The Median-of-Means (MoM) is a robust estimator widely used in machine learning that is known to be (minimax) optimal in scenarios where samples are i.i.d. In more grave scenarios, samples are contaminated by an adversary that can inspect and modify the data. Previous work has theoretically shown the suitability of the MoM estimator in certain contaminated settings. However, the (minimax) optimality of MoM and its limitations under adversarial contamination remain unknown beyond the Gaussian case. In this paper, we present upper and lower bounds for the error of MoM under adversarial contamination for multiple classes of distributions. In particular, we show that MoM is (minimax) optimal in the class of distributions with finite variance, as well as in the class of distributions with infinite variance and finite absolute $(1+r)$-th moment. We also provide lower bounds for MoM's error that match the order of the presented upper bounds, and show that MoM is sub-optimal for light-tailed distributions.

Spatial prediction refers to the estimation of unobserved values from spatially distributed observations. Although recent advances have improved the capacity to model diverse observation types, adoption in practice remains limited in industries that demand in-terpretability. To mitigate this gap, surrogate models that explain black-box predictors provide a promising path toward interpretable decision making. In this study, we propose a graph partitioning problem to construct spatial segments that minimize the sum of within-segment variances of individual predictions. The assignment of data points to segments can be formulated as a mixed-integer quadratic programming problem. While this formulation potentially enables the identification of exact segments, its computational complexity becomes prohibitive as the number of data points increases. Motivated by this challenge, we develop an approximation scheme that leverages the structural properties of graph partitioning. Experimental results demonstrate the computational efficiency of this approximation in identifying spatial segments.

We propose to perform mean-field variational inference (MFVI) in a rotated coordinate system that reduces correlations between variables. The rotation is determined by principal component analysis (PCA) of a cross-covariance matrix involving the target's score function. Compared with standard MFVI along the original axes, MFVI in this rotated system often yields substantially more accurate approximations with negligible additional cost. MFVI in a rotated coordinate system defines a rotation and a coordinatewise map that together move the target closer to Gaussian. Iterating this procedure yields a sequence of transformations that progressively transforms the target toward Gaussian. The resulting algorithm provides a computationally efficient way to construct flow-like transport maps: it requires only MFVI subproblems, avoids large-scale optimization, and yields transformations that are easy to invert and evaluate. In Bayesian inference tasks, we demonstrate that the proposed method achieves higher accuracy than standard MFVI, while maintaining much lower computational cost than conventional normalizing flows.

Independent Component Analysis (ICA) is a classical method for recovering latent variables with useful identifiability properties. For independent variables, cumulant tensors are diagonal; relaxing independence yields tensors whose zero structure generalizes diagonality. These models have been the subject of recent work in non-independent component analysis. We show that pairwise mean independence answers the question of how much one can relax independence: it is identifiable, any weaker notion is non-identifiable, and it contains the models previously studied as special cases. Our results apply to distributions with the required zero pattern at any cumulant tensor. We propose an algebraic recovery algorithm based on least-squares optimization over the orthogonal group. Simulations highlight robustness: enforcing full independence can harm estimation, while pairwise mean independence enables more stable recovery. These findings extend the classical ICA framework and provide a rigorous basis for blind source separation beyond independence.

Hierarchical data with multiple observations per group is ubiquitous in empirical sciences and is often analyzed using mixed-effects regression. In such models, Bayesian inference gives an estimate of uncertainty but is analytically intractable and requires costly approximation using Markov Chain Monte Carlo (MCMC) methods. Neural posterior estimation shifts the bulk of computation from inference time to pre-training time, amortizing over simulated datasets with known ground truth targets. We propose metabeta, a transformer-based neural network model for Bayesian mixed-effects regression. Using simulated and real data, we show that it reaches stable and comparable performance to MCMC-based parameter estimation at a fraction of the usually required time.

