The Geometry of Concept Learning

Neurons in sensory areas encode/represent stimuli. Surprisingly, recent studies have suggest that, even during persistent performance, these representations are not stable and change over the course of days and weeks. We examine stimulus representations from fluorescence recordings across hundreds of neurons in the visual cortex using in vivo two-photon calcium imaging and we corroborate previous studies finding that such representations change as experimental trials are repeated across days. This phenomenon has been termed "representational drift". In this study we geometrically characterize the properties of representational drift in the primary visual cortex of mice in two open datasets from the Allen Institute and propose a potential mechanism behind such drift. We observe representational drift both for passively presented stimuli, as well as for stimuli which are behaviorally relevant. Across experiments, the drift most often occurs along directions that have the most variance, leading to a significant turnover in the neurons used for a given representation. Interestingly, despite this significant change due to drift, linear classifiers trained to distinguish neuronal representations show little to no degradation in performance across days. The features we observe in the neural data are similar to properties of artificial neural networks where representations are updated by continual learning in the presence of dropout, i.e. a random masking of nodes/weights, but not other types of noise. Therefore, we conclude that a potential reason for the representational drift in biological networks is driven by an underlying dropout-like noise while continuously learning and that such a mechanism may be computational advantageous for the brain in the same way it is for artificial neural networks, e.g. preventing overfitting.

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“…We note that recently a similar quantification of feature spaces found success in analytically estimating error rates of few-shot learning [29].…”

Section: Feature Space and Geometric Measuresmentioning

confidence: 74%

“…all the variance is in the first PC dimension. This measure is often used as a measure of subspace dimensionality[27][28][29].…”

mentioning

confidence: 99%

The Geometry of Representational Drift in Natural and Artificial Neural Networks

Aitken

Garrett

Olsen

et al. 2021

Preprint

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“…How do high-dimensional models achieve better classification performance for novel categories? If we consider an idealized scenario in which categories are represented by spherical or elliptical manifolds, it is a geometric fact that projections of these manifolds onto linear readout dimensions will concentrate more around their manifold centroids as dimensionality increases (assuming that manifold radius is held constant) (Gorban, Makarov, & Tyukin, 2020; Gorban & Tyukin, 2018; Sorscher et al,2021). The reason for this is that in high dimensions, most of the manifold’s mass is concentrated along its equator, orthogonal to the linear readout dimension.…”

Section: Resultsmentioning

confidence: 99%

“…Classifying novel object categories To see how model ED affected generalization to the task of classifying novel object categories, we used a transfer learning paradigm following Sorscher et al (2021). For a given model layer, we obtained activations to images from M = 50 different categories each with N train = 50 samples.…”

Section: Predicting Neural Responsesmentioning

confidence: 99%

High-performing neural network models of visual cortex benefit from high latent dimensionality

Elmoznino

Bonner

2022

Preprint

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Geometric descriptions of deep neural networks (DNNs) have the potential to uncover core principles of computational models in neuroscience, while abstracting over the details of model architectures and training paradigms. Here we examined the geometry of DNN models of visual cortex by quantifying the latent dimensionality of their natural image representations. The prevailing view holds that optimal DNNs compress their representations onto low-dimensional manifolds to achieve invariance and robustness, which suggests that better models of visual cortex should have low-dimensional geometries. Surprisingly, we found a strong trend in the opposite direction---neural networks with high-dimensional image manifolds tend to have better generalization performance when predicting cortical responses to held-out stimuli in both monkey electrophysiology and human fMRI data. These findings held across a diversity of design parameters for DNNs, and they suggest a general principle whereby high-dimensional geometry confers a striking benefit to DNN models of visual cortex.

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“…The approach presented in this article can of course also be generalized to other domains and data sets such as the THINGS data base and its associated embeddings [26] or the recently published similarity ratings and embeddings for a subset of ImageNet [50]. It can furthermore be seen as a contribution to the currently emerging field of research which tries to align neural networks with psychological models of cognition [1,5,6,29,35,36,44,46,47,48,53,54,59,60].…”

Section: Discussionmentioning

confidence: 99%

Grounding Psychological Shape Space in Convolutional Neural Networks

Bechberger¹,

Kühnberger²

2021

Preprint

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Shape information is crucial for human perception and cognition, and should therefore also play a role in cognitive AI systems. We employ the interdisciplinary framework of conceptual spaces, which proposes a geometric representation of conceptual knowledge through low-dimensional interpretable similarity spaces. These similarity spaces are often based on psychological dissimilarity ratings for a small set of stimuli, which are then transformed into a spatial representation by a technique called multidimensional scaling. Unfortunately, this approach is incapable of generalizing to novel stimuli. In this paper, we use convolutional neural networks to learn a generalizable mapping between perceptual inputs (pixels of grayscale line drawings) and a recently proposed psychological similarity space for the shape domain. We investigate different network architectures (classification network vs. autoencoder) and different training regimes (transfer learning vs. multi-task learning). Our results indicate that a classification-based multi-task learning scenario yields the best results, but that its performance is relatively sensitive to the dimensionality of the similarity space.

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The Geometry of Concept Learning

Cited by 12 publications

References 50 publications

The Geometry of Representational Drift in Natural and Artificial Neural Networks

The Geometry of Representational Drift in Natural and Artificial Neural Networks

High-performing neural network models of visual cortex benefit from high latent dimensionality

Grounding Psychological Shape Space in Convolutional Neural Networks

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