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Generative recommendation (GR) is an emerging paradigm that tokenizes items into discrete tokens and learns to autoregressively generate the next tokens as predictions. While this token-generation paradigm is expected to surpass traditional transductive methods, potentially generating new items directly based on semantics, we empirically show that GR models predominantly generate items seen during training and struggle to recommend unseen items. In this paper, we propose SpecGR, a plug-and-play framework that enables GR models to recommend new items in an inductive setting. SpecGR uses a drafter model with inductive capability to propose candidate items, which may include both existing items and new items. The GR model then acts as a verifier, accepting or rejecting candidates while retaining its strong ranking capabilities. We further introduce the guided re-drafting technique to make the proposed candidates more aligned with the outputs of generative recommendation models, improving verification efficiency. We consider two variants for drafting: (1) using an auxiliary drafter model for better flexibility, or (2) leveraging the GR model’s own encoder for parameterefficient self-drafting. Extensive experiments on three realworld datasets demonstrate that SpecGR exhibits both strong inductive recommendation ability and the best overall performance among the compared methods. 

Generative recommendation (GR) is an emerging paradigm that tokenizes items into discrete tokens and learns to autoregressively generate the next tokens as predictions. While this token-generation paradigm is expected to surpass traditional transductive methods, potentially generating new items directly based on semantics, we empirically show that GR models predominantly generate items seen during training and struggle to recommend unseen items. In this paper, we propose SpecGR, a plug-and-play framework that enables GR models to recommend new items in an inductive setting. SpecGR uses a drafter model with inductive capability to propose candidate items, which may include both existing items and new items. The GR model then acts as a verifier, accepting or rejecting candidates while retaining its strong ranking capabilities. We further introduce the guided re-drafting technique to make the proposed candidates more aligned with the outputs of generative recommendation models, improving verification efficiency. We consider two variants for drafting: (1) using an auxiliary drafter model for better flexibility, or (2) leveraging the GR model’s own encoder for parameterefficient self-drafting. Extensive experiments on three realworld datasets demonstrate that SpecGR exhibits both strong inductive recommendation ability and the best overall performance among the compared methods. 

Offline preference alignment for language models such as Direct Preference Optimization (DPO) is favored for its effectiveness and simplicity, eliminating the need for costly reinforcement learning. Various offline algorithms have been developed for different data settings, yet they lack a unified understanding. In this study, we introduce Pior-Informed Preference Alignment (PIPA), a unified, RL-free probabilistic framework that formulates language model preference alignment as a Maximum Likelihood Estimation (MLE) problem with prior constraints. This method effectively accommodates both paired and unpaired data, as well as answer and step-level annotations. We illustrate that DPO and KTO are special cases with different prior constraints within our framework. By integrating different types of prior information, we developed two variations of PIPA: PIPA-M and PIPA-N. Both algorithms demonstrate a 3∼10% performance enhancement on the GSM8K and MATH benchmarks across all configurations, achieving these gains without additional training or computational costs compared to existing algorithms. 

Improvements in language models are often driven by improving the quality of the data we train them on, which can be limiting when strong supervision is scarce. In this work, we show that paired preference data consisting of individually weak data points can enable gains beyond the strength of each individual data point. We formulate the delta learning hypothesis to explain this phenomenon, positing that the relative quality delta between points suffices to drive learning via preference tuning--even when supervised finetuning on the weak data hurts. We validate our hypothesis in controlled experiments and at scale, where we post-train 8B models on preference data generated by pairing a small 3B model's responses with outputs from an even smaller 1.5B model to create a meaningful delta. Strikingly, on a standard 11-benchmark evaluation suite (MATH, MMLU, etc.), our simple recipe matches the performance of Tulu 3, a state-of-the-art open model tuned from the same base model while relying on much stronger supervisors (e.g., GPT-4o). Thus, delta learning enables simpler and cheaper open recipes for state-of-the-art post-training. To better understand delta learning, we prove in logistic regression that the performance gap between two weak teacher models provides useful signal for improving a stronger student. Overall, our work shows that models can learn surprisingly well from paired data that might typically be considered weak. 

Placing a dataset A={ai}i∈[n]⊂ℝd in radial isotropic position, i.e., finding an invertible R∈ℝd×d such that the unit vectors {(Rai)‖Rai‖−12}i∈[n] are in isotropic position, is a powerful tool with applications in functional analysis, communication complexity, coding theory, and the design of learning algorithms. When the transformed dataset has a second moment matrix within a exp(±ϵ) factor of a multiple of Id, we call R an ϵ-approximate Forster transform. We give a faster algorithm for computing approximate Forster transforms, based on optimizing an objective defined by Barthe [Barthe98]. When the transform has a polynomially-bounded aspect ratio, our algorithm uses O(ndω−1(nϵ)o(1)) time to output an ϵ-approximate Forster transform with high probability, when one exists. This is almost the natural limit of this approach, as even evaluating Barthe's objective takes O(ndω−1) time. Previously, the state-of-the-art runtime in this regime was based on cutting-plane methods, and scaled at least as ≈n3+n2dω−1. We also provide explicit estimates on the aspect ratio in the smoothed analysis setting, and show that our algorithm similarly improves upon those in the literature. To obtain our results, we develop a subroutine of potential broader interest: a reduction from almost-linear time sparsification of graph Laplacians to the ability to support almost-linear time matrix-vector products. We combine this tool with new stability bounds on Barthe's objective to implicitly implement a box-constrained Newton's method [CMTV17, ALOW17]. 

Training large language models (LLMs) increasingly relies on geographically distributed accelerators, causing prohibitive communication costs across regions and uneven utilization of heterogeneous hardware. We propose HALoS, a hierarchical asynchronous optimization framework that tackles these issues by introducing local parameter servers (LPSs) within each region and a global parameter server (GPS) that merges updates across regions. This hierarchical design minimizes expensive inter-region communication, reduces straggler effects, and leverages fast intra-region links. We provide a rigorous convergence analysis for HALoS under non-convex objectives, including theoretical guarantees on the role of hierarchical momentum in asynchronous training. Empirically, HALoS attains up to 7.5x faster convergence than synchronous baselines in geo-distributed LLM training and improves upon existing asynchronous methods by up to 2.1x. Crucially, HALoS preserves the model quality of fully synchronous SGD-matching or exceeding accuracy on standard language modeling and downstream benchmarks-while substantially lowering total training time. These results demonstrate that hierarchical, server-side update accumulation and global model merging are powerful tools for scalable, efficient training of new-era LLMs in heterogeneous, geo-distributed environments.