Seminars

Cognitive maps confer animals with flexible intelligence by representing spatial, temporal, and abstract relationships that can be used to shape thought, planning, and behavior. Cognitive maps have been observed in the hippocampus, but their algorithmic form and the processes by which they are learned remain obscure. Here, we employed large-scale, longitudinal two-photon calcium imaging to record activity from thousands of neurons in the CA1 region of the hippocampus while mice learned to efficiently collect rewards from two subtly different versions of linear tracks in virtual reality. The results provide a detailed view of the formation of a cognitive map in the hippocampus. Throughout learning, both the animal behavior and hippocampal neural activity progressed through multiple intermediate stages, gradually revealing improved task representation that mirrored improved behavioral efficiency. The learning process led to progressive decorrelations in initially similar hippocampal neural activity within and across tracks, ultimately resulting in orthogonalized representations resembling a state machine capturing the inherent struture of the task. We show that a Hidden Markov Model (HMM) and a biologically plausible recurrent neural network trained using Hebbian learning can both capture core aspects of the learning dynamics and the orthogonalized representational structure in neural activity. In contrast, we show that gradient-based learning of sequence models such as Long Short-Term Memory networks (LSTMs) and Transformers do not naturally produce such orthogonalized representations. We further demonstrate that mice exhibited adaptive behavior in novel task settings, with neural activity reflecting flexible deployment of the state machine. These findings shed light on the mathematical form of cognitive maps, the learning rules that sculpt them, and the algorithms that promote adaptive behavior in animals. The work thus charts a course toward a deeper understanding of biological intelligence and offers insights toward developing more robust learning algorithms in artificial intelligence.

Subsecond timing underlies nearly all sensory and motor activities across species and is critical to survival. While subsecond temporal information has been found across cortical and subcortical regions, it is unclear if it is generated locally and intrinsically or if it is a read out of a centralized clock-like mechanism. Indeed, mechanisms of subsecond timing at the circuit level are largely obscure. Primary sensory areas are well-suited to address these question as they have early access to sensory information and provide minimal processing to it: if temporal information is found in these regions, it is likely to be generated intrinsically and locally. We test this hypothesis by training mice to perform an audio-visual temporal pattern sensory discrimination task as we use 2-photon calcium imaging, a technique capable of recording population level activity at single cell resolution, to record activity in primary visual cortex (V1). We have found significant changes in network dynamics through mice’s learning of the task from naive to middle to expert levels. Changes in network dynamics and behavioral performance are well accounted for by an intrinsic model of timing in which the trajectory of q network through high dimensional state space represents temporal sensory information. Conversely, while we found evidence of other temporal encoding models, such as oscillatory activity, we did not find that they accounted for increased performance but were in fact correlated with the intrinsic model itself. These results provide insight into how subsecond temporal information is encoded mechanistically at the circuit level.

Higher cortical areas carry a wide range of sensory, cognitive, and motor signals supporting complex goal-directed behavior. These signals mix in heterogeneous responses of single neurons, making it difficult to untangle underlying mechanisms. I will present two approaches for revealing interpretable circuit mechanisms from heterogeneous neural responses during cognitive tasks. First, I will show a flexible nonparametric framework for simultaneously inferring population dynamics on single trials and tuning functions of individual neurons to the latent population state. When applied to recordings from the premotor cortex during decision-making, our approach revealed that populations of neurons encoded the same dynamic variable predicting choices, and heterogeneous firing rates resulted from the diverse tuning of single neurons to this decision variable. The inferred dynamics indicated an attractor mechanism for decision computation. Second, I will show an approach for inferring an interpretable network model of a cognitive task—the latent circuit—from neural response data. We developed a theory to causally validate latent circuit mechanisms via patterned perturbations of activity and connectivity in the high-dimensional network. This work opens new possibilities for deriving testable mechanistic hypotheses from complex neural response data.

The neurobiological mechanisms of arousal and anesthesia remain poorly understood. Recent evidence highlights the key role of interactions between the cerebral cortex and the diffusely projecting matrix thalamic nuclei. Here, we interrogate these processes in a whole-brain corticothalamic neural mass model endowed with targeted and diffusely projecting thalamocortical nuclei inferred from empirical data. This model captures key features seen in propofol anesthesia, including diminished network integration, lowered state diversity, impaired susceptibility to perturbation, and decreased corticocortical coherence. Collectively, these signatures reflect a suppression of information transfer across the cerebral cortex. We recover these signatures of conscious arousal by selectively stimulating the matrix thalamus, recapitulating empirical results in macaque, as well as wake-like information processing states that reflect the thalamic modulation of largescale cortical attractor dynamics. Our results highlight the role of matrix thalamocortical projections in shaping many features of complex cortical dynamics to facilitate the unique communication states supporting conscious awareness.

