dynamical systems
Latest
Federico Stella
The project will focus on the computational investigation of the role of neural reactivations in memory. Since their discovery neural reactivations happening during sleep have emerged as an exceptional tool to investigate the process of memory formation in the brain. This phenomenon has been mostly associated with the hippocampus, an area known for its role in the processing of new memories and their initial storage. Continuous advancements in data acquisition techniques are giving us an unprecedented access to the activity of large-scale networks during sleep, in the hippocampus and in other cortical regions. At the same time, our theoretical understanding of the computations underlying neural reactivations and more in general memory representations, has only began to take shape. Combining mathematical modeling of neural networks and analysis of existing dataset, we will address some key aspects of this phenomenon such as: 1) The role of different sleep phases in regulating the reactivation process and in modulating the evolution of a memory trace. 2) The relationship of hippocampal reactivations to the process of (semantic) learning and knowledge generalization. 3) The relevance of reactivation statistical properties for learning in cortico-hippocampal networks.
Probing neural population dynamics with recurrent neural networks
Large-scale recordings of neural activity are providing new opportunities to study network-level dynamics with unprecedented detail. However, the sheer volume of data and its dynamical complexity are major barriers to uncovering and interpreting these dynamics. I will present latent factor analysis via dynamical systems, a sequential autoencoding approach that enables inference of dynamics from neuronal population spiking activity on single trials and millisecond timescales. I will also discuss recent adaptations of the method to uncover dynamics from neural activity recorded via 2P Calcium imaging. Finally, time permitting, I will mention recent efforts to improve the interpretability of deep-learning based dynamical systems models.
Reimagining the neuron as a controller: A novel model for Neuroscience and AI
We build upon and expand the efficient coding and predictive information models of neurons, presenting a novel perspective that neurons not only predict but also actively influence their future inputs through their outputs. We introduce the concept of neurons as feedback controllers of their environments, a role traditionally considered computationally demanding, particularly when the dynamical system characterizing the environment is unknown. By harnessing a novel data-driven control framework, we illustrate the feasibility of biological neurons functioning as effective feedback controllers. This innovative approach enables us to coherently explain various experimental findings that previously seemed unrelated. Our research has profound implications, potentially revolutionizing the modeling of neuronal circuits and paving the way for the creation of alternative, biologically inspired artificial neural networks.
The balance hypothesis for the avian lumbosacral organ and an exploration of its morphological variation
The centrality of population-level factors to network computation is demonstrated by a versatile approach for training spiking networks
Neural activity is often described in terms of population-level factors extracted from the responses of many neurons. Factors provide a lower-dimensional description with the aim of shedding light on network computations. Yet, mechanistically, computations are performed not by continuously valued factors but by interactions among neurons that spike discretely and variably. Models provide a means of bridging these levels of description. We developed a general method for training model networks of spiking neurons by leveraging factors extracted from either data or firing-rate-based networks. In addition to providing a useful model-building framework, this formalism illustrates how reliable and continuously valued factors can arise from seemingly stochastic spiking. Our framework establishes procedures for embedding this property in network models with different levels of realism. The relationship between spikes and factors in such networks provides a foundation for interpreting (and subtly redefining) commonly used quantities such as firing rates.
Dynamic endocrine modulation of the nervous system
Sex hormones are powerful neuromodulators of learning and memory. In rodents and nonhuman primates estrogen and progesterone influence the central nervous system across a range of spatiotemporal scales. Yet, their influence on the structural and functional architecture of the human brain is largely unknown. Here, I highlight findings from a series of dense-sampling neuroimaging studies from my laboratory designed to probe the dynamic interplay between the nervous and endocrine systems. Individuals underwent brain imaging and venipuncture every 12-24 hours for 30 consecutive days. These procedures were carried out under freely cycling conditions and again under a pharmacological regimen that chronically suppresses sex hormone production. First, resting state fMRI evidence suggests that transient increases in estrogen drive robust increases in functional connectivity across the brain. Time-lagged methods from dynamical systems analysis further reveals that these transient changes in estrogen enhance within-network integration (i.e. global efficiency) in several large-scale brain networks, particularly Default Mode and Dorsal Attention Networks. Next, using high-resolution hippocampal subfield imaging, we found that intrinsic hormone fluctuations and exogenous hormone manipulations can rapidly and dynamically shape medial temporal lobe morphology. Together, these findings suggest that neuroendocrine factors influence the brain over short and protracted timescales.
Extracting computational mechanisms from neural data using low-rank RNNs
An influential theory in systems neuroscience suggests that brain function can be understood through low-dimensional dynamics [Vyas et al 2020]. However, a challenge in this framework is that a single computational task may involve a range of dynamic processes. To understand which processes are at play in the brain, it is important to use data on neural activity to constrain models. In this study, we present a method for extracting low-dimensional dynamics from data using low-rank recurrent neural networks (lrRNNs), a highly expressive and understandable type of model [Mastrogiuseppe & Ostojic 2018, Dubreuil, Valente et al. 2022]. We first test our approach using synthetic data created from full-rank RNNs that have been trained on various brain tasks. We find that lrRNNs fitted to neural activity allow us to identify the collective computational processes and make new predictions for inactivations in the original RNNs. We then apply our method to data recorded from the prefrontal cortex of primates during a context-dependent decision-making task. Our approach enables us to assign computational roles to the different latent variables and provides a mechanistic model of the recorded dynamics, which can be used to perform in silico experiments like inactivations and provide testable predictions.
