Behavioral Timescale Synaptic Plasticity (BTSP) for biologically plausible credit assignment across multiple layers via top-down gating of dendritic plasticity
A central problem in biological learning is how information about the outcome of a decision or behavior can be used to reliably guide learning across distributed neural circuits while obeying biological constraints. This “credit assignment” problem is commonly solved in artificial neural networks through supervised gradient descent and the backpropagation algorithm. In contrast, biological learning is typically modelled using unsupervised Hebbian learning rules. While these rules only use local information to update synaptic weights, and are sometimes combined with weight constraints to reflect a diversity of excitatory (only positive weights) and inhibitory (only negative weights) cell types, they do not prescribe a clear mechanism for how to coordinate learning across multiple layers and propagate error information accurately across the network. In recent years, several groups have drawn inspiration from the known dendritic non-linearities of pyramidal neurons to propose new learning rules and network architectures that enable biologically plausible multi-layer learning by processing error information in segregated dendrites. Meanwhile, recent experimental results from the hippocampus have revealed a new form of plasticity—Behavioral Timescale Synaptic Plasticity (BTSP)—in which large dendritic depolarizations rapidly reshape synaptic weights and stimulus selectivity with as little as a single stimulus presentation (“one-shot learning”). Here we explore the implications of this new learning rule through a biologically plausible implementation in a rate neuron network. We demonstrate that regulation of dendritic spiking and BTSP by top-down feedback signals can effectively coordinate plasticity across multiple network layers in a simple pattern recognition task. By analyzing hidden feature representations and weight trajectories during learning, we show the differences between networks trained with standard backpropagation, Hebbian learning rules, and BTSP.
Integrators in short- and long-term memory
The accumulation and storage of information in memory is a fundamental computation underlying animal behavior. In many brain regions and task paradigms, ranging from motor control to navigation to decision-making, such accumulation is accomplished through neural integrator circuits that enable external inputs to move a system’s population-wide patterns of neural activity along a continuous attractor. In the first portion of the talk, I will discuss our efforts to dissect the circuit mechanisms underlying a neural integrator from a rich array of anatomical, physiological, and perturbation experiments. In the second portion of the talk, I will show how the accumulation and storage of information in long-term memory may also be described by attractor dynamics, but now within the space of synaptic weights rather than neural activity. Altogether, this work suggests a conceptual unification of seemingly distinct short- and long-term memory processes.
Robustness in spiking networks: a geometric perspective
Neural systems are remarkably robust against various perturbations, a phenomenon that still requires a clear explanation. Here, we graphically illustrate how neural networks can become robust. We study spiking networks that generate low-dimensional representations, and we show that the neurons’ subthreshold voltages are confined to a convex region in a lower-dimensional voltage subspace, which we call a ‘bounding box.’ Any changes in network parameters (such as number of neurons, dimensionality of inputs, firing thresholds, synaptic weights, or transmission delays) can all be understood as deformations of this bounding box. Using these insights, we show that functionality is preserved as long as perturbations do not destroy the integrity of the bounding box. We suggest that the principles underlying robustness in these networks—low-dimensional representations, heterogeneity of tuning, and precise negative feedback—may be key to understanding the robustness of neural systems at the circuit level.
Generalizing theories of cerebellum-like learning
Since the theories of Marr, Ito, and Albus, the cerebellum has provided an attractive well-characterized model system to investigate biological mechanisms of learning. In recent years, theories have been developed that provide a normative account for many features of the anatomy and function of cerebellar cortex and cerebellum-like systems, including the distribution of parallel fiber-Purkinje cell synaptic weights, the expansion in neuron number of the granule cell layer and their synaptic in-degree, and sparse coding by granule cells. Typically, these theories focus on the learning of random mappings between uncorrelated inputs and binary outputs, an assumption that may be reasonable for certain forms of associative conditioning but is also quite far from accounting for the important role the cerebellum plays in the control of smooth movements. I will discuss in-progress work with Marjorie Xie, Samuel Muscinelli, and Kameron Decker Harris generalizing these learning theories to correlated inputs and general classes of smooth input-output mappings. Our studies build on earlier work in theoretical neuroscience as well as recent advances in the kernel theory of wide neural networks. They illuminate the role of pre-expansion structures in processing input stimuli and the significance of sparse granule cell activity. If there is time, I will also discuss preliminary work with Jack Lindsey extending these theories beyond cerebellum-like structures to recurrent networks.
STDP and the transfer of rhythmic signals in the brain
Rhythmic activity in the brain has been reported in relation to a wide range of cognitive processes. Changes in the rhythmic activity have been related to pathological states. These observations raise the question of the origin of these rhythms: can the mechanisms responsible for generation of these rhythms and that allow the propagation of the rhythmic signal be acquired via a process of learning? In my talk I will focus on spike timing dependent plasticity (STDP) and examine under what conditions this unsupervised learning rule can facilitate the propagation of rhythmic activity downstream in the central nervous system. Next, the I will apply the theory of STDP to the whisker system and demonstrate how STDP can shape the distribution of preferred phases of firing in a downstream population. Interestingly, in both these cases STDP dynamics does not relax to a fixed-point solution, rather the synaptic weights remain dynamic. Nevertheless, STDP allows for the system to retain its functionality in the face of continuous remodeling of the entire synaptic population.
A geometric framework to predict structure from function in neural networks
The structural connectivity matrix of synaptic weights between neurons is a critical determinant of overall network function. However, quantitative links between neural network structure and function are complex and subtle. For example, many networks can give rise to similar functional responses, and the same network can function differently depending on context. Whether certain patterns of synaptic connectivity are required to generate specific network-level computations is largely unknown. Here we introduce a geometric framework for identifying synaptic connections required by steady-state responses in recurrent networks of rectified-linear neurons. Assuming that the number of specified response patterns does not exceed the number of input synapses, we analytically calculate all feedforward and recurrent connectivity matrices that can generate the specified responses from the network inputs. We then use this analytical characterization to rigorously analyze the solution space geometry and derive certainty conditions guaranteeing a non-zero synapse between neurons.