I will discuss work with Jack Lindsey modeling reinforcement learning for action selection in the basal ganglia. I will argue that the presence of multiple brain regions, in addition to the basal ganglia, that contribute to motor control motivates the need for an off-policy basal ganglia learning algorithm. I will then describe a biological implementation of such an algorithm that predicts tuning of dopamine neurons to a quantity we call "action surprise," in addition to reward prediction error. In the same model, an implementation of learning from a motor efference copy also predicts a novel solution to the problem of multiplexing feedforward and efference-related striatal activity. The solution exploits the difference between D1 and D2-expressing medium spiny neurons and leads to predictions about striatal dynamics.

Like all neural tissue, the retina has a high metabolic demand, and requires a constant supply of oxygen. Second and third order neurons are supplied by the retinal circulation, whose characteristics are similar to brain circulation. However, the photoreceptor region, which occupies half of the retinal thickness, is avascular, and relies on diffusion of oxygen from the choroidal circulation, whose properties are very different, as well as the retinal circulation. By fitting diffusion models to oxygen measurements made with oxygen microelectrodes, it is possible to understand the relative roles of the two circulations under normal conditions of light and darkness, and what happens if the retina is detached or the retinal circulation is occluded. Most of this work has been done in vivo in rat, cat, and monkey, but recent work in the isolated mouse retina will also be discussed.

Synaptic plasticity is known to be a key player in the brain’s life-long learning abilities. However, due to experimental limitations, the nature of the local changes at individual synapses and their link with emerging network-level computations remain unclear. I will present a numerical, meta-learning approach to deduce plasticity rules from either neuronal activity data and/or prior knowledge about the network's computation. I will first show how to recover known rules, given a human-designed loss function in rate networks, or directly from data, using an adversarial approach. Then I will present how to scale-up this approach to recurrent spiking networks using simulation-based inference.

The predictive map hypothesis provides a promising framework to model representations in the hippocampal formation. I will introduce a tractable implementation of a predictive map called the successor representation (SR), before presenting data showing that rats and humans display SR-like navigational choices on a novel open-field maze. Next, I will show how such a predictive map could be implemented using spatial representations found in the hippocampal formation, before finally presenting how such learning might be well approximated by phenomena that exist in the spatial memory system - namely spike-timing dependent plasticity and theta phase precession.

Intelligent behavior depends on the brain’s ability to anticipate future events. However, the learning rules that enable neurons to predict and fire ahead of sensory inputs remain largely unknown. We propose a plasticity rule based on pre-dictive processing, where the neuron learns a low-rank model of the synaptic input dynamics in its membrane potential. Neurons thereby amplify those synapses that maximally predict other synaptic inputs based on their temporal relations, which provide a solution to an optimization problem that can be implemented at the single-neuron level using only local information. Consequently, neurons learn sequences over long timescales and shift their spikes towards the first inputs in a sequence. We show that this mechanism can explain the development of anticipatory motion signaling and recall in the visual system. Furthermore, we demonstrate that the learning rule gives rise to several experimentally observed STDP (spike-timing-dependent plasticity) mechanisms. These findings suggest prediction as a guiding principle to orchestrate learning and synaptic plasticity in single neurons.

It was long hypothesized that natural systems might take advantage of the extended temporal and spatial correlations close to the critical point to improve their computational capabilities. However, on the other side, different distances to criticality were inferred from the recordings of nervous systems. In my talk, I discuss how including additional constraints on the processing time can shift the optimal operating point of the recurrent networks. Moreover, the data from the visual cortex of the monkeys during the attentional task indicate that they flexibly change the closeness to the critical point of the local activity. Overall it suggests that, as we would expect from common sense, the optimal state depends on the task at hand, and the brain adapts to it in a local and fast manner.

