Although humans inherently have diverse values, current large language model (LLM) alignment methods often assume that aligning LLMs with the general public's preferences is optimal. A major challenge in adopting a more individualized approach to LLM alignment is its lack of scalability, as it involves repeatedly acquiring preference data and training new reward models and LLMs for each individual's preferences. To address these challenges, we propose a new paradigm where users specify what they value most within the system message, steering the LLM's generation behavior to better align with the user's intentions. However, a naive application of such an approach is non-trivial since LLMs are typically trained on a uniform system message (e.g., "You are a helpful assistant"), which limits their ability to generalize to diverse, unseen system messages.

Matrix sketching is a powerful tool for reducing the size of large data matrices. Yet there are fundamental limitations to this size reduction when we want to recover an accurate estimator for a task such as least square regression. We show that these limitations can be circumvented in the distributed setting by designing sketching methods that minimize the bias of the estimator, rather than its error. In particular, we give a sparse sketching method running in optimal space and current matrix multiplication time, which recovers a nearly-unbiased least squares estimator using two passes over the data. This leads to new communication-efficient distributed averaging algorithms for least squares and related tasks, which directly improve on several prior approaches. Our key novelty is a new bias analysis for sketched least squares, giving a sharp characterization of its dependence on the sketch sparsity. The techniques include new higher-moment restricted Bai-Silverstein inequalities, which are of independent interest to the non-asymptotic analysis of deterministic equivalents for random matrices that arise from sketching.

Surprisingly, however, the optimal rate in terms of Bellman error for the VI setup was not known, and finding a general acceleration mechanism has been an open problem. In this paper, we present the first accelerated VI for both the Bellman consistency and optimality operators. Our method, called Anc-VI, is based on an anchoring mechanism (distinct from Nesterov's acceleration), and it reduces the Bellman error faster than standard VI. In particular, Anc-VI exhibits a O(1/k)-rate for γ 1 or even γ = 1, while standard VI has rate O(1) for γ 1 1/k, where k is the iteration count. We also provide a complexity lower bound matching the upper bound up to a constant factor of 4, thereby establishing optimality of the accelerated rate of Anc-VI. Finally, we show that the anchoring mechanism provides the same benefit in the approximate VI and Gauss-Seidel VI setups as well.

Tensor Train (TT) decomposition is widely used in the machine learning and quantum physics communities as a popular tool to efficiently compress high-dimensional tensor data. In this paper, we propose an efficient algorithm to accelerate computing the TT decomposition with the Alternating Least Squares (ALS) algorithm relying on exact leverage scores sampling. For this purpose, we propose a data structure that allows us to efficiently sample from the tensor with time complexity logarithmic in the tensor size.

The aim of this paper is to address the challenge of gradual domain adaptation within a class of manifold-constrained data distributions.

A fundamental problem arising in many areas of machine learning is the evaluation of the likelihood of a given observation under different nominal distributions. Frequently, these nominal distributions are themselves estimated from data, which makes them susceptible to estimation errors. We thus propose to replace each nominal distribution with an ambiguity set containing all distributions in its vicinity and to evaluate an optimistic likelihood, that is, the maximum of the likelihood over all distributions in the ambiguity set. When the proximity of distributions is quantified by the Fisher-Rao distance or the Kullback-Leibler divergence, the emerging optimistic likelihoods can be computed efficiently using either geodesic or standard convex optimization techniques.

Turn-level dialogue evaluation models (TDEMs), using self-supervised learning (SSL) framework, have achieved state-of-the-art performance in open-domain dialogue evaluation. However, these models inevitably face two potential problems. First, they have low correlations with humans on medium coherence samples as the SSL framework often brings training data with unbalanced coherence distribution. Second, the SSL framework leads TDEM to nonuniform score distribution. There is a danger that the nonuniform score distribution will weaken the robustness of TDEM through our theoretical analysis.

Although recent efforts have extended Neural Radiance Fields (NeRF) into LiDAR point cloud synthesis, the majority of existing works exhibit a strong dependence on precomputed poses. However, point cloud registration methods struggle to achieve precise global pose estimation, whereas previous pose-free NeRFs overlook geometric consistency in global reconstruction. In light of this, we explore the geometric insights of point clouds, which provide explicit registration priors for reconstruction. Based on this, we propose Geometry guided Neural LiDAR Fields (GeoNLF), a hybrid framework performing alternately global neural reconstruction and pure geometric pose optimization. Furthermore, NeRFs tend to overfit individual frames and easily get stuck in local minima under sparse-view inputs. To tackle this issue, we develop a selective-reweighting strategy and introduce geometric constraints for robust optimization. Extensive experiments on NuScenes and KITTI-360 datasets demonstrate the superiority of GeoNLF in both novel view synthesis and multi-view registration of low-frequency large-scale point clouds.

We present a comprehensive study of surrogate loss functions for learning to defer. We introduce a broad family of surrogate losses, parameterized by a non-increasing function Ψ, and establish their realizable H-consistency under mild conditions. For cost functions based on classification error, we further show that these loss functions admit H-consistency bounds when the hypothesis set is symmetric and complete, a property satisfied by common neural network and linear function hypothesis sets. Our results also resolve an open question raised in previous work [Mozannar et al., 2023] by proving the realizable H-consistency and Bayes-consistency of a specific surrogate loss. Furthermore, we identify choices of Ψ that lead to H-consistent surrogate losses for any general cost function, thus achieving Bayesconsistency, realizable H-consistency, and H-consistency bounds simultaneously. We also investigate the relationship between H-consistency bounds and realizable H-consistency in learning to defer, highlighting key differences from standard classification. Finally, we empirically evaluate our proposed surrogate losses and compare them with existing baselines.

Gaussian processes (GPs) are flexible non-parametric models, with a capacity that grows with the available data. However, computational constraints with standard inference procedures have limited exact GPs to problems with fewer than about ten thousand training points, necessitating approximations for larger datasets. In this paper, we develop a scalable approach for exact GPs that leverages multi-GPU parallelization and methods like linear conjugate gradients, accessing the kernel matrix only through matrix multiplication. By partitioning and distributing kernel matrix multiplies, we demonstrate that an exact GP can be trained on over a million points, a task previously thought to be impossible with current computing hardware, in less than 2 hours. Moreover, our approach is generally applicable, without constraints to grid data or specific kernel classes.