Keynote & Tutorial

Monday, August 3, 4:30 – 6:15 pm, Skirball Theater

Play YouTube Recording

Adaptive, degenerate, and yet comparable? Rethinking representational comparisons

     
Erin Grant¹, Lukas Braun², Eleanor Holton³, Marvin Theiss⁴, ¹ University of Alberta, ² Allen Institute, ³ Princeton University, ⁴ University of Tübingen

Abstract

Comparing patterns of neural activity within and between biological and artificial systems has become a core methodology in neuroscience, psychology, and machine learning. Motivated by the goal of advancing our understanding of neural computation, representational comparisons are used to infer shared or divergent computations in minds and machines. However, neural network theory challenges the assumption that representational similarity generally provides a measure of computational similarity and vice versa. This tension arises from two defining features of biological and artificial neural networks: adaptivity and degeneracy. While internal representations are adapted to task demands and objectives, many distinct network configurations with distinct internal representations can implement the same behavior. Adaptivity therefore motivates the use of artificial neural networks as normative models of representation learning, whereas degeneracy challenges the assumption that comparing patterns of neural activity is, by itself, a well-posed basis for inferring and comparing computation. Starting from simple two-layer linear networks and extending to deep nonlinear networks, we show how function and neural representation are dissociable and reveal theoretically grounded conditions under which representational comparisons become scientifically meaningful. We argue that in light of degeneracy, a central object of study in cognitive computational neuroscience should be representational plurality: the existence of distinct neural geometries that support identical behavior but differ in their downstream computational affordances. We show how representational plurality can be identified and investigated through theoretically motivated task design and behavioral readouts. Overall, the keynote uses neural network theory to delineate when representational geometry can and cannot support inference about computation, and argues for going beyond naive representational comparisons towards the study of representational formation, differentiation, and adaptation.

Tutorial Outline

In the tutorial, participants will learn how neural network theory challenges three common assumptions underlying representational comparisons: (1) that functional equivalence implies representational alignment (Yamins et al., PNAS 2014), (2) that increasing task demands drive representational convergence (Poldrack, Synthese 2021; Cao & Yamins, Cognitive Systems Research 2024; Huh et al., ICML 2024), and (3) that each task has a privileged representation or representational geometry (Kriegeskorte et al., PNAS 2006; Kriegeskorte et al., Front Syst Neurosci 2008). The tutorial is designed for participants with basic familiarity with Python and NumPy; no knowledge of neural network training or specialized deep learning libraries is required.

In Part 1, we will use analytically tractable deep linear networks as a canonical model for mapping inputs to hidden activation patterns to outputs. Through small coding exercises and interactive visualizations, participants will develop intuition for how function and representation can be doubly dissociable: networks can implement identical or distinct functions while exhibiting identical or distinct representational geometries. This directly challenges the assumption that functional equivalence entails representational alignment.

In Part 2, we will extend the analysis to simple deep nonlinear networks. Using the XOR task, participants will learn to distinguish between degeneracies that can be uncovered using held-out data and degeneracies that preserve the input-output function for all possible inputs while changing internal representations. We will show how these degeneracies in detail depend on the nonlinear activation function and the level of overparameterization within the network. This shows that representational degeneracies in nonlinear networks are dissociable from task demands.

In Part 3, participants will perform a searchlight-like analysis of three networks that solve the same task using arbitrary task-agnostic, orthogonal, or task-specific representational geometries. They will learn how partially withheld training data and behavioral readouts can reveal otherwise hidden differences in representational geometry. This motivates representational plurality: the idea that multiple geometries can support the same task while differing in their downstream computational affordances, such as transfer or memorization.

Overall, the tutorial will give participants a theoretical and practical framework for dissociating function from representation, interpreting representational comparison methods more critically, and identifying experimental questions and testing hypotheses about the computational consequences of different representational geometries.