The adaptive moment estimation (Adam) optimizer proposed by Kingma & Ba (2014) is presumably the most popular stochastic gradient descent (SGD) optimization method for the training of deep neural networks (DNNs) in artificial intelligence (AI) systems. Despite its groundbreaking success in the training of AI systems, it still remains an open research problem to provide a complete error analysis of Adam, not only for optimizing DNNs but even when applied to strongly convex stochastic optimization problems (SOPs). Previous error analysis results for strongly convex SOPs in the literature provide conditional convergence analyses that rely on the assumption that Adam does not diverge to infinity but remains uniformly bounded. It is the key contribution of this work to establish uniform a priori bounds for Adam and, thereby, to provide -- for the first time -- an unconditional error analysis for Adam for a large class of strongly convex SOPs.
The shock response spectrum (SRS) is widely used to characterize the response of single-degree-of-freedom (SDOF) systems to transient accelerations. Because the mapping from acceleration time history to SRS is nonlinear and many-to-one, reconstructing time-domain signals from a target spectrum is inherently ill-posed. Conventional approaches address this problem through iterative optimization, typically representing signals as sums of exponentially decayed sinusoids, but these methods are computationally expensive and constrained by predefined basis functions.
We propose a conditional variational autoencoder (CVAE) that learns a data-driven inverse mapping from SRS to acceleration time series. Once trained, the model generates signals consistent with prescribed target spectra without requiring iterative optimization. Experiments demonstrate improved spectral fidelity relative to classical techniques, strong generalization to unseen spectra, and inference speeds three to six orders of magnitude faster. These results establish deep generative modeling as a scalable and efficient approach for inverse SRS reconstruction.
Adam Watts (Los Alamos National Laboratory), Andrew Jeon (Los Alamos National Laboratory), Destry Newton (Los Alamos National Laboratory) et al.· 0 citations
Entity alignment (EA) is critical for knowledge graph (KG) fusion. Existing EA models lack transferability and are incapable of aligning unseen KGs without retraining. While using graph foundation models (GFMs) offer a solution, we find that directly adapting GFMs to EA remains largely ineffective. This stems from a critical "reasoning horizon gap": unlike link prediction in GFMs, EA necessitates capturing long-range dependencies across sparse and heterogeneous KG structuresTo address this challenge, we propose a EA foundation model driven by a parallel encoding strategy. We utilize seed EA pairs as local anchors to guide the information flow, initializing and encoding two parallel streams simultaneously. This facilitates anchor-conditioned message passing and significantly shortens the inference trajectory by leveraging local structural proximity instead of global search. Additionally, we incorporate a merged relation graph to model global dependencies and a learnable interaction module for precise matching. Extensive experiments verify the effectiveness of our framework, highlighting its strong generalizability to unseen KGs.
Yuanning Cui, Zequn Sun, Wei Hu et al.· 0 citations
Optimizer design plays a central role in efficient language model pretraining, directly affecting optimization dynamics, convergence speed, and compute cost under fixed training budgets. Muon has emerged as a strong optimizer by orthogonalizing momentum updates, yielding a matrix-valued analogue of sign-based normalization. However, unlike Adam-style methods, Muon does not explicitly incorporate gradient-variance information into its updates. Motivated by Adam's variance-adaptive interpretation, we propose Muon-NSR and Muon-VS, two variance-adaptive Muon variants for language model pretraining. Muon-NSR applies noise-to-signal ratio (NSR) modulation before Newton--Schulz orthogonalization, whereas Muon-VS uses variance scaling (VS) without introducing any additional hyperparameters beyond those of Muon. Both methods preserve Muon's spectral normalization structure while requiring only one additional variance buffer. Experiments on Llama-style and GPT-2 pretraining across model scales from 125M to 1.2B parameters show that our methods improve over well-tuned Muon baselines and remain competitive with representative adaptive Muon-family baselines. On Llama-1.2B, Muon-VS achieves a 1.33$\times$ step-to-target speedup over a well-tuned Muon baseline, with Muon's final validation loss as the target. These results indicate that variance-adaptive modulation is a simple and effective mechanism for improving Muon-style optimizers in language model pretraining.
