In modern deep neural networks, the learning dynamics of individual neurons are often obscure, as the networks are trained via global optimization. Conversely, biological systems build on self-organized, local learning, achieving robustness and efficiency with limited global information. Here, we show how self-organization between individual artificial neurons can be achieved by designing abstract bio-inspired local learning goals. These goals are parameterized using a recent extension of information theory, Partial Information Decomposition (PID), which decomposes the information that a set of information sources holds about an outcome into unique, redundant and synergistic contributions. Our framework enables neurons to locally shape the integration of information from various input classes, i.e., feedforward, feedback, and lateral, by selecting which of the three inputs should contribute uniquely, redundantly or synergistically to the output. This selection is expressed as a weighted sum of PID terms, which, for a given problem, can be directly derived from intuitive reasoning or via numerical optimization, offering a window into understanding task-relevant local information processing. Achieving neuron-level interpretability while enabling strong performance using local learning, our work advances a principled information-theoretic foundation for local learning strategies.

We revisit the ``dataset classification'' experiment suggested by Torralba & Efros (2011) a decade ago, in the new era with large-scale, diverse, and hopefully less biased datasets as well as more capable neural network architectures. Surprisingly, we observe that modern neural networks can achieve excellent accuracy in classifying which dataset an image is from: e.g., we report 84.7% accuracy on held-out validation data for the three-way classification problem consisting of the YFCC, CC, and DataComp datasets. Our further experiments show that such a dataset classifier could learn semantic features that are generalizable and transferable, which cannot be explained by memorization. We hope our discovery will inspire the community to rethink issues involving dataset bias.

This paper investigates the conformal isometry hypothesis as a potential explanation for the hexagonal periodic patterns in grid cell response maps. We posit that grid cell activities form a high-dimensional vector in neural space, encoding the agent's position in 2D physical space. As the agent moves, this vector rotates within a 2D manifold in the neural space, driven by a recurrent neural network. The conformal hypothesis proposes that this neural manifold is a conformal isometric embedding of 2D physical space, where local physical distance is preserved by the embedding up to a scaling factor (or unit of metric). Such distance-preserving position embedding is indispensable for path planning in navigation, especially planning local straight path segments. We conduct numerical experiments to show that this hypothesis leads to the hexagonal grid firing patterns by learning maximally distance-preserving position embedding, agnostic to the choice of the recurrent neural network. Furthermore, we present a theoretical explanation of why hexagon periodic patterns emerge by minimizing our loss function by showing that hexagon flat torus is maximally distance preserving.

Biological and artificial neural systems form high-dimensional neural representations that underpin their computational capabilities. Methods for quantifying geometric similarity in neural representations have become a popular tool for identifying computational principles that are potentially shared across neural systems. These methods generally assume that neural responses are deterministic and static. However, responses of biological systems, and some artificial systems, are noisy and dynamically unfold over time. Furthermore, these characteristics can have substantial influence on a system’s computational capabilities. Here, we demonstrate that existing metrics can fail to capture key differences between neural systems with noisy dynamic responses. We then propose a metric for comparing the geometry of noisy neural trajectories, which can be derived as an optimal transport distance between Gaussian processes. We use the metric to compare models of neural responses in different regions of the motor system and to compare the dynamics of latent diffusion models for text-to-image synthesis.

It is a mystery how the brain decodes color vision purely from the optic nerve signals it receives, with a core inferential challenge being how it disentangles internal perception with the correct color dimensionality from the unknown encoding properties of the eye. In this paper, we introduce a computational framework for modeling this emergence of human color vision by simulating both the eye and the cortex. Existing research often overlooks how the cortex develops color vision or represents color space internally, assuming that the color dimensionality is known a priori; however, we argue that the visual cortex has the capability and the challenge of inferring the color dimensionality purely from fluctuations in the optic nerve signals. To validate our theory, we introduce a simulation engine for biological eyes based on established vision science and generate optic nerve signals resulting from looking at natural images. Further, we propose a bio-plausible model of cortical learning based on self-supervised prediction of optic nerve signal fluctuations under natural eye motions. We show that this model naturally learns to generate color vision by disentangling retinal invariants from the sensory signals. When the retina contains $N$ types of color photoreceptors, our simulation shows that $N$-dimensional color vision naturally emerges, verified through formal colorimetry. Using this framework, we also present the first simulation work that successfully boosts the color dimensionality, as observed in gene therapy on squirrel monkeys, and demonstrates the possibility of enhancing human color vision from 3D to 4D.

Understanding how sensory neurons exhibit selectivity to certain features and invariance to others is central to uncovering the computational principles underlying robustness and generalization in visual perception. Most existing methods for characterizing selectivity and invariance identify single or finite discrete sets of stimuli. Since these are only isolated measurements from an underlying continuous manifold, characterizing invariance properties accurately and comparing them across neurons with varying receptive field size, position, and orientation, becomes challenging. Consequently, a systematic analysis of invariance types at the population level remains under-explored. Building on recent advances in learning continuous invariance manifolds, we introduce a novel method to accurately identify and align invariance manifolds of visual sensory neurons, overcoming these challenges. Our approach first learns the continuous invariance manifold of stimuli that maximally excite a neuron modeled by a response-predicting deep neural network. It then learns an affine transformation on the pixel coordinates such that the same manifold activates another neuron as strongly as possible, effectively aligning their invariance manifolds spatially. This alignment provides a principled way to quantify and compare neuronal invariances irrespective of receptive field differences. Using simulated neurons, we demonstrate that our method accurately learns and aligns known invariance manifolds, robustly identifying functional clusters. When applied to macaque V1 neurons, it reveals functional clusters of neurons, including simple and complex cells. Overall, our method enables systematic, quantitative exploration of the neural invariance landscape, to gain new insights into the functional properties of visual sensory neurons.