State-of-the-art embeddings often capture distinct yet complementary discriminative features: For instance, one image embedding model may excel at distinguishing fine-grained textures, while another focuses on object-level structure. Motivated by this observation, we propose a principled approach to fuse such complementary representations through kernel multiplication. Multiplying the kernel similarity functions of two embeddings allows their discriminative structures to interact, producing a fused representation whose kernel encodes the union of the clusters identified by each parent embedding. This formulation also provides a natural way to construct joint kernels for paired multi-modal data (e.g., image-text tuples), where the product of modality-specific kernels inherits structure from both domains. We highlight that this kernel product is mathematically realized via the Kronecker product of the embedding feature maps, yielding our proposed KrossFuse framework for embedding fusion. To address the computational cost of the resulting high-dimensional Kronecker space, we further develop RP KrossFuse, a scalable variant that leverages random projections for efficient approximation. As a key application, we use this framework to bridge the performance gap between cross-modal embeddings (e.g., CLIP, BLIP) and unimodal experts (e.g., DINOv2, E5). Experiments show that RP KrossFuse effectively integrates these models, enhancing modality-specific performance while preserving cross-modal alignment.

Surrogate regret bounds, also known as excess risk bounds, bridge the gap between the convergence rates of surrogate and target losses. The regret transfer is lossless if the surrogate regret bound is linear. While convex smooth surrogate losses are appealing in particular due to the efficient estimation and optimization, the existence of a trade-off between the loss smoothness and linear regret bound has been believed in the community. Under this scenario, the better optimization and estimation properties of convex smooth surrogate losses may inevitably deteriorate after undergoing the regret transfer onto a target loss. We overcome this dilemma for arbitrary discrete target losses by constructing a convex smooth surrogate loss, which entails a linear surrogate regret bound composed with a tailored prediction link. The construction is based on Fenchel-Young losses generated by the convolutional negentropy, which are equivalent to the infimal convolution of a generalized negentropy and the target Bayes risk. Consequently, the infimal convolution enables us to derive a smooth loss while maintaining the surrogate regret bound linear. We additionally benefit from the infimal convolution to have a consistent estimator of the underlying class probability. Our results are overall a novel demonstration of how convex analysis penetrates into optimization and statistical efficiency in risk minimization.

Personalized alignment is essential for enabling large language models (LLMs) to engage effectively in user-centric dialogue. While recent prompt-based and offline optimization methods offer preliminary solutions, they fall short in coldstart scenarios and long-term personalization due to their inherently static and shallow designs. In this work, we introduce the Reinforcement Learning for Personalized Alignment (RLPA) framework, in which an LLM interacts with a simulated user model to iteratively infer and refine user profiles through dialogue. The training process is guided by a dual-level reward structure: the Profile Reward encourages accurate construction of user representations, while the Response Reward incentivizes generation of responses consistent with the inferred profile.

Value-based algorithms are a cornerstone of off-policy reinforcement learning due to their simplicity and training stability. However, their use has traditionally been restricted to discrete action spaces, as they rely on estimating Q-values for individual state-action pairs. In continuous action spaces, evaluating the Q-value over the entire action space becomes computationally infeasible. To address this, actor-critic methods are typically employed, where a critic is trained on off-policy data to estimate Q-values, and an actor is trained to maximize the critic's output. Despite their popularity, these methods often suffer from instability during training. In this work, we propose a purely value-based framework for continuous control that revisits structural maximization of Q-functions, introducing a set of key architectural and algorithmic choices to enable efficient and stable learning. We evaluate the proposed actor-free Q-learning approach on a range of standard simulation tasks, demonstrating performance and sample-efficiency on par with state-of-the-art baselines, without the cost of learning a separate actor. Particularly, in environments with constrained action spaces, where the value functions are typically non-smooth, our method with structural maximization outperforms traditional actor-critic methods with gradient-based maximization. We have released our code at https://github.com/USC-Lira/Q3C.

Reinforcement learning (RL) post-training is crucial for LLM alignment and reasoning, but existing policy-based methods, such as PPO and DPO, can fall short of fixing shortcuts inherited from pre-training. In this work, we introduce Q, a value-based algorithm for KL-regularized RL that guides the reference policy using the optimal regularized Q function. We propose to learn the optimal Q function using distributional RL on an aggregated online dataset. Unlike prior value-based baselines that guide the model using unregularized Q-values, our method is theoretically principled and provably learns the optimal policy for the KL-regularized RL problem. Empirically, Q outperforms prior baselines in math reasoning benchmarks while maintaining a smaller KL divergence to the reference policy. Theoretically, we establish a reduction from KL-regularized RL to no-regret online learning, providing the first bounds for deterministic MDPs under only realizability. Thanks to distributional RL, our bounds are also variance-dependent and converge faster when the reference policy has small variance. In sum, our results highlight Q as an effective approach for post-training LLMs, offering both improved performance and theoretical guarantees. The code can be found at https://github.com/jinpz/q_sharp.