Language models (LMs) are challenging to adapt to new data distributions by simple finetuning. This is due to the rigidity of their subword tokenizers, which typically remain unchanged during adaptation. This inflexibility often leads to inefficient tokenization, causing overfragmentation of out-of-distribution domains, unseen languages, or scripts. In this work, we develop byte-level LMs with learnable tokenizers to make tokenization adaptive. Our models include a submodule that learns to predict boundaries between the input byte sequence, encoding it into variable-length segments. Existing tokenizer-free methods train this boundary predictor using an auxiliary loss that enforces a fixed compression rate across the training corpus, introducing a new kind of rigidity. We propose FLEXITOKENS, a simplified training objective that enables significantly greater flexibility during adaptation. Evaluating across multiple multilingual benchmarks, morphologically diverse tasks, and domains, we demonstrate that FLEXITOKENS consistently reduces token over-fragmentation and achieves up to 10% improvements on downstream task performance compared to subword and other gradient-based tokenizers. Code and data for our experiments will be released at https://github.com/owos/flexitokens

Ensuring fairness in machine learning models is critical, particularly in high-stakes domains where biased decisions can lead to serious societal consequences. Existing preprocessing approaches generally lack transparent mechanisms for identifying which features or instances are responsible for unfairness. This obscures the rationale behind data modifications. We introduce FairSHAP, a novel pre-processing framework that leverages Shapley value attribution to improve both individual and group fairness. FairSHAP identifies fairness-critical instances in the training data using an interpretable measure of feature importance, and systematically modifies them through instance-level matching across sensitive groups. This process reduces discriminative risk - an individual fairness metric - while preserving data integrity and model accuracy. We demonstrate that FairSHAP significantly improves demographic parity and equality of opportunity across diverse tabular datasets, achieving fairness gains with minimal data perturbation and, in some cases, improved predictive performance. As a model-agnostic and transparent method, FairSHAP integrates seamlessly into existing machine learning pipelines and provides actionable insights into the sources of bias.Our code is on https://github.com/youlei202/FairSHAP.

To perform few-shot learning, language models extract signals from a few input-label pairs, aggregate these into a learned prediction rule, and apply this rule to new inputs. How is this implemented in the forward pass of modern transformer models? To explore this question, we study a structured family of few-shot learning tasks for which the true prediction rule is to add an integer $k$ to the input. We introduce a novel optimization method that localizes the model's few-shot ability to only a few attention heads. We then perform an in-depth analysis of individual heads, via dimensionality reduction and decomposition. As an example, on Llama-3-8B-instruct, we reduce its mechanism on our tasks to just three attention heads with six-dimensional subspaces, where four dimensions track the unit digit with trigonometric functions at periods $2$, $5$, and $10$, and two dimensions track magnitude with low-frequency components. To deepen our understanding of the mechanism, we also derive a mathematical identity relating ``aggregation'' and ``extraction'' subspaces for attention heads, allowing us to track the flow of information from individual examples to a final aggregated concept. Using this, we identify a self-correction mechanism where mistakes learned from earlier demonstrations are suppressed by later demonstrations. Our results demonstrate how tracking low-dimensional subspaces of localized heads across a forward pass can provide insight into fine-grained computational structures in language models.

Prompt optimization aims to systematically refine prompts to enhance a language model's performance on specific tasks. Fairness detection in Terms of Service (ToS) clauses is a challenging legal NLP task that demands carefully crafted prompts to ensure reliable results. However, existing prompt optimization methods are often computationally expensive due to inefficient search strategies and costly prompt candidate scoring. In this paper, we propose a framework that combines Monte Carlo Tree Search (MCTS) with a proxy prompt evaluator to more effectively explore the prompt space while reducing evaluation costs. Experiments demonstrate that our approach achieves higher classification accuracy and efficiency than baseline methods under a constrained computation budget.

We propose In-Context Clustering (ICC), a flexible LLM-based procedure for clustering data from diverse distributions. Unlike traditional clustering algorithms constrained by predefined similarity measures, ICC flexibly captures complex relationships among inputs through an attention mechanism. We show that pretrained LLMs exhibit impressive zero-shot clustering capabilities on text-encoded numeric data, with attention matrices showing salient cluster patterns. Spectral clustering using attention matrices offers surprisingly competitive performance. We further enhance the clustering capabilities of LLMs on numeric and image data through fine-tuning using the Next Token Prediction (NTP) loss. Moreover, the flexibility of LLM prompting enables text-conditioned image clustering, a capability that classical clustering methods lack. Our work extends in-context learning to an unsupervised setting, showcasing the effectiveness and flexibility of LLMs for clustering. Our code is available at https://agenticlearning.ai/icc.