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Understanding Post-Training Structural Changes in Large Language Models

ICLR 2026 Conference SubmissionAnonymous Authors
OpenReview Score: 6.0Download Report PDF
Large Language ModelsInstruction TuningLong-Chain-of-Thought (Long-CoT) DistillationSingular Value DecompositionStructural Changes in LLMs
Abstract:

Post-training fundamentally alters the behavior of large language models (LLMs), yet its impact on the internal parameter space remains poorly understood. In this work, we conduct a systematic singular value decomposition (SVD) analysis of principal linear layers in pretrained LLMs, focusing on two widely adopted post-training methods: instruction tuning and long-chain-of-thought (Long-CoT) distillation. Our analysis reveals two consistent and unexpected structural changes:(1) a near-uniform geometric scaling of singular values across layers, which theoretically modulates attention scores; and (2) highly consistent orthogonal transformations are applied to the left and right singular vectors of each matrix. Disrupting this orthogonal consistency leads to catastrophic performance degradation. Based on these findings, we propose a simple yet effective framework that interprets post-training as a reparameterization of fixed subspaces in the pretrained parameter space. Further experiments reveal that singular value scaling behaves as a secondary effect, analogous to a temperature adjustment, whereas the core functional transformation lies in the coordinated rotation of singular vectors. These results challenge the prevailing view of the parameter space in large models as a black box, uncovering the first clear regularities in how parameters evolve during training, and providing a new perspective for deeper investigation into model parameter changes.

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This report is AI-GENERATED using Large Language Models and WisPaper (A scholar search engine). It analyzes academic papers' tasks and contributions against retrieved prior work. While this system identifies POTENTIAL overlaps and novel directions, ITS COVERAGE IS NOT EXHAUSTIVE AND JUDGMENTS ARE APPROXIMATE. These results are intended to assist human reviewers and SHOULD NOT be relied upon as a definitive verdict on novelty.
NOTE that some papers exist in multiple, slightly different versions (e.g., with different titles or URLs). The system may retrieve several versions of the same underlying work. The current automated pipeline does not reliably align or distinguish these cases, so human reviewers will need to disambiguate them manually.
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Overview

Overall Novelty Assessment

The paper conducts systematic singular value decomposition analysis of weight matrices during post-training, revealing two structural patterns: near-uniform geometric scaling of singular values and consistent orthogonal transformations of singular vectors. It resides in the 'Singular Value Decomposition Analysis of Parameters' leaf, which currently contains only this paper within the broader 'Geometric and Spectral Analysis of Parameter Space' branch. This represents a relatively sparse research direction focused specifically on spectral methods for understanding post-training dynamics, distinct from the more crowded parameter-efficient fine-tuning methodologies that dominate the field.

The taxonomy shows the paper sits within a small geometric analysis branch (two leaves total) that contrasts sharply with the heavily populated parameter-efficient fine-tuning subtree containing over twenty papers across multiple leaves. The neighboring 'Representation Geometry Evolution' leaf examines learned representations rather than parameter-level structure, while the broader field emphasizes practical adaptation methods (LoRA variants, adapters, quantization) over structural interpretation. The paper's focus on SVD-based parameter analysis positions it at the intersection of theoretical understanding and post-training mechanics, bridging geometric insights with practical fine-tuning outcomes.

Among thirty candidates examined, the contribution-level analysis reveals mixed novelty signals. The systematic SVD analysis revealing structural changes (Contribution 1) examined ten candidates with zero refutations, suggesting this specific dual-pattern characterization may be novel. However, the mathematical framework interpreting post-training as subspace reparameterization (Contribution 2) found two refutable candidates among ten examined, indicating prior work on subspace-based interpretations exists. The claim of being the first systematic study across entire parameter space (Contribution 3) encountered one refutable candidate, suggesting similar comprehensive analyses may have been conducted previously.

Based on the limited search scope of thirty semantically similar papers, the work appears to offer genuine insights into SVD-based structural patterns during post-training, particularly the dual observation of singular value scaling and orthogonal consistency. The subspace reparameterization framework and systematic scope claims face more substantial prior work overlap. The sparse taxonomy leaf suggests this specific analytical approach remains underexplored, though the existence of refutable candidates indicates the broader conceptual territory has been partially mapped by earlier efforts.