Jingru Li, Yibo Fan, Huan Li· 0 citations
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Sampling from unnormalized probability densities is a pervasive challenge across the computational and physical sciences. Diffusion models provide a powerful generative framework for this task, but their success relies on accurately estimating the score of the perturbed target distribution. Current approaches face a dichotomy between two standard estimation methods: the Denoising Score Identity (DSI) requires data samples and exhibits high variance at low noise levels, whereas the Target Score Identity (TSI) relies on the energy function and suffers from diverging variance at high noise levels. In this work, we reconcile both approaches by introducing the Control Variate Score Identity (CVSI), an unbiased estimator with an analytically optimal, state- and time-dependent control coefficient that theoretically minimizes variance over the entire diffusion process. CVSI serves as a robust plug-in estimator that significantly enhances performance and efficiency in data-free sampler learning and training-free diffusion sampling. These gains scale to complex, high-dimensional energy-based models.
Khaled Kahouli, Romuald Elie, Klaus-Robert M\"uller et al.· 0 citations
As organizations increasingly deploy LLMs in sensitive domains such as legal, financial, and medical settings, ensuring alignment with internal organizational policies has become a priority. Existing content moderation frameworks remain largely confined to the safety domain and lack the robustness to capture nuanced organizational policies. LLM-as-a-judge and fine-tuning approaches, though flexible, introduce significant latency and training cost. To address these limitations, we frame policy violation detection as an out-of-distribution (OOD) problem in the model's activation space. We propose a training-free method that operates directly on the LLM internal representations, leveraging prior evidence that decision-relevant information is encoded within them. Inspired by whitening techniques, we derive policy-violation scores directly from normalized representations of LLM hidden activations. Our method requires only the policy text and a small number of illustrative samples, making it lightweight and easily deployable. We extensively evaluate our method across multiple LLMs and challenging policy benchmarks. It achieves up to 86.0% F1, outperforming both fine-tuned and LLM-as-a-judge baselines while requiring substantially less computation. Our code is publicly available at: https://github.com/FujitsuResearch/LLM-policy-violation-detection
Oren Rachmil, Avishag Shapira, Roy Betser et al.· 0 citations
Pretrained transformers provide rich, general-purpose embeddings, which are transferred to downstream tasks. However, current transfer strategies: fine-tuning and probing, either distort the pretrained geometric structure of the embeddings or lack sufficient expressivity to capture task-relevant signals. These issues become even more pronounced when supervised data are scarce. Here, we introduce Freeze, Diffuse, Decode (FDD), a novel diffusion-based framework that adapts pre-trained embeddings to downstream tasks while preserving their underlying geometric structure. FDD propagates supervised signal along the intrinsic manifold of frozen embeddings, enabling a geometry-aware adaptation of the embedding space. Applied to antimicrobial peptide design, FDD yields low-dimensional, predictive, and interpretable representations that support property prediction, retrieval, and latent-space interpolation.
Pankhil Gawade, Adam Izdebski, Myriam Lizotte et al.· 0 citations
Practical LLM agents often operate over multi-turn conversations where success is determined only after the full interaction ends. Most multi-turn RL methods train via on-policy rollouts, but unlike in single-turn RLHF, the policy cannot produce a trajectory alone, since an external environment must respond after each agent turn. For conversational agents, this environment is a user, but real users are generally unavailable inside the training loop and simulated users are difficult to build faithfully. Separately, real-world deployment is rarely fully online or fully offline. The common production pattern is called "batch online," where the current policy is deployed to collect a batch of interaction data, then retrained on that batch and redeployed. We show that this batch-online setting creates an opportunity for applying the classical approximate policy iteration algorithm. Our central observation is that running standard token-level, single-turn GRPO with a learned turn-level $Q$-function as the reward model is a policy improvement step for the multi-turn problem. Building on this, we present Iterative GRPO, which alternates between fitting $Q^\pi$ from logged Monte Carlo returns via standard reward modeling (policy evaluation) and running single-turn GRPO against $Q^\pi$ (policy improvement). During policy improvement, the learned $Q^\pi$ scores candidate responses by their expected downstream return, avoiding the need for simulator rollouts of the remaining conversation. Overall, this allows us to do principled multi-turn RL using only single-turn RLHF methods without an interactive environment or user simulator inside the training loop. We demonstrate the effectiveness of Iterative GRPO on six multi-turn negotiation environments.
