Variational Filtering for Bayesian Last Layers with an Independent Binary Probit Surrogate

Modern deep classifiers trained by gradient descent need many passes over the data to become accurate, and even then are not always well calibrated; post-hoc temperature scaling corrects calibration after training but cannot influence training-time accuracy or convergence. We propose a variational filtering algorithm for the last layer of deep classifiers, whose parameters are treated as the latent state of a linear-Gaussian state-space model. Each mini-batch is assimilated by an exact prediction step followed by a closed-form variational update, made conjugate by an independent binary probit (IBProbit) surrogate for the categorical likelihood. The filter's process noise stabilises the updates under feature drift and keeps the predictive distribution from collapsing to a point estimate, allowing the same procedure to be used for linear probing on a frozen backbone and for full-network fine-tuning. We evaluate on DINOv3 backbones against two baselines tuned under an identical protocol: AdamW with cross-entropy and post-hoc temperature scaling, and Variational Bayesian Last Layers (VBLL). As a linear probe on frozen features, IBProbit attains the best accuracy and negative log-likelihood on all five downstream tasks at the largest backbone, and on two of the five at the smallest. In out-of-distribution detection with CIFAR probes on the largest backbone, IBProbit reduces the false-positive rate at 95% true-positive rate by a factor of 1.4 to 3.2 relative to the better of the two baselines, on all three dataset pairs. When the whole network is fine-tuned on ImageNet-1k, IBProbit reaches the final performance of the cross-entropy baseline in half the wall-clock time.