Logit-Origin Centering for Singleton Test-Time Adaptation

Tabular data is used extensively in many real-world use cases. Deep learning models have been developed to deal with tabular data, but generally perform poorly when the test data distribution differs from that of the training data. Researchers have proposed test-time adaptation approaches to deal with this problem. The fully test-time adaptation (FTTA) setting involves adapting deployed classifiers to shifted target distributions using only unlabeled test data. Leading FTTA methods inherit a batch-dependent approach from computer vision literature. This paper demonstrates for the first time that such approaches degrade sharply in strict streaming regimes where examples arrive and must be classified one at a time. This occurs because at a batch size of one, batch-level statistics become unavailable or poorly estimated. We argue that singleton tabular FTTA is not merely a small-batch variant of ordinary FTTA, but a distinct identifiability problem where only the location of the model's score stream remains directly observable. To address this, we propose Prequential Logit-Origin Centering (PLOC), a lightweight approach that keeps the source model frozen and shifts the logit space at each step. PLOC stores only a single running number (the mean of past logits), requires no labels, estimates no priors, and bypasses weight updates entirely. A deferred variant applies a static shift that preserves the source ranking, and thus the AUROC, exactly. Evaluated across five tabular benchmarks, three architectures (MLP, FT-Transformer, and TabTransformer), and five independent source checkpoints, PLOC significantly outperforms strong tabular and entropy-based baselines.

Beyond the Simplex: Balanced Prototype Geometry for Scorer-Agnostic Open-Set Recognition

Open-set recognition (OSR) requires a classifier to reject inputs from unseen classes which is essential in safety-critical settings such as medical imaging. Simplex based methods, which fix class prototypes at the vertices of a regular simplex and then reject via a distance-ratio score, perform well empirically but lack theoretical justification, and existing analysis applies only when the embedding dimension d is at least C-1, which is the regime in which a regular simplex exists. We give a theoretical account of simplex-ratio OSR that holds in every embedding dimension, including d < C-1. Our analysis centers on balanced equal-norm codes: prototype configurations with equal lengths and zero sum, which exist for all d >= 2 and include the regular simplex as a special case. For these codes we show that an auxiliary squared ratio score has sublevel sets that are exact unions of Euclidean balls, which in turn bracket the acceptance region of the operational score; and we prove a sharp dichotomy: the prototypes attain one-distance symmetry, behaving like a regular simplex, if and only if d >= C-1, with controlled degradation governed by an explicit defect parameter below that threshold. We further show the false-acceptance rate decays exponentially in d under natural isotropy assumptions, and that the operational score is globally Lipschitz with compact acceptance regions. Empirically, we study balanced prototype geometry as both an analytic tool and a representation-learning prior, rather than as a stand-alone state-of-the-art detector. Across CIFAR and MedMNIST open-set splits, the geometry provides useful structure, but OSR performance remains strongly dependent on the scoring rule: raw ratio scores typically underperform nearest-neighbor and logit-based alternatives.