Activity dependent synaptic plasticity is considered to be a primary mechanism underlying learning and memory. Yet it is unclear whether plasticity rules such as STDP measured in vitro apply in vivo. Network models with STDP predict that activity patterns (e.g., place-cell spatial selectivity) should change much faster than observed experimentally. We address this gap by investigating a nonlinear calcium-based plasticity rule fit to experiments done in physiological conditions. In this model, LTP and LTD result from intracellular calcium transients arising almost exclusively from synchronous coactivation of pre- and postsynaptic neurons. We analytically approximate the full distribution of nonlinear calcium transients as a function of pre- and postsynaptic firing rates, and temporal correlations. This analysis directly relates activity statistics that can be measured in vivo to the changes in synaptic efficacy they cause. Our results highlight that both high-firing rates and temporal correlations can lead to significant changes to synaptic efficacy. Using a mean-field theory, we show that the nonlinear plasticity rule, without any fine-tuning, gives a stable, unimodal synaptic weight distribution characterized by many strong synapses which remain stable over long periods of time, consistent with electrophysiological and behavioral studies. Moreover, our theory explains how memories encoded by strong synapses can be preferentially stabilized by the plasticity rule. We confirmed our analytical results in a spiking recurrent network. Interestingly, although most synapses are weak and undergo rapid turnover, the fraction of strong synapses are sufficient for supporting realistic spiking dynamics and serve to maintain the network’s cluster structure. Our results provide a mechanistic understanding of how stable memories may emerge on the behavioral level from an STDP rule measured in physiological conditions. Furthermore, the plasticity rule we investigate is mathematically equivalent to other learning rules which rely on the statistics of coincidences, so we expect that our formalism will be useful to study other learning processes beyond the calcium-based plasticity rule.

One of Tali's cherished goals was to transform biology into physics. In his view, biologists were far too enamored by the details of the specific models they studied, losing sight of the big principles that may govern the behavior of these models. One such big principle that he suggested was the 'information bottleneck (IB) principle'. The iIB principle is an information-theoretical approach for extracting the relevant information that one random variable carries about another. Tali applied the IB principle to numerous problems in biology, gaining important insights in the process. Here I will describe two applications of the IB principle to neurobiological data. The first is the formalization of the notion of surprise that allowed us to rigorously estimate the memory duration and content of neuronal responses in auditory cortex, and the second is an application to behavior, allowing us to estimate 'optimal policies under information constraints' that shed interesting light on rat behavior.

CA3-CA1 synapses in the hippocampus are the initial locus of episodic memory. The action of acetylcholine alters cellular excitability, modifies neuronal networks, and triggers secondary signaling that directly affects long-term plasticity (LTP) (the cellular underpinning of memory). It is therefore considered a critical regulator of learning and memory in the brain. Its action via M4 metabotropic receptors in the presynaptic terminal of the CA3 neurons and M1 metabotropic receptors in the postsynaptic spines of CA1 neurons produce rich dynamics across multiple timescales. We developed a model to describe the activation of postsynaptic M1 receptors that leads to IP3 production from membrane PIP2 molecules. The binding of IP3 to IP3 receptors in the endoplasmic reticulum (ER) ultimately causes calcium release. This calcium release from the ER activates potassium channels like the calcium-activated SK channels and alters different aspects of synaptic signaling. In an independent signaling cascade, M1 receptors also directly suppress SK channels and the voltage-activated KCNQ2/3 channels, enhancing post-synaptic excitability. In the CA3 presynaptic terminal, we model the reduction of the voltage sensitivity of voltage-gated calcium channels (VGCCs) and the resulting suppression of neurotransmitter release by the action of the M4 receptors. Our results show that the reduced initial release probability because of acetylcholine alters short-term plasticity (STP) dynamics. We characterize the dichotomy of suppressing neurotransmitter release from CA3 neurons and the enhanced excitability of the postsynaptic CA1 spine. Mechanisms underlying STP operate over a few seconds, while those responsible for LTP last for hours, and both forms of plasticity have been linked with very distinct functions in the brain. We show that the concurrent suppression of neurotransmitter release and increased sensitivity conserves neurotransmitter vesicles and enhances the reliability in plasticity. Our work establishes a relationship between STP and LTP coordinated by neuromodulation with acetylcholine.

In the past several years, I have been involved in building a biologically realistic model of the monkey visual cortex. Work on one of the input layers (4Ca) of the primary visual cortex (V1) is now nearly complete, and I would like to share some of what I have learned with the community. After a brief overview of the model and its capabilities, I would like to focus on three sets of results that represent three different aspects of the modeling. They are: (i) emergent E-I dynamics in local circuits; (ii) how visual cortical neurons acquire their ability to detect edges and directions of motion, and (iii) a view across the cortical surface: nonequilibrium steady states (in analogy with statistical mechanics) and beyond.