Gradient boosting is widely popular due to its flexibility and predictive accuracy. However, statistical inference and uncertainty quantification for gradient boosting remain challenging and under-explored. We propose a unified framework for statistical inference in gradient boosting regression. Our framework integrates dropout or parallel training with a recently proposed regularization procedure called Boulevard that allows for a central limit theorem (CLT) for boosting. With these enhancements, we surprisingly find that increasing the dropout rate and the number of trees grown in parallel at each iteration substantially enhances signal recovery and overall performance. Our resulting algorithms enjoy similar CLTs, which we use to construct built-in confidence intervals, prediction intervals, and rigorous hypothesis tests for assessing variable importance in only O(nd2) time with the Nystr om method. Numerical experiments verify the asymptotic normality and demonstrate that our algorithms perform well, do not require early stopping, interpolate between regularized boosting and random forests, and confirm the validity of their built-in statistical inference procedures.

The diffusion inversion problem seeks to recover the latent generative trajectory of a diffusion model given a real image. Faithful inversion is critical for ensuring consistency in diffusion-based image editing. Prior works formulate this task as a fixed-point problem and solve it using numerical methods. However, achieving both accuracy and efficiency remains challenging, especially for few-step models and novel samples. In this paper, we propose PreciseInv, a general-purpose testtime optimization framework that enables fast and faithful inversion in as few as two inference steps.

Accurately estimating semantic aleatoric and epistemic uncertainties in large language models (LLMs) is particularly challenging in free-form question answering (QA), where obtaining stable estimates often requires many expensive generations. We introduce a diversity-steered sampler that discourages semantically redundant outputs during decoding, covers both autoregressive and masked diffusion paradigms, and yields substantial sampleefficiency gains. The key idea is to inject a continuous semantic-similarity penalty into the model's proposal distribution using a natural language inference (NLI) model lightly fine-tuned on partial prefixes or intermediate diffusion states. We debias downstream uncertainty estimates with importance reweighting and shrink their variance with control variates. Across four QA benchmarks, our method matches or surpasses baselines while covering more semantic clusters with the same number of samples. Being modular and requiring no gradient access to the base LLM, the framework promises to serve as a drop-in enhancement for uncertainty estimation in risk-sensitive model deployments.

Modern recommendation systems increasingly rely on dynamically routing diverse queries to multiple embedding models. Despite its practical significance, this problem remains poorly understood under realistic conditions like adversarial queries, bandit feedback, and limited observability of models. We formalize embedding model routing as an adversarial contextual linear bandit with low-rank experts, where contexts are queries, actions are items, and experts are the embedding models working on low-rank latent representation spaces. We first establish that standard regret notions suffer from structural misspecification or statistical intractability, and we identify a log-quadratic policy class that is expressive enough to capture query-dependent model routing, yet structured enough to allow efficient online learning. Second, we propose a policy gradient algorithm called Hypentropy Policy Gradient (HPG). It provably adapts to the unknown low-rank structure under incomplete information and attains $\tilde{\mathcal O}(s\sqrt{M T})$ linearized policy regret -- where $s, M$, and $T$ are the intrinsic rank of the experts, the number of models, and the number of rounds -- thus avoiding a curse of dimensionality. Finally, we also provide an computationally efficient and parameter-free implementation of HPG.

An artificial intelligence must have a model of its environment that is causal, supporting reasoning about interventions and counterfactuals, and also combinatorial, supporting generalization to unseen combinations of objects. In this work, we formally study when and how such a model can be learned. We develop relational structural causal models, extending structural causal models (Pearl 2009) to settings where objects and their relations vary. First, we show how answers to not only causal but also observational queries about unseen combinations of objects can not be identified without further assumptions. To enable such identification--including in the presence of unobserved confounding--we define relational causal graphs and derive symbolic identification criteria. Finally, we propose relational neural causal models, a provably correct approach that outperforms non-relational baselines on simulated traffic scenes with varying cars, signals, and pedestrians.