized TMS devices as versatile tools for basic and translational neuroscience and detail a hybrid, long-range neural network and NMDA- and opioid-receptor-dependent plasticity mechanism for durable pain relief. These findings point the way to mechanistically grounded, synergistic neurostimulation and drug therapies for brain diseases and disorders that jointly target neural circuit and molecular signaling pathways.

Classical models of movement control posit that striatal spiny projection neurons of the basal ganglia’s direct and indirect pathways (dSPNs and iSPNs) respectively promote and suppress movement. Supporting this view, physiological recordings have revealed imbalanced dSPN and iSPN activity levels during hypokinetic and hyperkinetic movement conditions. However, in normal brain states, dSPN and iSPN ensembles have approximately equal activation amplitudes and time courses, jointly encoding specific actions. How pathological movement conditions alter such action coding remains poorly understood. Here we imaged the concurrent dynamics of dSPNs and iSPNs in behaving mice across normal, hypokinetic, and hyperkinetic conditions, before and after administration of drug treatments used clinically. Analyses focused on resting periods and neural activity that immediately preceded movement, examining how SPNs encoded upcoming actions. In hypokinetic states, the dSPN population was hypoactive relative to the iSPN population, consistent with prior reports. Moreover, individual dSPNs and iSPNs that encoded upcoming locomotion exhibited a reduced measure of activity compared to the normal state; the extent of this reduction predicted the degree of decline in the occurrence of locomotion. Levodopa (L-DOPA) and amantadine treatments both improved locomotion frequency but acted via distinct mechanisms. L-DOPA rebalanced the activity of the dSPN and iSPN populations, whereas amantadine boosted the activity of individual locomotion-related dSPNs and iSPNs. In hyperkinetic states modeling L-DOPA-induced dyskinesia, dSPN populations were hyperactive relative to iSPN populations. Involuntary dyskinetic movements engaged individual dSPNs and iSPNs distinct from those encoding voluntary locomotion. Amantadine treatment reduced the resting activity of dyskinesia-but not locomotion-related SPNs without improving the overall dSPN and iSPN imbalance. These findings highlight the importance of SPN action coding, not merely the extent of activity balance, for normal and pathological movements. The results delineate two distinct therapeutic mechanisms, one that rebalances the activity of the direct and indirect pathways and another that selectively potentiates or depresses the activity of SPN populations encoding voluntary or involuntary actions. Overall, this study refines the understanding of striatal dysfunction in movement disorders, demonstrates that distinct neural populations underlie normal voluntary locomotion and involuntary dyskinetic movements, and defines two complementary routes for the development of symptomatic treatments. ### Competing Interest Statement The authors have declared no competing interest.

Short-term memory is essential for cognitive processing, yet our understanding of its neural mechanisms remains unclear. Neuroscience has long focused on how sequential activity patterns, where neurons fire one after another within large networks, can explain how information is maintained. While recurrent connections were shown to drive sequential dynamics, a mechanistic understanding of this process still remains unknown. In this work, we introduce two unique mechanisms that can support this form of short-term memory: slow-point manifolds generating direct sequences or limit cycles providing temporally localized approximations. Using analytical models, we identify fundamental properties that govern the selection of each mechanism. Precisely, on short-term memory tasks (delayed cue-discrimination tasks), we derive theoretical scaling laws for critical learning rates as a function of the delay period length, beyond which no learning is possible. We empirically verify these results by training and evaluating approximately 80,000 recurrent neural networks (RNNs), which are publicly available for further analysis. Overall, our work provides new insights into short-term memory mechanisms and proposes experimentally testable predictions for systems neuroscience.