Neurodegenerative diseases such as Alzheimer’s or Parkinson’s are devastating conditions with poorly understood mechanisms and no cure. Yet, a striking feature of these conditions is the characteristic pattern of invasion throughout the brain, leading to well-codified disease stages associated with various cognitive deficits and pathologies. How can we use mathematical modelling to gain insight into this process and, doing so, gain understanding about how the brain works? In this talk, I will show that by linking new mathematical theories to recent progress in imaging, we can unravel some of the universal features associated with dementia and, more generally, brain functions.

Classic studies show that in many species – from leech and cricket to primate – responses of neural populations can be quite successfully read out using a measure neural population activity termed the population vector. However, despite its successes, detailed analyses have shown that the standard population vector discards substantial amounts of information contained in the responses of a neural population, and so is unlikely to accurately describe how signal communication between parts of the nervous system. I will describe recent theoretical results showing how to modify the population vector expression in order to read out neural responses without information loss, ideally. These results make it possible to quantify the contribution of weakly tuned neurons to perception. I will also discuss numerical methods that can be used to minimize information loss when reading out responses of large neural populations.

Rajanlab designs neural network models constrained by experimental data, and reverse engineers them to figure out how brain circuits function in health and disease. Recently, we have been developing a powerful new theory-based framework for “in-vivo tract tracing” from multi-regional neural activity collected experimentally. We call this framework CURrent-Based Decomposition (CURBD). CURBD employs recurrent neural networks (RNNs) directly constrained, from the outset, by time series measurements acquired experimentally, such as Ca2+ imaging or electrophysiological data. Once trained, these data-constrained RNNs let us infer matrices quantifying the interactions between all pairs of modeled units. Such model-derived “directed interaction matrices” can then be used to separately compute excitatory and inhibitory input currents that drive a given neuron from all other neurons. Therefore different current sources can be de-mixed – either within the same region or from other regions, potentially brain-wide – which collectively give rise to the population dynamics observed experimentally. Source de-mixed currents obtained through CURBD allow an unprecedented view into multi-region mechanisms inaccessible from measurements alone. We have applied this method successfully to several types of neural data from our experimental collaborators, e.g., zebrafish (Deisseroth lab, Stanford), mice (Harvey lab, Harvard), monkeys (Rudebeck lab, Sinai), and humans (Rutishauser lab, Cedars Sinai), where we have discovered both directed interactions brain wide and inter-area currents during different types of behaviors. With this powerful framework based on data-constrained multi-region RNNs and CURrent Based Decomposition (CURBD), we ask if there are conserved multi-region mechanisms across different species, as well as identify key divergences.

Regulation of information flow in the brain is critical for many forms of behavior. In the process of sensory based decision-making, decisions about future actions are held in memory until enacted, making them potentially vulnerable to distracting sensory input. Therefore, gating of information flow from sensory to motor areas could protect memory from interference during decision-making, but the underlying network mechanisms are not understood. I will present our recent experimental and modeling work describing how information flow from the sensory cortex can be gated by state-dependent frontal cortex dynamics during decision-making in mice. Our results show that communication between brain regions can be regulated via attractor dynamics, which control the degree of commitment to an action, and reveal a novel mechanism of gating of neural information.

Birdsong emerges when a set of highly interconnected brain areas manage to generate a complex output. The similarities between birdsong production and human speech have positioned songbirds as unique animal models for studying learning and production of this complex motor skill. In this work, we developed a low dimensional model for a neural network in which the variables were the average activities of different neural populations within the nuclei of the song system. This neural network is active during production, perception and learning of birdsong. We performed electrophysiological experiments to record neural activity from one of these nuclei and found that the low dimensional model could reproduce the neural dynamics observed during the experiments. Also, this model could reproduce the respiratory motor patterns used to generate song. We showed that sparse activity in one of the neural nuclei could drive a more complex activity downstream in the neural network. This interdisciplinary work shows how low dimensional neural models can be a valuable tool for studying the emergence of complex motor tasks

Many networks in the nervous system possess an abundance of inhibition, which serves to shape and stabilize neural dynamics. The neurons in such networks exhibit intricate patterns of connectivity whose structure controls the allowed patterns of neural activity. In this work, we examine inhibitory threshold-linear networks whose dynamics are constrained by an underlying directed graph. We develop a set of parameter-independent graph rules that enable us to predict features of the dynamics, such as emergent sequences and dynamic attractors, from properties of the graph. These rules provide a direct link between the structure and function of these networks, and may provide new insights into how connectivity shapes dynamics in real neural circuits.