Nonlinear computations in spiking neural networks through multiplicative synapses
The brain efficiently performs nonlinear computations through its intricate networks of spiking neurons, but how this is done remains elusive. While recurrent spiking networks implementing linear computations can be directly derived and easily understood (e.g., in the spike coding network (SCN) framework), the connectivity required for nonlinear computations can be harder to interpret, as they require additional non-linearities (e.g., dendritic or synaptic) weighted through supervised training. Here we extend the SCN framework to directly implement any polynomial dynamical system. This results in networks requiring multiplicative synapses, which we term the multiplicative spike coding network (mSCN). We demonstrate how the required connectivity for several nonlinear dynamical systems can be directly derived and implemented in mSCNs, without training. We also show how to precisely carry out higher-order polynomials with coupled networks that use only pair-wise multiplicative synapses, and provide expected numbers of connections for each synapse type. Overall, our work provides an alternative method for implementing nonlinear computations in spiking neural networks, while keeping all the attractive features of standard SCNs such as robustness, irregular and sparse firing, and interpretable connectivity. Finally, we discuss the biological plausibility of mSCNs, and how the high accuracy and robustness of the approach may be of interest for neuromorphic computing.
Flexible multitask computation in recurrent networks utilizes shared dynamical motifs
Flexible computation is a hallmark of intelligent behavior. Yet, little is known about how neural networks contextually reconfigure for different computations. Humans are able to perform a new task without extensive training, presumably through the composition of elementary processes that were previously learned. Cognitive scientists have long hypothesized the possibility of a compositional neural code, where complex neural computations are made up of constituent components; however, the neural substrate underlying this structure remains elusive in biological and artificial neural networks. Here we identified an algorithmic neural substrate for compositional computation through the study of multitasking artificial recurrent neural networks. Dynamical systems analyses of networks revealed learned computational strategies that mirrored the modular subtask structure of the task-set used for training. Dynamical motifs such as attractors, decision boundaries and rotations were reused across different task computations. For example, tasks that required memory of a continuous circular variable repurposed the same ring attractor. We show that dynamical motifs are implemented by clusters of units and are reused across different contexts, allowing for flexibility and generalization of previously learned computation. Lesioning these clusters resulted in modular effects on network performance: a lesion that destroyed one dynamical motif only minimally perturbed the structure of other dynamical motifs. Finally, modular dynamical motifs could be reconfigured for fast transfer learning. After slow initial learning of dynamical motifs, a subsequent faster stage of learning reconfigured motifs to perform novel tasks. This work contributes to a more fundamental understanding of compositional computation underlying flexible general intelligence in neural systems. We present a conceptual framework that establishes dynamical motifs as a fundamental unit of computation, intermediate between the neuron and the network. As more whole brain imaging studies record neural activity from multiple specialized systems simultaneously, the framework of dynamical motifs will guide questions about specialization and generalization across brain regions.
Neural Population Dynamics for Skilled Motor Control
The ability to reach, grasp, and manipulate objects is a remarkable expression of motor skill, and the loss of this ability in injury, stroke, or disease can be devastating. These behaviors are controlled by the coordinated activity of tens of millions of neurons distributed across many CNS regions, including the primary motor cortex. While many studies have characterized the activity of single cortical neurons during reaching, the principles governing the dynamics of large, distributed neural populations remain largely unknown. Recent work in primates has suggested that during the execution of reaching, motor cortex may autonomously generate the neural pattern controlling the movement, much like the spinal central pattern generator for locomotion. In this seminar, I will describe recent work that tests this hypothesis using large-scale neural recording, high-resolution behavioral measurements, dynamical systems approaches to data analysis, and optogenetic perturbations in mice. We find, by contrast, that motor cortex requires strong, continuous, and time-varying thalamic input to generate the neural pattern driving reaching. In a second line of work, we demonstrate that the cortico-cerebellar loop is not critical for driving the arm towards the target, but instead fine-tunes movement parameters to enable precise and accurate behavior. Finally, I will describe my future plans to apply these experimental and analytical approaches to the adaptive control of locomotion in complex environments.
Credit Assignment in Neural Networks through Deep Feedback Control
The success of deep learning sparked interest in whether the brain learns by using similar techniques for assigning credit to each synaptic weight for its contribution to the network output. However, the majority of current attempts at biologically-plausible learning methods are either non-local in time, require highly specific connectivity motives, or have no clear link to any known mathematical optimization method. Here, we introduce Deep Feedback Control (DFC), a new learning method that uses a feedback controller to drive a deep neural network to match a desired output target and whose control signal can be used for credit assignment. The resulting learning rule is fully local in space and time and approximates Gauss-Newton optimization for a wide range of feedback connectivity patterns. To further underline its biological plausibility, we relate DFC to a multi-compartment model of cortical pyramidal neurons with a local voltage-dependent synaptic plasticity rule, consistent with recent theories of dendritic processing. By combining dynamical system theory with mathematical optimization theory, we provide a strong theoretical foundation for DFC that we corroborate with detailed results on toy experiments and standard computer-vision benchmarks.
