Towards Efficient LLMs Annealing with Principled Sample Selection

• URL: http://arxiv.org/abs/2605.31175v1
• Date: Fri, 29 May 2026 11:42:55 GMT
• Title: Towards Efficient LLMs Annealing with Principled Sample Selection
• Abstract summary: We argue that optimal convergence requires gradient updates to satisfy heterogeneous constraints across different eigen-directions.<n>We propose DiReCT, a novel framework that reformulates sample selection in the annealing stage as a constrained optimization problem.
• Score: 8.369375549294046
• License: http://creativecommons.org/licenses/by-sa/4.0/
• Abstract: The annealing phase is a pivotal convergence stage in LLM pre-training that ultimately determines final model quality. However, effectively selecting training data during this phase remains a key challenge. Current strategies rely on empirical heuristics, such as domain filtering or context extension, which lack a principled grounding in optimization theory. In this work, we characterize the annealing phase through the lens of the loss landscape's spectral geometry. We argue that optimal convergence requires gradient updates to satisfy heterogeneous constraints across different eigen-directions. Building on this insight, we formulate data selection as a problem of satisfying these directional constraints. To this end, we propose DiReCT (Directionally-Restrained Constrained Training), a novel framework that reformulates sample selection in the annealing stage as a constrained optimization problem. By imposing explicit directional constraints on per-sample gradients based on the spectral properties of the Hessian, DiReCT identifies samples that align with the optimal curvature-aware descent path. Extensive experiments across various model scales demonstrate that DiReCT consistently achieves state-of-the-art performance. For future research, code is available at https://github.com/xuyj233/Direct.

Related papers

• A Defense of the Quadratic Model [71.57026347416729]
  We stress test the simplest possible model of optimization -- the quadratic model.<n>We show that it can be predictive surprisingly in an LLM setting with 150M parameters and 3B training tokens.
  arXiv  Detail & Related papers  (2026-07-23T18:02:03Z)
• Curvature-Adaptive Consistency Flow Matching: Autonomous Trajectory Optimization via Reinforcement Learning [8.422673935994451]
  consistency distillation has significantly accelerated the inference of diffusion models.<n>We propose Curvature-Adaptive Consistency Flow Matching to address the limitations of static sampling.<n>Our approach achieves new state-of-the-art results on large-scale models such as FLUX and SDXL.
  arXiv  Detail & Related papers  (2026-06-21T08:49:50Z)
• Quantum Tilted Loss in Variational Optimization: Theory and Applications [2.274915755738124]
  We introduce the Quantum Tilted Loss (QTL) to reshape the optimization landscape.<n>QTL can amplify gradient signals in structured settings while preserving the problem's true global minima.<n>We formalize this trainability-estimability trade-off, demonstrating how aggressive tilting fundamentally shifts the optimization bottleneck.
  arXiv  Detail & Related papers  (2026-05-04T17:25:43Z)
• Score-Guided Proximal Projection: A Unified Geometric Framework for Rectified Flow Editing [1.0312968200748118]
  Rectified Flow models achieve state-of-the-art generation quality, yet controlling them for precise tasks remains a challenge.<n>Current approaches bifurcate into inversion-based guidance, which suffers from "geometric locking"<n>We propose Score-Guided Proximal Projection, a unified framework that bridges the gap between deterministic optimization and contraction sampling.
  arXiv  Detail & Related papers  (2026-03-05T23:44:45Z)
• Provably Convergent Decentralized Optimization over Directed Graphs under Generalized Smoothness [1.5892054128426507]
  Hessian norm is allowed to grow linearly with the gradient norm, thereby accommodating rapidly varying gradients beyond Lipschitz smoothness.<n>We integrate gradient-tracking techniques with gradient clipping to ensure accurate convergence over directed communication graphs.<n>Our results remain valid even when the gradient dissimilarity is unbounded, making the proposed framework more applicable to realistic heterogeneous data environments.
  arXiv  Detail & Related papers  (2026-01-07T04:25:33Z)
• Stable Coresets via Posterior Sampling: Aligning Induced and Full Loss Landscapes [7.446140380340418]
  Coreset selection aims to accelerate training by identifying small, representative subsets of data that approximate the performance of the full dataset.<n> gradient based methods stand out due to their strong theoretical underpinnings and practical benefits, particularly under limited data budgets.<n>We propose a novel framework that addresses these limitations. First, we establish a connection between posterior sampling and loss landscapes, enabling robust coreset selection even in high data corruption scenarios.
  arXiv  Detail & Related papers  (2025-11-21T17:00:00Z)
• Closed-Form Last Layer Optimization [72.49151473937319]
  Under a squared loss, the optimal solution to the linear last layer weights is known in closed-form.<n>We show this is equivalent to alternating between gradient descent steps on the backbone and closed-form updates on the last layer.
  arXiv  Detail & Related papers  (2025-10-06T09:14:39Z)
• Diffusion Models as Constrained Samplers for Optimization with Unknown Constraints [55.39203337683045]
  We propose to perform optimization within the data manifold using diffusion models.<n>Depending on the differentiability of the objective function, we propose two different sampling methods.<n>Our method achieves better or comparable performance with previous state-of-the-art baselines.
  arXiv  Detail & Related papers  (2024-02-28T03:09:12Z)
• Stable Nonconvex-Nonconcave Training via Linear Interpolation [51.668052890249726]
  This paper presents a theoretical analysis of linearahead as a principled method for stabilizing (large-scale) neural network training. We argue that instabilities in the optimization process are often caused by the nonmonotonicity of the loss landscape and show how linear can help by leveraging the theory of nonexpansive operators.
  arXiv  Detail & Related papers  (2023-10-20T12:45:12Z)
• Temporal-spatial model via Trend Filtering [12.875863572064986]
  This research focuses on the estimation of a non-parametric regression function designed for data with simultaneous time and space dependencies. A unique phase transition phenomenon, previously uncharted in Trend Filtering studies, emerges through our analysis.
  arXiv  Detail & Related papers  (2023-08-30T17:50:00Z)
• Sampling from Gaussian Process Posteriors using Stochastic Gradient Descent [43.097493761380186]
  gradient algorithms are an efficient method of approximately solving linear systems. We show that gradient descent produces accurate predictions, even in cases where it does not converge quickly to the optimum. Experimentally, gradient descent achieves state-of-the-art performance on sufficiently large-scale or ill-conditioned regression tasks.
  arXiv  Detail & Related papers  (2023-06-20T15:07:37Z)
• Zeroth-Order Hybrid Gradient Descent: Towards A Principled Black-Box Optimization Framework [100.36569795440889]
  This work is on the iteration of zero-th-order (ZO) optimization which does not require first-order information. We show that with a graceful design in coordinate importance sampling, the proposed ZO optimization method is efficient both in terms of complexity as well as as function query cost.
  arXiv  Detail & Related papers  (2020-12-21T17:29:58Z)
• On the Convergence Rate of Projected Gradient Descent for a Back-Projection based Objective [58.33065918353532]
  We consider a back-projection based fidelity term as an alternative to the common least squares (LS) We show that using the BP term, rather than the LS term, requires fewer iterations of optimization algorithms.
  arXiv  Detail & Related papers  (2020-05-03T00:58:23Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.