Understanding how neural networks learn and organize features is central to understanding their behavior. Much existing theory of feature learning has focused on the emergence of a global low-dimensional representation. We show that this picture is incomplete. In regression problems with clustered data, we demonstrate that multilayer perceptrons (MLPs) naturally develop monosemantic specialized neurons: individual neurons become strongly aligned with a specific predictive feature relevant to a particular region of the input space. Rather than learning a single global low-dimensional representation, MLPs learn a collection of local low-dimensional representations. We show that this ability to specialize gives MLPs a provable data-efficiency advantage over feature-learning methods based on a global low-dimensional representation.
We here study whether training biases can make hidden neurons specialize in minimal one-hidden-layer MLPs, and whether such specialization improves prototype-based reconstruction of the training dataset from the learned weights. We consider Gaussianactivation MLPs of width equal to dataset size and compare three structural losses that respectively encourage coverage of the training samples, separation between neuron-induced prototypes, and low overlap of hidden responses, against the standard fitting baseline. Experiments on uniformly sampled one-dimensional datasets show a stable pattern from N = 3 to N = 100 across 480 controlled runs. Coverage regularization gives the lowest mean reconstruction error at every tested size and raises the prototype-usage specialization ratio relative to the standard baseline, while separation has mixed effects and overlap penalties are systematically harmful. We show that the harm is not an optimization failure: overlap-active approaches fit the data as well as overlap-free ones but route the optimizer to a degenerate equilibrium in which prototype centers are pushed outside the convex hull of the training inputs. Coverage cannot reward this expulsion and acts as an attractor: separation admits it only at large temperature and overlap admits it at the nominal hyperparameter choice. A direct τ-sweep on the separation-only mask and a prototype-position visualization at N = 100 confirm the mechanism. The findings yield a simple design principle for prototype-recoverability-aware training: every repulsive structural loss must be compensated by a compatible attractor, or it will collapse the latent geometry it was meant to refine.
Dimensionality reduction has proven powerful for identifying neural manifolds, which are low-dimensional structures underlying high-dimensional neural activity. These low-dimensional representations have improved the interpretability of population-level coding. Yet whether such low-dimensional representations are biologically relevant and confer functional advantages in learning systems, or merely reflect neuron-level activity, remains contested in neuroscience. We show that an explicit information bottleneck forcing a recurrent neural network to learn a low-dimensional representation is necessary for rotational and out-of-distribution generalisation in a time-series prediction task. Using information-theoretic measures of causal emergence, we characterise the dynamics of this representation across the memorisation-to-generalisation transition, finding a non-monotonic trajectory which shows an initial decrease, a minimum, and a subsequent rise to a maximum, even as prediction loss falls monotonically. This trajectory scales with task complexity, and the magnitude of emergent structure reliably predicts generalisation performance. Analysis of CA1 hippocampal activity in mice learning an alternating maze task reveals analogous non-monotonic emergence dynamics that track behavioural performance. Together, these findings indicate that the ability of neural networks to learn compact, distributed and emergent representations confers a functional advantage for generalisation, supporting a causal role for learned representations in cognition.
Modularity in deep neural networks has been proposed as a means of improving both interpretability and training by promoting disentangled representations and reducing redundancy. In this work, we study the emergence of modular structure through competition dynamics between groups of neurons during training. We introduce a method that (i) maintains near-baseline accuracy, (ii) induces usage-based modularity by sparsely routing inputs to neuron groups, and (iii) encourages specialization of these modules, such that their activations are correlated with input classes. We evaluate the proposed approach on ImageNet-100 and CIFAR-100 and show that with it, specialized modules emerge without module-level supervision. These modules capture a meaningful high-level structure in the data, with individual modules responding to semantic categories (e.g., dogs or vehicles). We also study the emergence of a hierarchical partition of sub-tasks depending on the number of modules. Our results suggest that competitive dynamics can serve as a simple mechanism for inducing functional modularity in standard architectures.