Abrupt learning is a common phenomenon in recurrent neural networks (RNNs) trained on working memory tasks. In such cases, the networks develop transient slow regions in state space that extend the effective timescales of computation. However, the mechanisms driving sudden performance improvements and their causal role remain unclear. To address this gap, we introduce the ghost mechanism, a process by which dynamical systems exhibit transient slowdown near the remnant of a saddle-node bifurcation. By reducing the high-dimensional dynamics near ghost points, we derive a one-dimensional canonical form that analytically captures learning as a process controlled by a single scale parameter. Using this model, we study a form of abrupt learning emerging from ghost points and identify a critical learning rate that scales as an inverse power law with the timescale of the learned computation. Beyond this rate, learning collapses through two interacting modes: (i) vanishing gradients and (ii) oscillatory gradients near minima. These features can lock the system into high-confidence but incorrect predictions when parameter updates trigger a no-learning zone, a region of parameter space where gradients vanish. We validate these predictions in low-rank RNNs, where ghost points precede abrupt transitions, and further demonstrate their generality in full-rank RNNs trained on canonical working memory tasks. Our theory offers two approaches to address these learning difficulties: increasing trainable ranks stabilizes learning trajectories, while reducing output confidence mitigates entrapment in no-learning zones. Overall, the ghost mechanism reveals how the computational demands of a task constrain the optimization landscape, demonstrating that well-known learning difficulties in RNNs partly arise from the dynamical systems they must learn to implement.

Fluorescent genetically encoded voltage indicators report transmembrane potentials of targeted cell types. However, voltage-imaging instrumentation has lacked the sensitivity to track spontaneous or evoked high-frequency voltage oscillations in neural populations. Here, we describe two complementary TEMPO (transmembrane electrical measurements performed optically) voltage-sensing technologies that capture neural oscillations up to ∼100 Hz. Fiber-optic TEMPO achieves ∼10-fold greater sensitivity than prior photometric voltage sensing, allows hour-long recordings, and monitors two neuron classes per fiber-optic probe in freely moving mice. With it, we uncovered cross-frequency-coupled theta- and gamma-range oscillations and characterized excitatory-inhibitory neural dynamics during hippocampal ripples and visual cortical processing. The TEMPO mesoscope images voltage activity in two cell classes across an ∼8-mm-wide field of view in head-fixed animals. In awake mice, it revealed sensory-evoked excitatory-inhibitory neural interactions and traveling gamma and 3-7 Hz waves in visual cortex and bidirectional propagation directions for both hippocampal theta and beta waves. These technologies have widespread applications probing diverse oscillations and neuron-type interactions in healthy and diseased brains.

The capacity to engineer organisms with multiple transgenic components is crucial to synthetic biology and basic biology research. For the former field, transgenic organisms allow the creation of novel biological functions; for the latter, such organisms provide potent means of dissecting complex biological pathways. However, the size limitations of a single transgenesis event and challenges associated with the assembly of multiple DNA fragments hinder the efficient integration of multiple transgenes. To overcome these hurdles, here we introduce a building block for synthetic design termed an integrated genetic array (IGA), which incorporates all genetic components into a single locus to prevent their separation during genetic manipulations. Since the natural recombination rate for genes located in the same locus is near zero, to construct IGAs we developed the Super Recombinator (SuRe) system, which uses CRISPR/Cas9, alone or in combination with site-specific serine recombinases, for in vivo transgene recombination at a single genomic locus. SuRe effectively doubles the number of elements assembled in each recombination round, exponentially accelerating IGA construction. By preventing the separation of transgenic elements, SuRe greatly reduces screening burdens, as validated here through studies of Drosophila melanogaster and Caenorhabditis elegans . To optimize SuRe, we compared CRISPR/Cas9-induced homology-directed recombination to site-specific recombination using various serine recombinases. Optimized versions of SuRe achieved efficiency and fidelity values near their theoretical maxima and allowed the generation of recombinant products up to 4.2 Mbp in size in Drosophila . Using SuRe, we created fruit flies with 12 transgenic elements for fluorescence voltage imaging of neural activity in precisely defined cell-types. Mathematical modeling of the scalability of SuRe to large transgene assemblies showed that integration times and gene assembly workloads respectively scale logarithmically and linearly with the number of transgenes, both major improvements over conventional approaches. Overall, SuRe enables the efficient integration of multiple genes at individual loci, up to the chromosomal scale. ### Competing Interest Statement The authors of this manuscript (J Luo, MJ Schnitzer, C Huang) are also inventors on the related patent application "Genetic tools for recombining transgenes at the same locus" (US Patent App. 18/248,978, 2023).

