Safe deployment of machine learning (ML) models in safety-critical domains such as medical imaging requires detecting inputs with characteristics not seen during training, known as out-of-distribution (OOD) detection, to prevent unreliable predictions. Effective OOD detection after deployment could benefit from access to the training data, enabling direct comparison between test samples and the training data distribution to identify differences. State-of-the-art OOD detection methods, however, either discard the training data after deployment or assume that test samples and training data are centrally stored together, an assumption that rarely holds in real-world settings. This is because shipping the training data with the deployed model is usually impossible due to the size of training databases, as well as proprietary or privacy constraints. We introduce the Isolation Network, an OOD detection framework that quantifies the difficulty of separating a target test sample from the training data by solving a binary classification task.

The very challenging task of learning solution operators of PDEs on arbitrary domains accurately and efficiently is of vital importance to engineering and industrial simulations. Despite the existence of many operator learning algorithms to approximate such PDEs, we find that accurate models are not necessarily computationally efficient and vice versa. We address this issue by proposing a geometry aware operator transformer (GAOT) for learning PDEs on arbitrary domains. GAOT combines novel multiscale attentional graph neural operator encoders and decoders, together with geometry embeddings and (vision) transformer processors to accurately map information about the domain and the inputs into a robust approximation of the PDE solution. Multiple innovations in the implementation of GAOT also ensure computational efficiency and scalability. We demonstrate this significant gain in both accuracy and efficiency of GAOT over several baselines on a large number of learning tasks from a diverse set of PDEs, including achieving state of the art performance on three large scale three-dimensional industrial CFD datasets. Our project page for accessing the source code is available at camlab-ethz.github.io/GAOT.

However, deploying these models can be unreliable when significant distribution gaps exist between training and test data, while fine-tuning for diverse scenarios is often costly. This creates a need for methods that can efficiently adapt to new data at test time without expensive retraining. Cache-based test-time adapters serve this purpose by storing representative test samples to guide subsequent classifications. Yet, these methods typically employ naive cache management with limited capacity, leading to severe catastrophic forgetting when samples are inevitably dropped during updates. In this paper, we propose Dota(DistributiOnal Test-time Adaptation), a simple yet effective method addressing this limitation. Crucially, instead of merely memorizing individual test samples, Dotacontinuously estimates the underlying distribution of the test data stream. Test-time posterior probabilities are then computed using these dynamically estimated distributions via Bayes' theorem for adaptation. This distribution-centric approach enables the model to continually learn and adapt to the deployment environment. Extensive experiments validate that Dota significantly mitigates forgetting and achieves state-of-the-art performance compared to existing methods.

Test-time adaptation (TTA) for Vision-Language Models (VLMs) aims to enhance performance on unseen test data. However, existing methods struggle to achieve robust and continuous knowledge accumulation during test time. To address this, we propose Statistics Caching test-time Adaptation (SCA), a novel cachebased approach. Unlike traditional feature-caching methods prone to forgetting, SCA continuously accumulates task-specific knowledge from all encountered test samples. By formulating the reuse of past features as a least squares problem, SCA avoids storing raw features and instead maintains compact, incrementally updated feature statistics. This design enables efficient online adaptation without the limitations of fixed-size caches, ensuring that the accumulated knowledge grows persistently over time. Furthermore, we introduce adaptive strategies that leverage the VLM's prediction uncertainty to reduce the impact of noisy pseudolabels and dynamically balance multiple prediction sources, leading to more robust and reliable performance. Extensive experiments demonstrate that SCA achieves compelling performance while maintaining competitive computational efficiency. The code is available at this link.

