Use of machine learning to perform database operations, such as indexing, cardinality estimation, and sorting, is shown to provide substantial performance benefits. However, when datasets change and data distribution shifts, empirical results also show performance degradation for learned models, possibly to worse than non-learned alternatives. This, together with a lack of theoretical understanding of learned methods undermines their practical applicability, since there are no guarantees on how well the models will perform after deployment. In this paper, we present the first known theoretical characterization of the performance of learned models in dynamic datasets, for the aforementioned operations. Our results show novel theoretical characteristics achievable by learned models and provide bounds on the performance of the models that characterize their advantages over non-learned methods, showing why and when learned models can outperform the alternatives. Our analysis develops the distribution learnability framework and novel theoretical tools which build the foundation for the analysis of learned database operations in the future.

Environment annotations are essential for the success of many out-of-distribution (OOD) generalization methods. Unfortunately, these are costly to obtain and often limited by human annotators' biases. To achieve robust generalization, it is essential to develop algorithms for automatic environment discovery within datasets. Current proposals, which divide examples based on their training error, suffer from one fundamental problem. These methods introduce hyper-parameters and early-stopping criteria, which require a validation set with human-annotated environments, the very information subject to discovery. In this paper, we propose Cross-Risk Minimization (XRM) to address this issue. XRM trains twin networks, each learning from one random half of the training data, while imitating confident held-out mistakes made by its sibling. XRM provides a recipe for hyper-parameter tuning, does not require early-stopping, and can discover environments for all training and validation data. Algorithms built on top of XRM environments achieve oracle worst-group-accuracy, addressing a long-standing challenge in OOD generalization.

We tackle the challenge of predicting models' Out-of-Distribution (OOD) performance using in-distribution (ID) measurements without requiring OOD data. Existing evaluations with ``Effective robustness'', which use ID accuracy as an indicator of OOD accuracy, encounter limitations when models are trained with diverse supervision and distributions, such as class labels (*Vision Models, VMs, on ImageNet*) and textual descriptions (*Visual-Language Models, VLMs, on LAION*). VLMs often generalize better to OOD data than VMs despite having similar or lower ID performance. To improve the prediction of models' OOD performance from ID measurements, we introduce the *Lowest Common Ancestor (LCA)-on-the-Line* framework. This approach revisits the established concept of LCA distance, which measures the hierarchical distance between labels and predictions within a predefined class hierarchy, such as WordNet. We assess 75 models using ImageNet as the ID dataset and five significantly shifted OOD variants, uncovering a strong linear correlation between ID LCA distance and OOD top-1 accuracy. Our method provides a compelling alternative for understanding why VLMs tend to generalize better. Additionally, we propose a technique to construct a taxonomic hierarchy on any dataset using $K$-means clustering, demonstrating that LCA distance is robust to the constructed taxonomic hierarchy. Moreover, we demonstrate that aligning model predictions with class taxonomies, through soft labels or prompt engineering, can enhance model generalization. Open source code in our [Project Page](https://elvishelvis.github.io/papers/lca/).

Test-time adaptation has proven effective in adapting a given trained model to unseen test samples with potential distribution shifts. However, in real-world scenarios, models are usually deployed on resource-limited devices, e.g., FPGAs, and are often quantized and hard-coded with non-modifiable parameters for acceleration. In light of this, existing methods are often infeasible since they heavily depend on computation-intensive backpropagation for model updating that may be not supported. To address this, we propose a test-time Forward-Optimization Adaptation (FOA) method. In FOA, we seek to solely learn a newly added prompt (as model's input) via a derivative-free covariance matrix adaptation evolution strategy. To make this strategy work stably under our online unsupervised setting, we devise a novel fitness function by measuring test-training statistic discrepancy and model prediction entropy. Moreover, we design an activation shifting scheme that directly tunes the model activations for shifted test samples, making them align with the source training domain, thereby further enhancing adaptation performance. Without using any backpropagation and altering model weights, FOA runs on quantized 8-bit ViT outperforms gradient-based TENT on full-precision 32-bit ViT, while achieving an up to 24-fold memory reduction on ImageNet-C. The source code is available at: https://github.com/mr-eggplant/FOA.