This paper presents a probabilistic framework for online test-time adaptation problems. In them, a model is trained on labeled data but must adapt to unlabeled data at test time under the assumption that training and test distributions potentially differ, that is, there might have been a distributional shift. The framework is based on a state-space modelling architecture from which parameter learning, parameter time evolution, prior tuning, and prediction can be characterized.

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The emergence of large-scale pre-trained point cloud models has significantly advanced 3D scene understanding, but adapting these models to specific downstream tasks typically demands full fine-tuning, incurring high computational and storage costs. Parameter-efficient fine-tuning (PEFT) techniques, successful in natural language processing and 2D vision tasks, would underperform when naively applied to 3D point cloud models due to significant geometric and spatial distribution shifts. Existing PEFT methods commonly treat points as orderless tokens, neglecting important local spatial structures and global geometric contexts in 3D modeling. To bridge this gap, we introduce the Geometric Encoding Mixer (GEM), a novel geometry-aware PEFT module specifically designed for 3D point cloud transformers. GEM explicitly integrates fine-grained local positional encodings with a lightweight latent attention mechanism to capture comprehensive global context, thereby effectively addressing the spatial and geometric distribution mismatch. Extensive experiments demonstrate that GEM achieves performance comparable to or sometimes even exceeding full fine-tuning, while only updating 1.6% of the model's parameters, fewer than other PEFT methods. With significantly reduced training time and memory requirements, our approach thus sets a new benchmark for efficient, scalable, and geometry-aware fine-tuning of large-scale 3D point cloud models. Code is available at https://github.com/LiyaoTang/GEM.

The deployment of data-driven models in 6G wireless networks is increasingly challenged by frequent distribution shifts that degrade performance over time. Unsupervised Domain Adaptation (UDA) offers an alternative approach by adapting the trained model to a shifted domain without requiring labels. However, UDA pipelines are often more complex than single-task training due to additional modules and optimization procedures, raising a practical question: do the benefits of adaptation come at a higher energy cost, and how does this trade-off compare to retraining when labeling effort is also considered? In this work, we investigate the energy consumption of UDA and compare it to single task. We further propose a way to determine the minimum number of target domains for which UDA becomes more energy-efficient than retraining, taking into account the labeling cost. Our results aim to clarify when UDA should be preferred over classical train-from-scratch approaches from an energy and labeling-aware perspective.

A central goal in nonparametric statistics is adaptation: the ability of an estimator to perform simultaneously and optimally across a wide variety of settings with little to no tuning. When inference is carried out over a class of functional spaces, it is desirable that the estimator automatically adapts to unknown features of these spaces, such as smoothness, geometry, sparsity or other finer structural properties. A large body of literature has focused on adaptation: Lepski's method Lepski ı [1990, 1991], thresholding Donoho et al. [1995] and model selection Barron et al. [1999] are amongst the most well-known nonBayesian approaches. Bayesian methods, on the other hand, have a natural ability to achieve adaptation, as we discuss in more detail below, by choosing prior distributions that are flexible enough to achieve this task (one possibility is for instance to draw certain prior parameters at random in a hierarchical Bayes fashion). Recently, motivated by the remarkable empirical success of deep learning methods, there has been a growing interest in understanding how neural networks can automatically learn structural parameters, such as smoothness of functions or'effective' dimensions, for instance in regression settings exhibiting a compositional structure as in Schmidt-Hieber [2020], Kohler and Langer [2021] or for data lying on geometric structures (e.g.

Diffusion models are known to exploit unknown low-dimensional structure to accelerate sampling. However, existing convergence theory under low-dimensional data structure has largely focused on update rules with narrowly prescribed coefficient choices. This raises a fundamental question: is adaptation to low-dimensional structure sensitive to the precise choice of update coefficients? In this paper, we show that such adaptation is a robust property of diffusion models. For a broad class of update coefficients, we prove that $\widetilde{O}(k/\varepsilon)$ iterations suffice to generate an $\varepsilon$-accurate sample in total variation (TV) distance, independently of the ambient dimension. Our framework substantially broadens the class of diffusion samplers known to enjoy low dimensional adaptation and applies to several commonly used methods in practice. These results provide a theoretical justification for the empirical effectiveness of diffusion samplers across different coefficient choices when applied to structured, high-dimensional data.