Although individual neurons and neural populations exhibit the phenomenon of representational drift, perceptual and behavioral outputs of many neural circuits can remain stable across time scales over which representational drift is substantial. These observations motivate a dynamical systems framework for neural network activity that focuses on the concept of latent processing units, core elements for robust coding and computation embedded in collective neural dynamics. Our theoretical treatment of these latent processing units yields five key attributes of computing through neural network dynamics. First, neural computations that are low-dimensional can nevertheless generate high-dimensional neural dynamics. Second, the manifolds defined by neural dynamical trajectories exhibit an inherent coding redundancy as a direct consequence of the universal computing capabilities of the underlying dynamical system. Third, linear readouts or decoders of neural population activity can suffice to optimally subserve downstream circuits controlling behavioral outputs. Fourth, whereas recordings from thousands of neurons may suffice for near optimal decoding from instantaneous neural activity patterns, experimental access to millions of neurons may be necessary to predict neural ensemble dynamical trajectories across timescales of seconds. Fifth, despite the variable activity of single cells, neural networks can maintain stable representations of the variables computed by the latent processing units, thereby making computations robust to representational drift. Overall, our framework for latent computation provides an analytic description and empirically testable predictions regarding how large systems of neurons perform robust computations via their collective dynamics.

Training recurrent neural networks (RNNs) is a high-dimensional process that requires updating numerous parameters. Therefore, it is often difficult to pinpoint the underlying learning mechanisms. To address this challenge, we propose to gain mechanistic insights into the phenomenon of abrupt learning by studying RNNs trained to perform diverse short-term memory tasks. In these tasks, RNN training begins with an initial search phase. Following a long period of plateau in accuracy, the values of the loss function suddenly drop, indicating abrupt learning. Analyzing the neural computation performed by these RNNs reveals geometric restructuring (GR) in their phase spaces prior to the drop. To promote these GR events, we introduce a temporal consistency regularization that accelerates (bioplausible) training, facilitates attractor formation, and enables efficient learning in strongly connected networks. Our findings offer testable predictions for neuroscientists and emphasize the need for goal-agnostic secondary mechanisms to facilitate learning in biological and artificial networks.

Placebo effects are notable demonstrations of mind-body interactions1,2. During pain perception, in the absence of any treatment, an expectation of pain relief can reduce the experience of pain-a phenomenon known as placebo analgesia3-6. However, despite the strength of placebo effects and their impact on everyday human experience and the failure of clinical trials for new therapeutics7, the neural circuit basis of placebo effects has remained unclear. Here we show that analgesia from the expectation of pain relief is mediated by rostral anterior cingulate cortex (rACC) neurons that project to the pontine nucleus (rACC→Pn)-a precerebellar nucleus with no established function in pain. We created a behavioural assay that generates placebo-like anticipatory pain relief in mice. In vivo calcium imaging of neural activity and electrophysiological recordings in brain slices showed that expectations of pain relief boost the activity of rACC→Pn neurons and potentiate neurotransmission in this pathway. Transcriptomic studies of Pn neurons revealed an abundance of opioid receptors, further suggesting a role in pain modulation. Inhibition of the rACC→Pn pathway disrupted placebo analgesia and decreased pain thresholds, whereas activation elicited analgesia in the absence of placebo conditioning. Finally, Purkinje cells exhibited activity patterns resembling those of rACC→Pn neurons during pain-relief expectation, providing cellular-level evidence for a role of the cerebellum in cognitive pain modulation. These findings open the possibility of targeting this prefrontal cortico-ponto-cerebellar pathway with drugs or neurostimulation to treat pain.

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.