Dynamical Neuromorphic Systems
In this talk, I aim to show that the dynamical properties of emerging nanodevices can accelerate the development of smart, and environmentally friendly chips that inherently learn through their physics. The goal of neuromorphic computing is to draw inspiration from the architecture of the brain to build low-power circuits for artificial intelligence. I will first give a brief overview of the state of the art of neuromorphic computing, highlighting the opportunities offered by emerging nanodevices in this field, and the associated challenges. I will then show that the intrinsic dynamical properties of these nanodevices can be exploited at the device and algorithmic level to assemble systems that infer and learn though their physics. I will illustrate these possibilities with examples from our work on spintronic neural networks that communicate and compute through their microwave oscillations, and on an algorithm called Equilibrium Propagation that minimizes both the error and energy of a dynamical system.
Stability-Flexibility Dilemma in Cognitive Control: A Dynamical System Perspective
Constraints on control-dependent processing have become a fundamental concept in general theories of cognition that explain human behavior in terms of rational adaptations to these constraints. However, theories miss a rationale for why such constraints would exist in the first place. Recent work suggests that constraints on the allocation of control facilitate flexible task switching at the expense of the stability needed to support goal-directed behavior in face of distraction. We formulate this problem in a dynamical system, in which control signals are represented as attractors and in which constraints on control allocation limit the depth of these attractors. We derive formal expressions of the stability-flexibility tradeoff, showing that constraints on control allocation improve cognitive flexibility but impair cognitive stability. We provide evidence that human participants adapt higher constraints on the allocation of control as the demand for flexibility increases but that participants deviate from optimal constraints. In continuing work, we are investigating how collaborative performance of a group of individuals can benefit from individual differences defined in terms of balance between cognitive stability and flexibility.
Linking dimensionality to computation in neural networks
The link between behavior, learning and the underlying connectome is a fundamental open problem in neuroscience. In my talk I will show how it is possible to develop a theory that bridges across these three levels (animal behavior, learning and network connectivity) based on the geometrical properties of neural activity. The central tool in my approach is the dimensionality of neural activity. I will link animal complex behavior to the geometry of neural representations, specifically their dimensionality; I will then show how learning shapes changes in such geometrical properties and how local connectivity properties can further regulate them. As a result, I will explain how the complexity of neural representations emerges from both behavioral demands (top-down approach) and learning or connectivity features (bottom-up approach). I will build these results regarding neural dynamics and representations starting from the analysis of neural recordings, by means of theoretical and computational tools that blend dynamical systems, artificial intelligence and statistical physics approaches.
Neural manifolds for the stable control of movement
Animals perform learned actions with remarkable consistency for years after acquiring a skill. What is the neural correlate of this stability? We explore this question from the perspective of neural populations. Recent work suggests that the building blocks of neural function may be the activation of population-wide activity patterns: neural modes that capture the dominant co-variation patterns of population activity and define a task specific low dimensional neural manifold. The time-dependent activation of the neural modes results in latent dynamics. We hypothesize that the latent dynamics associated with the consistent execution of a behaviour need to remain stable, and use an alignment method to establish this stability. Once identified, stable latent dynamics allow for the prediction of various behavioural features via fixed decoder models. We conclude that latent cortical dynamics within the task manifold are the fundamental and stable building blocks underlying consistent behaviour.
Modeling gait dynamics with switching non-linear dynamical systems
Bernstein Conference 2024
Neural manifold discovery via dynamical systems
Bernstein Conference 2024
Using Dynamical Systems Theory to Improve Temporal Credit Assignment in Spiking Neural Networks
Bernstein Conference 2024
Data-driven dynamical systems model of epilepsy development simulates intervention strategies
COSYNE 2022
Dynamical systems analysis reveals a novel hypothalamic encoding of state in nodes controlling social behavior
COSYNE 2022
Modeling multi-region neural communication during decision making with recurrent switching dynamical systems
COSYNE 2022
Modeling multi-region neural communication during decision making with recurrent switching dynamical systems
COSYNE 2022
Decomposed linear dynamical systems for C. elegans functional connectivity
COSYNE 2023
Parsing neural dynamics with infinite recurrent switching linear dynamical systems
COSYNE 2023
Capturing condition dependence in neural dynamics with Gaussian process linear dynamical systems
COSYNE 2025
Neural manifold discovery via dynamical systems
COSYNE 2025
Task Structures Shape Underlying Dynamical Systems That Implement Computation
COSYNE 2025
Understanding the effects of neural perturbations using cell-type dynamical systems
COSYNE 2025
Decomposed Linear Dynamical Systems (dLDS) for learning the latent components of neural dynamics
Neuromatch 5
dynamical systems coverage
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