Publications

We present effective Geometric measures from Correlated Manifold Capacity theory (GCMC) for probing the functional structure in neural representations. We utilize a statistical physics approach to establish analytical connections between neural co-variabilities and downstream read-out efficiency. These effective geometric measures capture both stimulus-driven and behavior-driven structures in neural population activities, while extracting computationally-relevant information from neural data into intuitive and interpretable analysis descriptors. [pdf] bioRxiv, 2024

Humans and animals can recognize latent structures in their environment and apply this information to efficiently navigate the world. Several recent works argue that the brain supports these abilities by forming neural representations that encode such latent structures in flexible, generalizable ways. However, it remains unclear what aspects of neural population activity are contributing to these computational capabilities. Here, we develop an analytical theory linking the mesoscopic statistics of a neural population’s activity to generalization performance on a multi-task learning problem. [pdf] aRxiv, 2024

Recently, growth in our understanding of the computations performed in both biological and artificial neural networks has largely been driven by either low-level mechanistic studies or global normative approaches. However, concrete methodologies for bridging the gap between these levels of abstraction remain elusive. In this work, we investigate the internal mechanisms of neural networks through the lens of neural population geometry, aiming to provide understanding at an intermediate level of abstraction, as a way to bridge that gap [pdf] [bib] Conference on Parsimony and Learning, 2024

Prior to the onset of vision, neurons in the developing mammalian retina spontaneously fire in correlated activity patterns known as retinal waves. Experimental evidence suggests that retinal waves strongly influence the emergence of sensory representations before visual experience. We aim to model this early stage of functional development by using movies of neurally active developing retinas as pre-training data for neural networks [pdf] UniReps workshop, NeurIPS, 2023

Many different state-of-the-art deep neural networks yield similar neural predictions, but it remains unclear how to differentiate among models that perform equally well at predicting neural responses. To gain insight into this, we use a recent theoretical framework that relates the generalization error from regression to the spectral bias of the model activations and the alignment of the neural responses onto the learnable subspace of the model. [pdf] [bib] [code] Spotlight paper, NeurIPS, 2023

Self-supervised Learning (SSL) provides a strategy for constructing useful representations of images without relying on hand-assigned labels. Many such methods aim to map distinct views of the same scene or object to nearby points in the representation space, while employing some constraint to prevent representational collapse. Here we recast the problem in terms of efficient coding by adopting manifold capacity.[pdf][bib] NeurIPS, 2023

Social learning (SL) through experience with conspecifics can facilitate the acquisition of many behaviors. Thus, when Mongolian gerbils are exposed to a demonstrator performing an auditory discrimination task, their subsequent task acquisition is facilitated, even in the absence of visual cues. Here, we show that transient inactivation of auditory cortex (AC) during exposure caused a significant delay in task acquisition during the subsequent practice phase, suggesting that AC activity is necessary for SL. [pdf][bib] Nature Communications, 2023

In this letter, we calculate how correlations between object representations affect the capacity, a measure of linear separability. We show that for spherical object manifolds, introducing correlations between centroids effectively pushes the spheres closer together, while introducing correlations between the spheres’ axes effectively shrinks their radii, revealing a duality between neural correlations and geometry [pdf][bib][code] Physical Review Letters, 2023

[pdf][bib] Trends in Cognitive Sciences, 2023

[pdf] [bib] PNAS, 2023

Understanding the asymptotic behavior of gradient-descent training of deep neural networks is essential for revealing inductive biases and improving network performance. We derive the infinite-time training limit of a mathematically tractable class of deep nonlinear neural networks, gated linear networks (GLNs), and generalize these results to gated networks described by general homogeneous polynomials. [pdf] [bib] arXiv, 2022

Local divisive normalization provides a phenomenological description of many nonlinear response properties of neurons across visual cortical areas. To gain insight into the utility of this operation, we studied the effects on AlexNet of a local divisive normalization between features, with learned parameters. [pdf] [bib] ICLR, 2022