However, deploying these models can be unreliable when significant distribution gaps exist between training and test data, while fine-tuning for diverse scenarios is often costly. Cache-based test-time adapters offer an efficient alternative by storing representative test samples to guide subsequent classifications. Yet, these methods typically employ naive cache management with limited capacity, leading to severe catastrophic forgetting when samples are inevitably dropped during updates. In this paper, we propose DOTA (DistributiOnal Test-time Adaptation), a simple yet effective method addressing this limitation. Crucially, instead of merely memorizing individual test samples, DOTA continuously estimates the underlying distribution of the test data stream. Test-time posterior probabilities are then computed using these dynamically estimated distributions via Bayes' theorem for adaptation. This distribution-centric approach enables the model to continually learn and adapt to the deployment environment. Extensive experiments validate that DOTA significantly mitigates forgetting and achieves state-of-the-art performance compared to existing methods.

This paper addresses structured out-of-distribution (OOD) testing in high-stakes machine learning applications. Traditional conformal methods rely on joint exchangeability, making it difficult to incorporate auxiliary information such as spatiotemporal or grouping structures. To overcome this limitation, we propose the structure-adaptive conformal q-value (SCQ), a significance index that integrates individual test evidence with structural patterns. We also develop pseudo-score-guided transductive automated model selection (P-TAMS), which adapts conformalized model selection to structured OOD testing across a toolbox of candidate models. Together, SCQ and P-TAMS form a unified framework under pairwise exchangeability, providing finite-sample error-rate control, improved power, and enhanced interpretability. Experiments on simulated and real data demonstrate that the proposed approach controls the false discovery rate and performs well across diverse settings.

The promising zero-shot generalization of vision-language models such as CLIP has led to their adoption using prompt learning for numerous downstream tasks. Previous works have shown test-time prompt tuning using entropy minimization to adapt text prompts for unseen domains. While effective, this overlooks the key cause for performance degradation to unseen domains - distribution shift. In this work, we explicitly handle this problem by aligning the out-of-distribution (OOD) test sample statistics to those of the source data using prompt tuning. We use a single test sample to adapt multi-modal prompts at test time by minimizing the feature distribution shift to bridge the gap in the test domain. Evaluating against the domain generalization benchmark, our method improves zero-shot top1 accuracy beyond existing prompt-learning techniques, with a 3.08%improvement over the baseline MaPLe. In cross-dataset generalization with unseen categories across 10 datasets, our method improves consistently across all datasets compared to the existing state-of-the-art.

We used the largest batch size that could fit in memory on our limited hardware, which was 256 for an image size of 224x224. For the learning rate (Adam [2] optimizer) we searched in the range of {0.001, 0.0001, 1e04, 5e-4, 5e-5}, with weight decay {0, 5e-4. We chose a weight decay of 5e-5 and learning rate of 5e-4 until the 4:6 split and 1e-4 afterwards. We chose a prototype dimension of 256, backbone output of 512, 2 graph layers, graph hidden dimension of 512, λh of 10, Clst and Sep of 0.01. UT-Zappos we again used the Adam optimizer, with learning rate in the ranges {5e-5, 5e-4, 5e-3}, and weight decay {0, 5e-4.

Proof of Proposition 1. Due to Jensen's inequality and the fact that, by assumption, the distribution of human predictions P(h|x) is not a point-mass, it holds that Eh[`(h(x),y) |x] > `(µh(x),y). Proof of Theorem 3. We first provide the proof of the unconstrained case. Note that the above problem is a linear program and it decouples with respect to x. Therefore, for each x, the optimal solution is clearly given by: π m(d= 1 |x) = 1 if Ey|x[`(m(x),y) Eh|x[`(h,y)]] >0 0 otherwise Next, we provide the proof of the constrained case. To this aim, we consider the dual formulation of the optimization problem, where we only introduce a Lagrangian multiplier τP,b for the first constraint, i.e., maximize Ex π(x) Ey,h|x[`(h,y)] Ey|x[`(m(x),y)] + Ex [τP,b(π(x) b)] (13) subject to 0 π(x) 1 x X. (14) 13 The inner minimization problem can be solved using the similar argument for the unconstrained case.