Human brain achieves dynamic stability-plasticity balance through synaptic homeostasis, a self-regulatory mechanism that stabilizes critical memory traces while preserving optimal learning capacities. Inspired by this biological principle, we propose SPICED: a neuromorphic framework that integrates the synaptic homeostasis mechanism for unsupervised continual EEG decoding, particularly addressing practical scenarios where new individuals with inter-individual variability emerge continually. SPICED comprises a novel synaptic network that enables dynamic expansion during continual adaptation through three bio-inspired neural mechanisms: (1) critical memory reactivation, which mimics brain functional specificity, selectively activates task-relevant memories to facilitate adaptation; (2) synaptic consolidation, which strengthens these reactivated critical memory traces and enhances their replay prioritizations for further adaptations and (3) synaptic renormalization, which are periodically triggered to weaken global memory traces to preserve learning capacities. The interplay within synaptic homeostasis dynamically strengthens task-discriminative memory traces and weakens detrimental memories.

Vision-Language Models (VLMs) excel at zero-shot inference but often degrade under test-time domain shifts. For this reason, episodic test-time adaptation strategies have recently emerged as powerful techniques for adapting VLMs to a single unlabeled image. However, existing adaptation strategies, such as test-time prompt tuning, typically require backpropagating through large encoder weights or altering core model components. In this work, we introduce Spectrum-Aware Test-Time Steering (STS), a lightweight adaptation framework that extracts a spectral subspace from the textual embeddings to define principal semantic directions and learns to steer latent representations in a spectrum-aware manner by adapting a small number of per-sample shift parameters to minimize entropy across augmented views. STS operates entirely at inference in the latent space, without backpropagation through or modification of the frozen encoders. Building on standard evaluation protocols, our comprehensive experiments demonstrate that STS largely surpasses or compares favorably against state-of-the-art test-time adaptation methods, while introducing only a handful of additional parameters and achieving inference speeds up to 8 faster with a 12 smaller memory footprint than conventional test-time prompt tuning. The code is available at https://github.com/kdafnis/STS.

Organisms constantly pivot between tasks such as evading predators, foraging, traversing rugged terrain, and socializing, often within milliseconds. Remarkably, they preserve knowledge of once-learned environments sans catastrophic forgetting, a phenomenon neuroscientists hypothesize, is due to a singular neural circuitry dynamically overlayed by neuromodulatory agents such as dopamine and acetylcholine. In parallel, deep learning research addresses analogous challenges via domain generalization (DG) and continual learning (CL), yet these methods remain siloed, despite the brain's ability to perform them seamlessly. In particular, prior work has not explored architectures involving associative memories (AMs), which are an integral part of biological systems, to jointly address these tasks. We propose Memory-Integrated Reconfigurable Adapters (MIRA), a unified framework that integrates Hopfield-style associative memory modules atop a shared backbone. These memory modules store adapter-weight updates as values and retrieve them via learned keys. Associative memory keys are learned post-hoc to index and retrieve an affine combination of stored adapter updates for any given task or domain on a per-sample basis. By varying only the task-specific objectives, we demonstrate that MIRA seamlessly accommodates domain shifts and sequential task exposures under one roof. Empirical evaluations on standard benchmarks confirm that our AM-augmented architecture significantly enhances adaptability and retention: in DG, MIRA achieves SoTA out-of-distribution accuracy, and in incremental learning settings, it outperforms architectures explicitly designed to handle catastrophic forgetting using generic CL algorithms.

In real-world environments, a well-designed model must be capable of handling dynamically evolving distributions, where both in-distribution (ID) and out-ofdistribution (OOD) samples appear unpredictably and individually, making realtime adaptation particularly challenging. While open-set test-time adaptation has demonstrated effectiveness in adjusting to distribution shifts, existing methods often rely on batch processing and struggle to manage single-sample data stream in open-set environments.