We highlight recent studies of neural population geometry: untangling in perception, classification theory of manifolds, abstraction in cognitive systems, topology underlying cognitive maps, dynamic untangling in motor systems, and a dynamic approach to cognition. [pdf] [bib] Current Opinion in Neurobiology, 2021

Here, we explore the extent to which a globally broadcast learning signal, coupled with local weight updates, enables training of DNNs. We present both a learning rule, called global error-vector broadcasting (GEVB), and a class of DNNs, called vectorized nonnegative networks (VNNs), inwhich this learning rule operates. [pdf] [code] [bib] NeurIPS, 2021

Using recently developed geometrical techniques from computational neuroscience, we investigate how adversarial perturbations influence the internal representations of standard, adversarially trained, and biologically-inspired stochastic networks. We find distinct geometric signatures for each type of network, revealing different mechanisms for achieving robust representations. [pdf] [code] [bib] NeurIPS, 2021

It is not entirely clear what aspects of sentence-level syntax are captured by vector-based language representations, nor how (if at all) they are built along the stacked layers of the network. In this paper, we aim to address such questions with a general class of interventional, input perturbation-based analyses of representations from pretrained language models. Importing from computational and cognitive neuroscience the notion of representational invariance, we perform a series of probes designed to test the sensitivity of these representations to several kinds of structure in sentences. [pdf] [bib] ACL Workshop, Representation Learning for NLP, 2021

Although adversarial training is successful at mitigating adversarial attacks, the behavioral differences between adversarially-trained (AT) models and standard models are still poorly understood. Motivated by a recent study on learning robustness without input perturbations by distilling an AT model, we explore what is learned during adversarial training by analyzing the distribution of logits in AT models. [pdf] [bib] arXiv, 2021

To examine the structure of when and where memorization occurs in a deep network, we use a recently developed replica-based mean field theoretic geometric analysis method. We find that all layers preferentially learn from examples which share features, and link this behavior to generalization performance.[pdf] [bib] ICLR, 2021

We utilize mean-field theoretic manifold analysis, a recent technique from computational neuroscience that connects geometry of feature representations with linear separability of classes, to analyze language representations from large-scale contextual embedding models. We explore representations from different model families (BERT, RoBERTa, GPT, etc.) and find evidence for emergence of linguistic manifolds across layer depth (e.g., manifolds for part-of-speech tags), especially in ambiguous data (i.e, words with multiple part-of-speech tags, or part-of-speech classes including many words). [pdf] [code] [bib] ICML, 2020

We demonstrate that changes in the geometry of the associated object manifolds underlie this improved capacity, and shed light on the functional roles different levels in the hierarchy play to achieve it, through orchestrated reduction of manifolds’ radius, dimensionality and inter-manifold correlations. [pdf] [code] [bib] Nature Communications, 2020

In this work, we investigate the robustness to perturbations in neural networks by juxtaposing experimental results regarding the covariance spectrum of neural representations in the mouse V1 (Stringer et al) with artificial neural networks. We use adversarial robustness to probe Stringer et al's theory regarding the causal role of a 1/n covariance spectrum. [pdf] [bib] NeurIPS, 2020

Deep neural networks have achieved impressive performance in audio processing applications, both as sub-components of larger systems and as complete end-to-end systems by themselves. Despite their empirical successes, comparatively little is understood about how these audio models accomplish these tasks.In this work, we employ a recently developed statistical mechanical theory that connects geometric properties of network representations and the separability of classes to probe how information is untangled within neural networks trained to recognize speech. [pdf] [code] [bib] NeurIPS, 2019

We develop a statistical mechanical theory for the linear classification of manifolds with arbitrary geometry, revealing a remarkable relation to the mathematics of conic decomposition. We show how special anchor points on the manifolds can be used to define novel geometrical measures of radius and dimension, which can explain the classification capacity for manifolds of various geometries. [pdf] [bib] Physical Review X, 2018

[pdf] [bib] Neural Computation, 2018

We present a theory that characterizes the ability of a linear readout network, the perceptron, to classify objects from variable neural responses. We show how the readout perceptron capacity depends on the dimensionality, size, and shape of the object manifolds in its input neural representation. [pdf] [bib] Physical Review E, 2016