Carlos Stein Naves de Brito

Carlos Stein Brito

Model regularization requires extensive manual tuning to balance complexity against overfitting. Cross-regularization resolves this tradeoff by directly adapting regularization parameters through validation gradients during training. The method splits parameter optimization - training data guides feature learning while validation data shapes complexity controls - converging provably to cross-validation optima. When implemented through noise injection in neural networks, this approach reveals striking patterns: unexpectedly high noise tolerance and architecture-specific regularization that emerges organically during training. Beyond complexity control, the framework integrates seamlessly with data augmentation, uncertainty calibration and growing datasets while maintaining single-run efficiency through a simple gradient-based approach.

Carlos Stein Brito

Despite its long history, Bayesian neural networks (BNNs) and variational training remain underused in practice: standard Gaussian posteriors misalign with network geometry, KL terms can be brittle in high dimensions, and implementations often add complexity without reliably improving uncertainty. We revisit the problem through the lens of normalization. Because normalization layers neutralize the influence of weight magnitude, we model uncertainty \emph{only in weight directions} using a von Mises-Fisher posterior on the unit sphere. High-dimensional geometry then yields a single, interpretable scalar per layer--the effective post-normalization noise $σ_{\mathrm{eff}}$--that (i) corresponds to simple additive Gaussian noise in the forward pass and (ii) admits a compact, dimension-aware KL in closed form. We derive accurate, closed-form approximations linking concentration $κ$ to activation variance and to $σ_{\mathrm{eff}}$ across regimes, producing a lightweight, implementation-ready variational unit that fits modern normalized architectures and improves calibration without sacrificing accuracy. This dimension awareness is critical for stable optimization in high dimensions. In short, by aligning the variational posterior with the network's intrinsic geometry, BNNs can be simultaneously principled, practical, and precise.

Carlos S. N. Brito, Wulfram Gerstner

The development of sensory receptive fields has been modeled in the past by a variety of models including normative models such as sparse coding or independent component analysis and bottom-up models such as spike-timing dependent plasticity or the Bienenstock-Cooper-Munro model of synaptic plasticity. Here we show that the above variety of approaches can all be unified into a single common principle, namely Nonlinear Hebbian Learning. When Nonlinear Hebbian Learning is applied to natural images, receptive field shapes were strongly constrained by the input statistics and preprocessing, but exhibited only modest variation across different choices of nonlinearities in neuron models or synaptic plasticity rules. Neither overcompleteness nor sparse network activity are necessary for the development of localized receptive fields. The analysis of alternative sensory modalities such as auditory models or V2 development lead to the same conclusions. In all examples, receptive fields can be predicted a priori by reformulating an abstract model as nonlinear Hebbian learning. Thus nonlinear Hebbian learning and natural statistics can account for many aspects of receptive field formation across models and sensory modalities.