Comparison-based preference learning has become central to the alignment of AI models with human preferences. However, these methods may behave counterintuitively. After empirically observing that, when accounting for a preference for response $y$ over $z$, the model may actually decrease the probability (and reward) of generating $y$ (an observation also made by others), this paper investigates the root causes of (non) monotonicity, for a general comparison-based preference learning framework that subsumes Direct Preference Optimization (DPO), Generalized Preference Optimization (GPO) and Generalized Bradley-Terry (GBT). Under mild assumptions, we prove that such methods still satisfy what we call local pairwise monotonicity. We also provide a bouquet of formalizations of monotonicity, and identify sufficient conditions for their guarantee, thereby providing a toolbox to evaluate how prone learning models are to monotonicity violations. These results clarify the limitations of current methods and provide guidance for developing more trustworthy preference learning algorithms.

We study the Logistic Contextual Slate Bandit problem, where, at each round, an agent selects a slate of $N$ items from an exponentially large set (of size $2^{Ω(N)}$) of candidate slates provided by the environment. A single binary reward, determined by a logistic model, is observed for the chosen slate. Our objective is to develop algorithms that maximize cumulative reward over $T$ rounds while maintaining low per-round computational costs. We propose two algorithms, Slate-GLM-OFU and Slate-GLM-TS, that accomplish this goal. These algorithms achieve $N^{O(1)}$ per-round time complexity via local planning (independent slot selections), and low regret through global learning (joint parameter estimation). We provide theoretical and empirical evidence supporting these claims. Under a well-studied diversity assumption, we prove that Slate-GLM-OFU incurs only $\tilde{O}(\sqrt{T})$ regret. Extensive experiments across a wide range of synthetic settings demonstrate that our algorithms consistently outperform state-of-the-art baselines, achieving both the lowest regret and the fastest runtime. Furthermore, we apply our algorithm to select in-context examples in prompts of Language Models for solving binary classification tasks such as sentiment analysis. Our approach achieves competitive test accuracy, making it a viable alternative in practical scenarios.

We study the memory complexity of machine unlearning algorithms that provide strong data deletion guarantees to the users. Formally, consider an algorithm for a particular learning task that initially receives a training dataset. Then, after learning, it receives data deletion requests from a subset of users (of arbitrary size), and the goal of unlearning is to perform the task as if the learner never received the data of deleted users. In this paper, we ask how many bits of storage are needed to be able to delete certain training samples at a later time. We focus on the task of realizability testing, where the goal is to check whether the remaining training samples are realizable within a given hypothesis class \(\mathcal{H}\). Toward that end, we first provide a negative result showing that the VC dimension is not a characterization of the space complexity of unlearning. In particular, we provide a hypothesis class with constant VC dimension (and Littlestone dimension), but for which any unlearning algorithm for realizability testing needs to store \(Ω(n)\)-bits, where \(n\) denotes the size of the initial training dataset. In fact, we provide a stronger separation by showing that for any hypothesis class \(\mathcal{H}\), the amount of information that the learner needs to store, so as to perform unlearning later, is lower bounded by the \textit{eluder dimension} of \(\mathcal{H}\), a combinatorial notion always larger than the VC dimension. We complement the lower bound with an upper bound in terms of the star number of the underlying hypothesis class, albeit in a stronger ticketed-memory model proposed by Ghazi et al. (2023). Since the star number for a hypothesis class is never larger than its Eluder dimension, our work highlights a fundamental separation between central and ticketed memory models for machine unlearning.

Neural network training is inherently sensitive to initialization and the randomness induced by stochastic gradient descent. However, it is unclear to what extent such effects lead to meaningfully different networks, either in terms of the models' weights or the underlying functions that were learned. In this work, we show that during the initial "chaotic" phase of training, even extremely small perturbations reliably causes otherwise identical training trajectories to diverge-an effect that diminishes rapidly over training time. We quantify this divergence through (i) $L^2$ distance between parameters, (ii) the loss barrier when interpolating between networks, (iii) $L^2$ and barrier between parameters after permutation alignment, and (iv) representational similarity between intermediate activations; revealing how perturbations across different hyperparameter or fine-tuning settings drive training trajectories toward distinct loss minima. Our findings provide insights into neural network training stability, with practical implications for fine-tuning, model merging, and diversity of model ensembles.

Machine unlearning focuses on efficiently removing specific data from trained models, addressing privacy and compliance concerns with reasonable costs. Although exact unlearning ensures complete data removal equivalent to retraining, it is impractical for large-scale models, leading to growing interest in inexact unlearning methods. However, the lack of formal guarantees in these methods necessitates the need for robust evaluation frameworks to assess their privacy and effectiveness. In this work, we first identify several key pitfalls of the existing unlearning evaluation frameworks, e.g., focusing on average-case evaluation or targeting random samples for evaluation, incomplete comparisons with the retraining baseline. Then, we propose RULI (Rectified Unlearning Evaluation Framework via Likelihood Inference), a novel framework to address critical gaps in the evaluation of inexact unlearning methods. RULI introduces a dual-objective attack to measure both unlearning efficacy and privacy risks at a per-sample granularity. Our findings reveal significant vulnerabilities in state-of-the-art unlearning methods, where RULI achieves higher attack success rates, exposing privacy risks underestimated by existing methods. Built on a game-based foundation and validated through empirical evaluations on both image and text data (spanning tasks from classification to generation), RULI provides a rigorous, scalable, and fine-grained methodology for evaluating unlearning techniques.

