Symmetry-Based Representations for Artificial and Biological General Intelligence

Abstract

Biological intelligence is remarkable in its ability to produce complex behavior in many diverse situations through data efficient, generalizable, and transferable skill acquisition. It is believed that learning “good” sensory representations is important for enabling this, however there is little agreement as to what a good representation should look like. In this review article we are going to argue that symmetry transformations are a fundamental principle that can guide our search for what makes a good representation. The idea that there exist transformations (symmetries) that affect some aspects of the system but not others, and their relationship to conserved quantities has become central in modern physics, resulting in a more unified theoretical framework and even ability to predict the existence of new particles. Recently, symmetries have started to gain prominence in machine learning too, resulting in more data efficient and generalizable algorithms that can mimic some of the complex behaviors produced by biological intelligence. Finally, first demonstrations of the importance of symmetry transformations for representation learning in the brain are starting to arise in neuroscience. Taken together, the overwhelming positive effect that symmetries bring to these disciplines suggest that they may be an important general framework that determines the structure of the universe, constrains the nature of natural tasks and consequently shapes both biological and artificial intelligence.

Compositional Sequence Generation in the Entorhinal–Hippocampal System

“…In the present context of dynamical systems, propagators correspond to a group of symmetries acting upon the set of distributions of states in the system. This perspective highlights connections to recent work in unsupervised learning seeking to extract disentangled representations from a given source of data [ 52 , 53 ], which coalesced around the concept of identifying independent symmetries within a dataset [ 54 , 55 , 56 ]. With respect to our work, each of these symmetries would be identified with a particular generator and associated grid module, which could then be generatively composed in the EHC architectures we have outlined.…”

Abstraction of reward context facilitates relative reward coding in neural populations of the anterior cingulate cortex

“…In machine learning, the ability to represent a task-relevant feature invariant to others in the environment can lead to efficient performance of high-level tasks. For instance, object representations that are invariant to illumination or orientation improve object recognition performance (57). In broader cognitive operations, concept abstraction allows behavior to be more flexible by adapting to different scenarios and transferring to new tasks.…”

“…Learning invariant representations can be accomplished by decomposing inputs into separate generative factors, such that each factor’s representation lies in its own subspace that is invariant to transformations defined by the others. This process is referred to as ‘untangling’ or ‘disentangling’ and has been identified as part of the solution to many complex tasks in neuroscience and machine learning (60, 61, 62, 63, 64). For instance, disentangled representations of cue valence and response direction in our task would mean that the transformation of moving in the neural activity space from left to right motor responses should not affect the representation of cue valence, which is consistent with our data.…”

“…Since disentangled representations in general need not be defined in linear spaces, the associated transformations need not be linear with respect to the representation’s embedding vector space (here the neural activity space). However, if the transformations are indeed linear, they preserve the structure of the embedding vector space, and the associated representations have been referred to as ‘linearly disentangled’ (60). The theory of abstraction described by Bernardi et al .…”

Spatio-temporally separable non-linear latent factor learning: an application to somatomotor cortex fMRI data

“…The distributions are referred to as the factors f t in this work. The reason we model the factors as distributions is that the loss function of variational autoencoders [26] has been shown to encourage disentanglement of the separate factors in each distribution [3,[16][17][18].…”