Existing training-time safety alignment techniques for large language models (LLMs) remain vulnerable to jailbreak attacks. Direct preference optimization (DPO), a widely deployed alignment method, exhibits limitations in both experimental and theoretical contexts as its loss function proves suboptimal for refusal learning. Through gradient-based analysis, we identify these shortcomings and propose an improved safety alignment that disentangles DPO objectives into two components: (1) robust refusal training, which encourages refusal even when partial unsafe generations are produced, and (2) targeted unlearning of harmful knowledge. This approach significantly increases LLM robustness against a wide range of jailbreak attacks, including prefilling, suffix, and multi-turn attacks across both in-distribution and out-of-distribution scenarios. Furthermore, we introduce a method to emphasize critical refusal tokens by incorporating a reward-based token-level weighting mechanism for refusal learning, which further improves the robustness against adversarial exploits. Our research also suggests that robustness to jailbreak attacks is correlated with token distribution shifts in the training process and internal representations of refusal and harmful tokens, offering valuable directions for future research in LLM safety alignment. The code is available at https://github.com/wicai24/DOOR-Alignment.

This work studies the problem of large language model (LLM) unlearning, aiming to remove unwanted data influences (e.g., copyrighted or harmful content) while preserving model utility. Despite the increasing demand for unlearning, a technically-grounded optimization framework is lacking. Gradient ascent (GA)-type methods, though widely used, are suboptimal as they reverse the learning process without controlling optimization divergence (i.e., deviation from the pre-trained state), leading to risks of model collapse. Negative preference optimization (NPO) has been proposed to address this issue and is considered one of the state-of-the-art LLM unlearning approaches. In this work, we revisit NPO and identify another critical issue: reference model bias. This bias arises from using the reference model (i.e., the model prior to unlearning) to assess unlearning success, which can lead to a misleading impression of the true data-wise unlearning effectiveness. Specifically, it could cause (a) uneven allocation of optimization power across forget data with varying difficulty levels, and (b) ineffective gradient weight smoothing during the early stages of unlearning optimization. To overcome these challenges, we propose a simple yet effective unlearning optimization framework, called SimNPO, showing that simplicity—removing the reliance on a reference model (through the lens of simple preference optimization)—benefits unlearning. We provide deeper insights into SimNPO's advantages, including an analysis based on mixtures of Markov chains. Extensive experiments further validate its efficacy on benchmarks like TOFU, MUSE, and WMDP.

Contrastive learning---a modern approach to extract useful representations from unlabeled data by training models to distinguish similar samples from dissimilar ones---has driven significant progress in foundation models. In this work, we develop a new theoretical framework for analyzing data augmentation-based contrastive learning, with a focus on SimCLR as a representative example. Our approach is based on the concept of \emph{approximate sufficient statistics}, which we extend beyond its original definition in~\cite{oko2025statistical} for contrastive language-image pretraining (CLIP) using KL-divergence. We generalize it to equivalent forms and general $f$-divergences, and show that minimizing SimCLR and other contrastive losses yields encoders that are approximately sufficient. Furthermore, we demonstrate that these near-sufficient encoders can be effectively adapted to downstream regression and classification tasks, with performance depending on their sufficiency and the error induced by data augmentation in contrastive learning. Concrete examples in linear regression and topic classification are provided to illustrate the broad applicability of our results.

Neural scaling laws suggest that the test error of large language models trained online decreases polynomially as the model size and data size increase. However, such scaling can be unsustainable when running out of new data. In this work, we show that data reuse can improve existing scaling laws in linear regression. Specifically, we derive sharp test error bounds on $M$-dimensional linear models trained by multi-pass *stochastic gradient descent* (multi-pass SGD) on $N$ data with sketched features. Assuming that the data covariance has a power-law spectrum of degree $a$, and that the true parameter follows a prior with an aligned power-law spectrum of degree $b-a$ (with $a > b > 1$), we show that multi-pass SGD achieves a test error of $\Theta(M^{1-b} + L^{(1-b)/a})$, where $L \lesssim N^{a/b}$ is the number of iterations. In the same setting, one-pass SGD only attains a test error of $\Theta(M^{1-b} + N^{(1-b)/a})$ (see, e.g., Lin et al., 2024). This suggests an improved scaling law via data reuse (i.e., choosing $L>N$) in data-constrained regimes. Numerical simulations are also provided to verify our theoretical findings.