Generating rational and generally accurate responses to tasks, often accompanied by example demonstrations, highlights Large Language Model's (LLM's) remarkable In-Context Learning (ICL) capabilities without requiring updates to the model's parameter space. Despite having an ongoing exploration focused on the inference from a document-level concept, its behavior in learning well-defined functions or relations in context needs a careful investigation. In this article, we present the performance of ICL on partially ordered relation by introducing the notion of inductively increasing complexity in prompts. In most cases, the saturated performance of the chosen metric indicates that while ICL offers some benefits, its effectiveness remains constrained as we increase the complexity in the prompts even in presence of sufficient demonstrative examples. The behavior is evident from our empirical findings and has further been theoretically justified in term of its implicit optimization process. The code is available here.

We analyzes the logit dynamics of softmax policy gradient methods. We derive the exact formula for the L2 norm of the logit update vector: $$ \|Δ\mathbf{z}\|_2 \propto \sqrt{1-2P_c + C(P)} $$ This equation demonstrates that update magnitudes are determined by the chosen action's probability ($P_c$) and the policy's collision probability ($C(P)$), a measure of concentration inversely related to entropy. Our analysis reveals an inherent self-regulation mechanism where learning vigor is automatically modulated by policy confidence, providing a foundational insight into the stability and convergence of these methods.

Fair clustering has become a socially significant task with the advancement of machine learning technologies and the growing demand for trustworthy AI. Group fairness ensures that the proportions of each sensitive group are similar in all clusters. Most existing group-fair clustering methods are based on the $K$-means clustering and thus require the distance between instances and the number of clusters to be given in advance. To resolve this limitation, we propose a fair Bayesian model-based clustering called Fair Bayesian Clustering (FBC). We develop a specially designed prior which puts its mass only on fair clusters, and implement an efficient MCMC algorithm. Advantages of FBC are that it can infer the number of clusters and can be applied to any data type as long as the likelihood is defined (e.g., categorical data). Experiments on real-world datasets show that FBC (i) reasonably infers the number of clusters, (ii) achieves a competitive utility-fairness trade-off compared to existing fair clustering methods, and (iii) performs well on categorical data.

Contrastive self-supervised learning based on point-wise comparisons has been widely studied for vision tasks. In the visual cortex of the brain, neuronal responses to distinct stimulus classes are organized into geometric structures known as neural manifolds. Accurate classification of stimuli can be achieved by effectively separating these manifolds, akin to solving a packing problem. We introduce Contrastive Learning As Manifold Packing (CLAMP), a self-supervised framework that recasts representation learning as a manifold packing problem. CLAMP introduces a loss function inspired by the potential energy of short-range repulsive particle systems, such as those encountered in the physics of simple liquids and jammed packings. In this framework, each class consists of sub-manifolds embedding multiple augmented views of a single image. The sizes and positions of the sub-manifolds are dynamically optimized by following the gradient of a packing loss. This approach yields interpretable dynamics in the embedding space that parallel jamming physics, and introduces geometrically meaningful hyperparameters within the loss function. Under the standard linear evaluation protocol, which freezes the backbone and trains only a linear classifier, CLAMP achieves competitive performance with state-of-the-art self-supervised models. Furthermore, our analysis reveals that neural manifolds corresponding to different categories emerge naturally and are effectively separated in the learned representation space, highlighting the potential of CLAMP to bridge insights from physics, neural science, and machine learning.

Probabilistic forecasts are typically obtained using state-of-the-art statistical and machine learning models, with model parameters estimated by optimizing a proper scoring rule over a set of training data. If the model class is not correctly specified, then the learned model will not necessarily issue forecasts that are calibrated. Calibrated forecasts allow users to appropriately balance risks in decision making, and it is particularly important that forecast models issue calibrated predictions for extreme events, since such outcomes often generate large socio-economic impacts. In this work, we study how the loss function used to train probabilistic forecast models can be adapted to improve the reliability of forecasts made for extreme events. We investigate loss functions based on weighted scoring rules, and additionally propose regularizing loss functions using a measure of tail miscalibration. We apply these approaches to a hierarchy of increasingly flexible forecast models for UK wind speeds, including simple parametric models, distributional regression networks, and conditional generative models. We demonstrate that state-of-the-art models do not issue calibrated forecasts for extreme wind speeds, and that the calibration of forecasts for extreme events can be improved by suitable adaptations to the loss function during model training. This, however, introduces a trade-off between calibrated forecasts for extreme events and calibrated forecasts for more common outcomes.