Overfitting Mitigation via Singular Value Decomposition in Minimum Bayes Risk Decoding

Minimum Bayes Risk (MBR) decoding enables high-quality text generation by selecting the hypothesis that maximizes a utility metric over sampled pseudo-references. However, it is highly susceptible to metric overfitting: it can irregularly inflate the chosen utility metric at the direct expense of other unoptimized evaluation metrics. To mitigate this, we introduce SVD-MBR, which frames the pairwise utility matrix as a noisy information signal. By computing a low-rank approximation via Singular Value Decomposition (SVD) and retaining only the top-$k$ components, we effectively decouple true consensus from metric noise. Experiments demonstrate that SVD-MBR successfully regularizes decoding, yielding substantial gains across a range of generalized metrics. Furthermore, we reveal that this denoising is metric-dependent: neural metrics encode a robust low-rank consensus ideal for SVD, whereas surface-level metrics struggle to separate signal from metric noise.

CORAM: Coherent Orthogonal Rotation for Model Merging

Merging finetuned models combines specialized capabilities without joint training or access to the original data. Most methods operate by linear arithmetic in Euclidean weight space, which cannot carry the geometry of the update. Orthogonal Model Merging (OrthoMerge) uses a single orthogonal transform for each weight matrix, but such a transform cannot change singular values. We propose CORAM, which partitions each target matrix into row slices, represents every expert slice by its singular value decomposition in the corresponding base-model SVD frame, and merges the task-specific factors on their corresponding manifolds. Because manifold averaging contracts the merged update, CORAM applies an amplification coefficient $λ=κ\hat{c}$. The scale c_hat is estimated from the expert and merged update norms and is approximately $\sqrt{N}$ for $N$ experts with comparable update magnitudes. The restoration strength kappa is selected from the dispersion of expert updates without evaluating candidate merged models. This rule remains within 0.72 points of the best swept value on all evaluated suites. CORAM also includes spread slicing to distribute highly updated rows across slices and a residual pathway for non-target layers. Across four suites covering three model families, 3B to 9B scales, and language and vision-language experts, CORAM improves over OrthoMerge by 0.25 to 1.35 points and matches or exceeds the strongest weight-space baselines.

Diffract: Spectral View of LLM Domain Adaptation

We study continual pre-training (CPT) as a mechanism for adapting general-purpose large language models to specialized domains: mathematics, instruction, code, and natural text. Using singular value decomposition of weight matrices, we find that CPT leaves singular value spectra largely invariant, with adaptation driven mainly by changes in singular vectors. An analysis of attention-head projection matrices reveals strong, domain-dependent head heterogeneity, which we exploit to define a head importance criterion: up to 60% of head updates can be removed without measurable quality loss. Selectively rewinding low-importance heads to their pre-trained state improves benchmark accuracy by up to 4% versus the fully trained baseline. Finally, we identify domain connectivity - linear interpolation between CPT checkpoints yields smooth domain-quality interpolation without notable degradation on either domain - and release Diffract, an open-source toolkit for scalable spectral analysis of billion-parameter models.

Can Spectral-Clipping Enable Better Learning While Forgetting Less for Low-Rank Adaptation?

In recent years, low-rank adaptation (LoRA) has emerged as a significant paradigm that freezes pre-trained weights and introduces small, learnable adapters instead of fine-tuning the full set of parameters. In this work, we uncover several key insights regarding the singular components of network parameters based on Singular Value Decomposition (SVD). Firstly, the principal singular components with large singular values in pre-trained network parameters can be effectively reused during fine-tuning, whereas the minor components with smaller singular values are more task-specific and require substantial adaptation. Secondly, we first establish the theoretical connection that the uncontrolled growth of singular values in LoRA adapters leads to the forgetting of pre-trained knowledge -- a well-known issue referred to as catastrophic forgetting. Building on these observations, we propose SCLoRA, which injects parameterized singular components with spectral clipping into the pre-trained model in a way that is aware of the spectral distribution of the pre-trained model. SCLoRA effectively adapts to new tasks by focusing updates on components that require adaptation, while simultaneously alleviating catastrophic forgetting. We conduct extensive experiments and demonstrate that SCLoRA not only improves downstream performance but also effectively retains pre-trained knowledge.