Demystifying Manifold Constraints in LLM Pre-training

• URL: http://arxiv.org/abs/2605.04418v1
• Date: Wed, 06 May 2026 02:22:06 GMT
• Title: Demystifying Manifold Constraints in LLM Pre-training
• Abstract summary: This paper systematically demystifies the role of explicit manifold constraints in large language model (LLM) pre-training.<n>By introducing the Msign-Aligned Constrained (MACRO)-a provably convergent, single-loop optimization framework-our study disentangles weight regularization normalizations from interacting mechanisms like RMS and decoupled weight decay.
• Score: 9.002615433212988
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The empirical success of large language model (LLM) pre-training relies heavily on heuristic stabilization techniques, such as explicit normalization layers and weight decay. While recent constrained optimization approaches that explicitly restrict weights may improve numerical stability and performance, the mechanism and motivation for adding constraints still remain elusive. This paper systematically demystifies the role of explicit manifold constraints in LLM pre-training. By introducing the Msign-Aligned Constrained Riemannian Optimizer (MACRO)-a provably convergent, single-loop optimization framework-our study disentangles weight regularization heuristics from interacting mechanisms like RMS normalization and decoupled weight decay. Theoretical analyses and comprehensive empirical evaluations reveal that manifold constraints independently bound forward activation scales and enforce stable rotational equilibrium, thereby subsuming the roles of these heuristic mechanisms. Evaluations on large-scale LLM architectures demonstrate that MACRO achieves highly competitive performance while rigorously preserving the theoretical guarantees of exact Riemannian optimization.

Related papers

• Stabilizing Policy Optimization via Logits Convexity [59.242732612484474]
  We show that the convexity of the supervised fine-tuning loss with respect to model logits plays a key role in enabling stable training.<n>Motivated by this observation, we propose Logits Convex Optimization (LCO), a simple yet effective policy optimization framework.
  arXiv  Detail & Related papers  (2026-03-01T07:40:12Z)
• Astro: Activation-guided Structured Regularization for Outlier-Robust LLM Post-Training Quantization [56.5199302532159]
  We propose an Activation-guided Structured Regularization framework to suppress the negative effects of outliers.<n>Astro actively reconstructs intrinsically robust weights, aggressively suppressing weight outliers corresponding to high-magnitude activations.<n>Astro achieves highly competitive performance; notably, on LLaMA-2-7B, it achieves better performance than complex learning-based rotation methods with almost 1/3 of the quantization time.
  arXiv  Detail & Related papers  (2026-02-07T15:50:18Z)
• ODELoRA: Training Low-Rank Adaptation by Solving Ordinary Differential Equations [54.886931928255564]
  Low-rank adaptation (LoRA) has emerged as a widely adopted parameter-efficient fine-tuning method in deep transfer learning.<n>We propose a novel continuous-time optimization dynamic for LoRA factor matrices in the form of an ordinary differential equation (ODE)<n>We show that ODELoRA achieves stable feature learning, a property that is crucial for training deep neural networks at different scales of problem dimensionality.
  arXiv  Detail & Related papers  (2026-02-07T10:19:36Z)
• Breaking the Stochasticity Barrier: An Adaptive Variance-Reduced Method for Variational Inequalities [0.0]
  We propose VR-A-A (VarianceReduced-Ascent with Armijo) as a novel algorithm for non-con optimization tasks.<n>We show that our method effectively suppresses limit cycles and accelerates convergence with reduced dependence on manual learning scheduling.
  arXiv  Detail & Related papers  (2026-01-30T14:43:07Z)
• Why Self-Rewarding Works: Theoretical Guarantees for Iterative Alignment of Language Models [50.248686344277246]
  Self-Rewarding Language Models (SRLMs) achieve notable success in iteratively improving alignment without external feedback.<n>This paper provides the first rigorous theoretical guarantees for SRLMs.
  arXiv  Detail & Related papers  (2026-01-30T03:45:43Z)
• SIGMA: Scalable Spectral Insights for LLM Collapse [51.863164847253366]
  We introduce SIGMA (Spectral Inequalities for Gram Matrix Analysis), a unified framework for model collapse.<n>By utilizing benchmarks that deriving and deterministic bounds on the matrix's spectrum, SIGMA provides a mathematically grounded metric to track the contraction of the representation space.<n>We demonstrate that SIGMA effectively captures the transition towards states, offering both theoretical insights into the mechanics of collapse.
  arXiv  Detail & Related papers  (2026-01-06T19:47:11Z)
• Multiscale Aggregated Hierarchical Attention (MAHA): A Game Theoretic and Optimization Driven Approach to Efficient Contextual Modeling in Large Language Models [0.0]
  Multiscale Aggregated Hierarchical Attention (MAHA) is a novel architectural framework that reformulates the attention mechanism through hierarchical decomposition and mathematically rigorous aggregation.<n>MAHA dynamically partitions the input sequence into hierarchical scales via learnable downsampling operators.<n> Experimental evaluations demonstrate that MAHA achieves superior scalability; empirical FLOPs analysis confirms an 81% reduction in computational cost at a sequence length of 4096 compared to standard attention.
  arXiv  Detail & Related papers  (2025-12-16T21:27:21Z)
• MaP: A Unified Framework for Reliable Evaluation of Pre-training Dynamics [72.00014675808228]
  Instability in Large Language Models evaluation process obscures true learning dynamics.<n>We introduce textbfMaP, a framework that integrates underlineMerging underlineand the underlinePass@k metric.<n>Experiments show that MaP yields significantly smoother performance curves, reduces inter-run variance, and ensures more consistent rankings.
  arXiv  Detail & Related papers  (2025-10-10T11:40:27Z)
• Force Matching with Relativistic Constraints: A Physics-Inspired Approach to Stable and Efficient Generative Modeling [26.145559807686706]
  We introduce Force Matching (ForM), a framework for generative modeling that incorporates special relativistic mechanics.<n>ForM imposes a velocity constraint, ensuring that sample velocities remain bounded within a constant limit.<n>We show that ForM provides a promising pathway toward achieving stable, efficient, and flexible generative processes.
  arXiv  Detail & Related papers  (2025-02-12T06:30:01Z)
• Learning Dynamic Representations via An Optimally-Weighted Maximum Mean Discrepancy Optimization Framework for Continual Learning [16.10753846850319]
  Continual learning allows models to persistently acquire and retain information.<n> catastrophic forgetting can severely impair model performance.<n>We introduce a novel framework termed Optimally-Weighted Mean Discrepancy (OWMMD), which imposes penalties on representation alterations.
  arXiv  Detail & Related papers  (2025-01-21T13:33:45Z)

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.