Aligning large language models (LLMs) with human objectives is crucial for real-world applications. However, fine-tuning LLMs for alignment often suffers from unstable training and requires substantial computing resources. Test-time alignment techniques, such as prompting and guided decoding, do not modify the underlying model, and their performance remains dependent on the original model's capabilities. To address these challenges, we propose aligning LLMs through representation editing. The core of our method is to view a pre-trained autoregressive LLM as a discrete-time stochastic dynamical system. To achieve alignment for specific objectives, we introduce external control signals into the state space of this language dynamical system. We train a value function directly on the hidden states according to the Bellman equation, enabling gradient-based optimization to obtain the optimal control signals at test time. Our experiments demonstrate that our method outperforms existing test-time alignment techniques while requiring significantly fewer resources compared to fine-tuning methods.

We consider metrical task systems on general metric spaces with $n$ points, and show that any fully randomized algorithm can be turned into a randomized algorithm that uses only $2\log n$ random bits, and achieves the same competitive ratio up to a factor $2$. This provides the first order-optimal barely random algorithms for metrical task systems, i.e. which use a number of random bits that does not depend on the number of requests addressed to the system. We discuss implications on various aspects of online decision making such as: distributed systems, advice complexity and transaction costs, suggesting broad applicability. We put forward an equivalent view that we call collective metrical task systems where $k$ agents in a metrical task system team up, and suffer the average cost paid by each agent. Our results imply that such team can be $O(\log^2 n)$-competitive as soon as $k\geq n^2$. In comparison, a single agent is always $\Omega(n)$-competitive.

Given the high economic and environmental costs of using large vision or language models, analog in-memory accelerators present a promising solution for energy-efficient AI. While inference on analog accelerators has been studied recently, the training perspective is underexplored. Recent studies have shown that the workhorse of digital AI training - stochastic gradient descent (SGD) algorithm converges inexactly when applied to model training on non-ideal devices. This paper puts forth a theoretical foundation for gradient-based training on analog devices. We begin by characterizing the non-convergent issue of SGD, which is caused by the asymmetric updates on the analog devices. We then provide a lower bound of the asymptotic error to show that there is a fundamental performance limit of SGD-based analog training rather than an artifact of our analysis. To address this issue, we study a heuristic analog algorithm called Tiki-Taka that has recently exhibited superior empirical performance compared to SGD. We rigorously show its ability to converge to a critical point exactly and hence eliminate the asymptotic error. The simulations verify the correctness of the analyses.

Deformable shapes provide important and complex geometric features of objects presented in images. However, such information is oftentimes missing or underutilized as implicit knowledge in many image analysis tasks. This paper presents Geo-SIC, the first deep learning model to learn deformable shapes in a deformation space for an improved performance of image classification. We introduce a newly designed framework that (i) simultaneously derives features from both image and latent shape spaces with large intra-class variations; and (ii) gains increased model interpretability by allowing direct access to the underlying geometric features of image data. In particular, we develop a boosted classification network, equipped with an unsupervised learning of geometric shape representations characterized by diffeomorphic transformations within each class. In contrast to previous approaches using pre-extracted shapes, our model provides a more fundamental approach by naturally learning the most relevant shape features jointly with an image classifier. We demonstrate the effectiveness of our method on both simulated 2D images and real 3D brain magnetic resonance (MR) images. Experimental results show that our model substantially improves the image classification accuracy with an additional benefit of increased model interpretability. Our code is publicly available at https://github.com/jw4hv/Geo-SIC.

The field of face recognition (FR) has undergone significant advancements with the rise of deep learning. Recently, the success of unsupervised learning and graph neural networks has demonstrated the effectiveness of data structure information. Considering that the FR task can leverage large-scale training data, which intrinsically contains significant structure information, we aim to investigate how to encode such critical structure information into the latent space. As revealed from our observations, directly aligning the structure information between the input and latent spaces inevitably suffers from an overfitting problem, leading to a structure collapse phenomenon in the latent space. To address this problem, we propose TopoFR, a novel FR model that leverages a topological structure alignment strategy called PTSA and a hard sample mining strategy named SDE. Concretely, PTSA uses persistent homology to align the topological structures of the input and latent spaces, effectively preserving the structure information and improving the generalization performance of FR model. To mitigate the impact of hard samples on the latent space structure, SDE accurately identifies hard samples by automatically computing structure damage score (SDS) for each sample, and directs the model to prioritize optimizing these samples. Experimental results on popular face benchmarks demonstrate the superiority of our TopoFR over the state-of-the-art methods.

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Recent advancements in visualizing deep neural networks provide insights into their structures and mesh extraction from Continuous Piecewise Affine (CPWA) functions. Meanwhile, developments in neural surface representation learning incorporate non-linear positional encoding, addressing issues like spectral bias; however, this poses challenges in applying mesh extraction techniques based on CPWA functions.

Adapting large language models (LLMs) for specific tasks usually involves fine-tuning through reinforcement learning with human feedback (RLHF) on preference data. While these data often come from diverse labelers' groups (e.g., different demographics, ethnicities, company teams, etc.), traditional RLHF approaches adopt a one-size-fits-all approach, i.e., they indiscriminately assume and optimize a single preference model, thus not being robust to unique characteristics and needs of the various groups. To address this limitation, we propose a novel Group Robust Preference Optimization (GRPO) method to align LLMs to individual groups' preferences robustly. Our approach builds upon reward-free direct preference optimization methods, but unlike previous approaches, it seeks a robust policy which maximizes the worst-case group performance. To achieve this, GRPO adaptively and sequentially weights the importance of different groups, prioritizing groups with worse cumulative loss. We theoretically study the feasibility of GRPO and analyze its convergence for the log-linear policy class. By fine-tuning LLMs with GRPO using diverse group-based global opinion data, we significantly improved performance for the worst-performing groups, reduced loss imbalances across groups, and improved probability accuracies compared to non-robust baselines.

Two-stage recommender systems play a crucial role in efficiently identifying relevant items and personalizing recommendations from a vast array of options. This paper, based on an error decomposition framework, analyzes the generalization error for two-stage recommender systems with a tree structure, which consist of an efficient tree-based retriever and a more precise yet time-consuming ranker. We use the Rademacher complexity to establish the generalization upper bound for various tree-based retrievers using beam search, as well as for different ranker models under a shifted training distribution. Both theoretical insights and practical experiments on real-world datasets indicate that increasing the branches in tree-based retrievers and harmonizing distributions across stages can enhance the generalization performance of two-stage recommender systems.

Many zeroth-order (ZO) optimization algorithms have been developed to solve nonconvex minimax problems in machine learning and computer vision areas. However, existing ZO minimax algorithms have high complexity and rely on some strict restrictive conditions for ZO estimations. To address these issues, we design a new unified ZO gradient descent extragradient ascent (ZO-GDEGA) algorithm, which reduces the overall complexity to $\mathcal{O}(d\epsilon^{-6})$ to find an $\epsilon$-stationary point of the function $\psi$ for nonconvex-concave (NC-C) problems, where $d$ is the variable dimension. To the best of our knowledge, ZO-GDEGA is the first ZO algorithm with complexity guarantees to solve stochastic NC-C problems. Moreover, ZO-GDEGA requires weaker conditions on the ZO estimations and achieves more robust theoretical results. As a by-product, ZO-GDEGA has advantages on the condition number for the NC-strongly concave case. Experimentally, ZO-GDEGA can generate more effective poisoning attack data with an average accuracy reduction of 5\%. The improved AUC performance also verifies the robustness of gradient estimations.