Taxonomy

Core-task Taxonomy Papers
50
3
Claimed Contributions
30
Contribution Candidate Papers Compared
3
Refutable Paper

Research Landscape Overview

Core task: Understanding structural changes in large language model parameters during post-training. The field has organized itself around several complementary perspectives on how LLM parameters evolve after initial pretraining. At the highest level, researchers pursue geometric and spectral analyses that probe the intrinsic structure of weight matrices—often through singular value decomposition or subspace characterizations—to reveal how fine-tuning reshapes parameter distributions. In parallel, a large body of work focuses on parameter-efficient fine-tuning (PEFT) methods such as LoRA and prefix tuning, which modify only a small subset of weights while preserving most pretrained knowledge. Full-model fine-tuning approaches, by contrast, update all parameters and tend to yield stronger task performance at higher computational cost. Additional branches address compression and quantization (e.g., GPTQ[26], SmoothQuant[34]) to reduce memory footprints, catastrophic phenomena like forgetting and alignment brittleness, specialized techniques for domains such as code or vision, and distributed or federated settings that must coordinate updates across multiple nodes. Comprehensive surveys (e.g., PEFT Comprehensive Survey[18], PEFT Methodologies Survey[39]) synthesize these threads, highlighting trade-offs between efficiency, performance, and robustness. Several active lines of work reveal contrasting priorities: some studies emphasize low-rank decompositions to isolate which subspaces carry task-relevant information (Singular Value Finetuning[29], SVD-LLM[38]), while others explore how gradient flow and representation geometry shift during adaptation (Representation Geometry Tracing[1], Subspace Optimization[37]). Post-Training Structural Changes[0] sits squarely within the geometric and spectral analysis branch, using singular value decomposition to track how weight matrices evolve across fine-tuning stages. Its emphasis on decomposing parameter updates into interpretable components aligns closely with works like Singular Value Finetuning[29] and SVD-LLM[38], which similarly leverage spectral methods to understand or guide adaptation. By contrast, nearby efforts in PEFT (e.g., LLM-Adapters[12], PEFT Design Spaces[30]) prioritize practical efficiency over deep structural insight, while full-model studies (Full Parameter Finetuning[13]) accept higher costs for maximal expressiveness. Open questions remain about how these structural signatures relate to downstream robustness, generalization, and the risk of catastrophic forgetting.

Claimed Contributions

Systematic SVD analysis revealing two structural changes in post-training

The authors conduct a systematic singular value decomposition analysis of principal linear layers in pretrained LLMs, uncovering two consistent structural phenomena that occur during post-training: near-uniform geometric scaling of singular values and highly consistent orthogonal transformations of singular vectors.

10 retrieved papers
Mathematical framework interpreting post-training as subspace reparameterization

The authors propose a mathematical framework that describes post-training as a reparameterization process operating on fixed subspaces in the pretrained parameter space, providing a new perspective for understanding parameter evolution during training.

10 retrieved papers
Can Refute
First systematic study of structural changes across entire parameter space

The authors present the first comprehensive analysis of how post-training affects the entire parameter space of LLMs, examining singular value structures of principal linear layers rather than focusing on individual neurons or external behaviors as in prior work.

10 retrieved papers
Can Refute

Core Task Comparisons

Comparisons with papers in the same taxonomy category

Within the taxonomy built over the current TopK core-task papers, the original paper is assigned to a leaf with no direct siblings and no cousin branches under the same grandparent topic. In this retrieved landscape, it appears structurally isolated, which is one partial signal of novelty, but still constrained by search coverage and taxonomy granularity.

Contribution Analysis

Detailed comparisons for each claimed contribution

Contribution

Systematic SVD analysis revealing two structural changes in post-training

The authors conduct a systematic singular value decomposition analysis of principal linear layers in pretrained LLMs, uncovering two consistent structural phenomena that occur during post-training: near-uniform geometric scaling of singular values and highly consistent orthogonal transformations of singular vectors.

Contribution

Mathematical framework interpreting post-training as subspace reparameterization

The authors propose a mathematical framework that describes post-training as a reparameterization process operating on fixed subspaces in the pretrained parameter space, providing a new perspective for understanding parameter evolution during training.

Contribution

First systematic study of structural changes across entire parameter space

The authors present the first comprehensive analysis of how post-training affects the entire parameter space of LLMs, examining singular value structures of principal linear layers rather than focusing on individual neurons or external behaviors as in prior work.

Table of Contents

Understanding Post-Training Structural Changes in Large Language Models | Novelty Validation