Relating circuit dynamics to computation: robustness and dimension-specific computation in cortical dynamics
Neural dynamics represent the hard-to-interpret substrate of circuit computations. Advances in large-scale recordings have highlighted the sheer spatiotemporal complexity of circuit dynamics within and across circuits, portraying in detail the difficulty of interpreting such dynamics and relating it to computation. Indeed, even in extremely simplified experimental conditions, one observes high-dimensional temporal dynamics in the relevant circuits. This complexity can be potentially addressed by the notion that not all changes in population activity have equal meaning, i.e., a small change in the evolution of activity along a particular dimension may have a bigger effect on a given computation than a large change in another. We term such conditions dimension-specific computation. Considering motor preparatory activity in a delayed response task we utilized neural recordings performed simultaneously with optogenetic perturbations to probe circuit dynamics. First, we revealed a remarkable robustness in the detailed evolution of certain dimensions of the population activity, beyond what was thought to be the case experimentally and theoretically. Second, the robust dimension in activity space carries nearly all of the decodable behavioral information whereas other non-robust dimensions contained nearly no decodable information, as if the circuit was setup to make informative dimensions stiff, i.e., resistive to perturbations, leaving uninformative dimensions sloppy, i.e., sensitive to perturbations. Third, we show that this robustness can be achieved by a modular organization of circuitry, whereby modules whose dynamics normally evolve independently can correct each other’s dynamics when an individual module is perturbed, a common design feature in robust systems engineering. Finally, we will recent work extending this framework to understanding the neural dynamics underlying preparation of speech.
From spikes to factors: understanding large-scale neural computations
It is widely accepted that human cognition is the product of spiking neurons. Yet even for basic cognitive functions, such as the ability to make decisions or prepare and execute a voluntary movement, the gap between spikes and computation is vast. Only for very simple circuits and reflexes can one explain computations neuron-by-neuron and spike-by-spike. This approach becomes infeasible when neurons are numerous the flow of information is recurrent. To understand computation, one thus requires appropriate abstractions. An increasingly common abstraction is the neural ‘factor’. Factors are central to many explanations in systems neuroscience. Factors provide a framework for describing computational mechanism, and offer a bridge between data and concrete models. Yet there remains some discomfort with this abstraction, and with any attempt to provide mechanistic explanations above that of spikes, neurons, cell-types, and other comfortingly concrete entities. I will explain why, for many networks of spiking neurons, factors are not only a well-defined abstraction, but are critical to understanding computation mechanistically. Indeed, factors are as real as other abstractions we now accept: pressure, temperature, conductance, and even the action potential itself. I use recent empirical results to illustrate how factor-based hypotheses have become essential to the forming and testing of scientific hypotheses. I will also show how embracing factor-level descriptions affords remarkable power when decoding neural activity for neural engineering purposes.
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.
Spontaneous Emergence of Computation in Network Cascades
Neuronal network computation and computation by avalanche supporting networks are of interest to the fields of physics, computer science (computation theory as well as statistical or machine learning) and neuroscience. Here we show that computation of complex Boolean functions arises spontaneously in threshold networks as a function of connectivity and antagonism (inhibition), computed by logic automata (motifs) in the form of computational cascades. We explain the emergent inverse relationship between the computational complexity of the motifs and their rank-ordering by function probabilities due to motifs, and its relationship to symmetry in function space. We also show that the optimal fraction of inhibition observed here supports results in computational neuroscience, relating to optimal information processing.
Reconstruct cellular dynamics from single cell data
Recent advances of single cell techniques catalyzed quantitative studies on the dynamics of cell phenotypic transitions (CPT) emerging as a new field. However, fixed cell-based approaches have fundamental limits on revealing temporal information, and fluorescence-based live cell imaging approaches are technically challenging for multiplex long-term imaging. To tackle the challenges, we developed an integrated experimental/computational platform for reconstructing single cell phenotypic transition dynamics. Experimentally, we developed a live-cell imaging platform to record the phenotypic transition path of A549 VIM-RFP reporter cell line and unveil parallel paths of epithelial-to-mesenchymal transition (EMT). Computationally, we modified a finite temperature string method to reconstruct the reaction coordinate from the paths, and reconstruct a corresponding quasi-potential, which reveals that the EMT process resembles a barrier-less relaxation process. Our work demonstrates the necessity of extracting dynamical information of phenotypic transitions and the existence of a unified theoretical framework describing transition and relaxation dynamics in systems with and without detailed balance.
NMC4 Panel: Can we understand how the brain computes or should we focus on understanding learning
Panelists: - Surya Ganguli, Matteo Carandini, Anna Schapiro,Blake Richards. Moderator: Konrad Kording
Computational Neuroscience
Strong and weak principles of neural dimension reduction
Large-scale, single neuron resolution recordings are inherently high-dimensional, with as many dimensions as neurons. To make sense of them, for many the answer is: reduce the number of dimensions. In this talk I argue we can distinguish weak and strong principles of neural dimension reduction. The weak principle is that dimension reduction is a convenient tool for making sense of complex neural data. The strong principle is that dimension reduction moves us closer to how neural circuits actually operate and compute. Elucidating these principles is crucial, for which we subscribe to provides radically different interpretations of the same dimension reduction techniques applied to the same data. I outline experimental evidence for each principle, but illustrate how we could make either the weak or strong principles appear to be true based on innocuous looking analysis decisions. These insights suggest arguments over low and high-dimensional neural activity need better constraints from both experiment and theory.
Connectivity and computation in the cerebral cortex
Neuroscientists believe that perception, action and cognition arise from brain’s activity. A major challenge in neuroscience is to understand how brain’s complex circuits give rise to activity patterns that support these different functions. I will discuss different ways of mapping neural circuits in the brain, and how we can relate the structure of neural circuits to the computations that take place within them, with an emphasis on the visual system.
Computations in the basal ganglia
Synaptic, cellular, and circuit mechanisms for learning: insights from electric fish
Understanding learning in neural circuits requires answering a number of difficult questions: (1) What is the computation being performed and what is its behavioral significance? (2) What are the inputs required for the computation and how are they represented at the level of spikes? (3) What are the sites and rules governing plasticity, i.e. how do pre and post-synaptic activity patterns produce persistent changes in synaptic strength? (4) How does network connectivity and dynamics shape the computation being performed? I will discuss joint experimental and theoretical work addressing these questions in the context of the electrosensory lobe (ELL) of weakly electric mormyrid fish.