Daniel R. Jiang, Ankur Samanta, Yukai Yang et al.· 0 citations
Transformers have achieved remarkable successes across a wide range of applications, yet the theoretical foundation of their model efficiency remains underexplored. In this work, we investigate how the model parameters -- mainly attention heads and head dimensions -- should be allocated across layers to balance expressivity and efficiency. We first provide mathematical analysis on the role of early layers in information extraction from an approximation perspective, with a theoretical characterization on the trade-off between the number of heads and head dimension under a fixed parameter budget. In addition, we uncover and prove the \emph{saturation} behavior of softmax activations: Continuously increasing head dimensions can lead to diminishing returns in learning errors, particularly for long sequences. Supported by both theory and experiments, this saturation pattern suggests that later layers can operate more efficiently with reduced parameters. Combining these insights, we propose principled strategies for allocating attention heads and dimensions across Transformers' layers, shedding light on theoretically-grounded model efficiency of Transformer-based architectures.
Ruoxi Yu, Haotian Jiang, Jingpu Cheng et al.· 0 citations
Reinforcement Learning (RL) has emerged as a central paradigm for advancing Large Language Models (LLMs), where both pre-training and RL post-training stages are grounded in the same log-likelihood formulation. In contrast, recent RL approaches for diffusion models, most notably Denoising Diffusion Policy Optimization (DDPO), optimize an objective different from the pretraining objectives--score/flow matching loss. In this work, we establish a novel theoretical analysis: DDPO is an implicit form of score/flow matching with noisy targets, which increases variance and slows convergence. Building on this analysis, we introduce Advantage Weighted Matching (AWM), a policy-gradient method for diffusion. It uses the score/flow-matching loss and reweights each sample by its advantage. In effect, AWM raises the influence of high-reward samples and suppresses low-reward ones while keeping the modeling objective identical to pretraining. This simple yet effective design yields substantial benefits: on the GenEval, OCR, and PickScore benchmarks, AWM delivers up to a $34\times$ speedup over Flow-GRPO (which builds on DDPO), when applied to Stable Diffusion 3.5 Medium and FLUX, without compromising generation quality. Code is available at https://github.com/scxue/advantage_weighted_matching
Shuchen Xue, Chongjian Ge, Shilong Zhang et al.· 0 citations
We study a compositional variant of kernel ridge regression in which the predictor is applied to a coordinate-wise reweighting of the inputs. Formulated as a variational problem, this model provides a tractable setting for studying feature learning in compositional architectures. From the perspective of variable selection, we show how relevant variables are recovered while noise variables are eliminated. We prove that both global minimizers and stationary points discard noise coordinates when the noise variables are Gaussian distributed. A central finding is that $\ell_1$-type kernels, such as the Laplace kernel, succeed in recovering features contributing to nonlinear effects at stationary points, whereas Gaussian kernels recover only linear ones.
The primary paradigm in Neural Combinatorial Optimization (NCO) consists of construction methods, where a neural network is trained to sequentially add one solution component at a time until a complete solution is formed. We observe that the typical changes to the state between two steps are small, since usually only the node added to the solution is removed from the state. An efficient model should be able to reuse computation from prior steps. To that end, we propose a recurrent encoder that computes state embeddings based not only on the current state but also on embeddings from the previous state. We show that this recurrent encoder can achieve equivalent or better performance than a non-recurrent encoder even with $3\times$ fewer layers, thus significantly improving latency. We demonstrate our findings on three different problems: the Traveling Salesman Problem (TSP), the Capacitated Vehicle Routing Problem (CVRP), and the Orienteering Problem (OP), and integrate the models into a large neighborhood search algorithm to showcase the practical relevance of our findings.
Tim Dernedde, Daniela Thyssens, Lars Schmidt-Thieme· 0 citations
A weeklong summer workshop brought higher education faculty to campus to explore how AI and machine learning materials can be adapted for their classrooms.
A new machine-learning framework aims to improve the success rate of computational protein design while moving away from results that reproduce sequences found in nature.
MIT News · Artificial Intelligence· news.mit.eduAug 24, 2026