Large transformer models pretrained on offline reinforcement learning datasets have demonstrated remarkable in-context reinforcement learning (ICRL) capabilities, where they can make good decisions when prompted with interaction trajectories from unseen environments. However, when and how transformers can be trained to perform ICRL have not been theoretically well-understood. In particular, it is unclear which reinforcement-learning algorithms transformers can perform in context, and how distribution mismatch in offline training data affects the learned algorithms. This paper provides a theoretical framework that analyzes supervised pretraining for ICRL. This includes two recently proposed training methods --- algorithm distillation and decision-pretrained transformers. First, assuming model realizability, we prove the supervised-pretrained transformer will imitate the conditional expectation of the expert algorithm given the observed trajectory. The generalization error will scale with model capacity and a distribution divergence factor between the expert and offline algorithms. Second, we show transformers with ReLU attention can efficiently approximate near-optimal online reinforcement learning algorithms like LinUCB and Thompson sampling for stochastic linear bandits, and UCB-VI for tabular Markov decision processes. This provides the first quantitative analysis of the ICRL capabilities of transformers pretrained from offline trajectories.

When predictions are performative, the choice of which predictor to deploy influences the distribution of future observations. The overarching goal in learning under performativity is to find a predictor that has low performative risk, that is, good performance on its induced distribution. One family of solutions for optimizing the performative risk, including bandits and other derivative-free methods, is agnostic to any structure in the performative feedback, leading to exceedingly slow convergence rates. A complementary family of solutions makes use of explicit models for the feedback, such as best-response models in strategic classification, enabling faster rates. However, these rates critically rely on the feedback model being correct. In this work we study a general protocol for making use of possibly misspecified models in performative prediction, called plug-in performative optimization. We show this solution can be far superior to model-agnostic strategies, as long as the misspecification is not too extreme. Our results support the hypothesis that models, even if misspecified, can indeed help with learning in performative settings.

Empirically, large-scale deep learning models often satisfy a neural scaling law: the test error of the trained model improves polynomially as the model size and data size grow. However, conventional wisdom suggests the test error consists of approximation, bias, and variance errors, where the variance error increases with model size. This disagrees with the general form of neural scaling laws, which predict that increasing model size monotonically improves performance. We study the theory of scaling laws in an infinite dimensional linear regression setup. Specifically, we consider a model with $M$ parameters as a linear function of sketched covariates. The model is trained by one-pass stochastic gradient descent (SGD) using $N$ data. Assuming the optimal parameter satisfies a Gaussian prior and the data covariance matrix has a power-law spectrum of degree $a>1$, we show that the reducible part of the test error is $\Theta(M^{-(a-1)} + N^{-(a-1)/a})$. The variance error, which increases with $M$, is dominated by the other errors due to the implicit regularization of SGD, thus disappearing from the bound. Our theory is consistent with the empirical neural scaling laws and verified by numerical simulation.

Estimation and inference in statistics pose significant challenges when data are collected adaptively. Even in linear models, the Ordinary Least Squares (OLS) estimator may fail to exhibit asymptotic normality for single coordinate estimation and have inflated error. This issue is highlighted by a recent minimax lower bound, which shows that the error of estimating a single coordinate can be enlarged by a multiple of $\sqrt{d}$ when data are allowed to be arbitrarily adaptive, compared with the case when they are i.i.d. Our work explores this striking difference in estimation performance between utilizing i.i.d. and adaptive data. We investigate how the degree of adaptivity in data collection impacts the performance of estimating a low-dimensional parameter component in high-dimensional linear models. We identify conditions on the data collection mechanism under which the estimation error for a low-dimensional parameter component matches its counterpart in the i.i.d. setting, up to a factor that depends on the degree of adaptivity. We show that OLS or OLS on centered data can achieve this matching error. In addition, we propose a novel estimator for single coordinate inference via solving a Two-stage Adaptive Linear Estimating equation (TALE). Under a weaker form of adaptivity in data collection, we establish an asymptotic normality property of the proposed estimator.

Modern machine learning methods are often overparametrized, allowing adaptation to the data at a fine level. This can seem puzzling; in the worst case, such models do not need to generalize. This puzzle inspired a great amount of work, arguing when overparametrization reduces test error, in a phenomenon called `double descent'. Recent work aimed to understand in greater depth why overparametrization is helpful for generalization. This lead to discovering the unimodality of variance as a function of the level of parametrization, and to decomposing the variance into that arising from label noise, initialization, and randomness in the training data to understand the sources of the error. In this work we develop a deeper understanding of this area. Specifically, we propose using the analysis of variance (ANOVA) to decompose the variance in the test error in a symmetric way, for studying the generalization performance of certain two-layer linear and non-linear networks. The advantage of the analysis of variance is that it reveals the effects of initialization, label noise, and training data more clearly than prior approaches. Moreover, we also study the monotonicity and unimodality of the variance components. While prior work studied the unimodality of the overall variance, we study the properties of each term in the variance decomposition. One of our key insights is that often, the interaction between training samples and initialization can dominate the variance; surprisingly being larger than their marginal effect. Also, we characterize `phase transitions' where the variance changes from unimodal to monotone. On a technical level, we leverage advanced deterministic equivalent techniques for Haar random matrices, that---to our knowledge---have not yet been used in the area. We verify our results in numerical simulations and on empirical data examples.