Curvature-Weighted Capacity Allocation: A Minimum Description Length Framework for Layer-Adaptive Large Language Model Optimization
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914361418711040 |
|---|---|
| author | Amaefuna, Theophilus Vaidya, Hitesh Chhabra, Anshuman Mali, Ankur |
| author_facet | Amaefuna, Theophilus Vaidya, Hitesh Chhabra, Anshuman Mali, Ankur |
| contents | Layer-wise capacity in large language models is highly non-uniform: some layers contribute disproportionately to loss reduction while others are near-redundant. Existing methods for exploiting this non-uniformity, such as influence-function-based layer scoring, produce sensitivity estimates but offer no principled mechanism for translating them into allocation or pruning decisions under hardware constraints. We address this gap with a unified, curvature-aware framework grounded in the Minimum Description Length (MDL) principle. Our central quantity is the curvature-adjusted layer gain $ζ_k^2 = g_k^\top \widetilde{H}_{kk}^{-1} g_k$, which we show equals twice the maximal second-order reduction in empirical risk achievable by updating layer $k$ alone, and which strictly dominates gradient-norm-based scores by incorporating local curvature. Normalizing these gains into layer quality scores $q_k$, we formulate two convex MDL programs: a capacity allocation program that distributes expert slots or LoRA rank preferentially to high-curvature layers under diminishing returns, and a pruning program that concentrates sparsity on low-gain layers while protecting high-gain layers from degradation. Both programs admit unique closed-form solutions parameterized by a single dual variable, computable in $O(K \log 1/\varepsilon)$ via bisection. We prove an $O(δ^2)$ transfer regret bound showing that source-domain allocations remain near-optimal on target tasks when curvature scores drift by $δ$, with explicit constants tied to the condition number of the target program. Together, these results elevate layer-wise capacity optimization from an empirical heuristic to a theoretically grounded, computationally efficient framework with provable optimality and generalization guarantees. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_00910 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Curvature-Weighted Capacity Allocation: A Minimum Description Length Framework for Layer-Adaptive Large Language Model Optimization Amaefuna, Theophilus Vaidya, Hitesh Chhabra, Anshuman Mali, Ankur Information Theory Artificial Intelligence Machine Learning Layer-wise capacity in large language models is highly non-uniform: some layers contribute disproportionately to loss reduction while others are near-redundant. Existing methods for exploiting this non-uniformity, such as influence-function-based layer scoring, produce sensitivity estimates but offer no principled mechanism for translating them into allocation or pruning decisions under hardware constraints. We address this gap with a unified, curvature-aware framework grounded in the Minimum Description Length (MDL) principle. Our central quantity is the curvature-adjusted layer gain $ζ_k^2 = g_k^\top \widetilde{H}_{kk}^{-1} g_k$, which we show equals twice the maximal second-order reduction in empirical risk achievable by updating layer $k$ alone, and which strictly dominates gradient-norm-based scores by incorporating local curvature. Normalizing these gains into layer quality scores $q_k$, we formulate two convex MDL programs: a capacity allocation program that distributes expert slots or LoRA rank preferentially to high-curvature layers under diminishing returns, and a pruning program that concentrates sparsity on low-gain layers while protecting high-gain layers from degradation. Both programs admit unique closed-form solutions parameterized by a single dual variable, computable in $O(K \log 1/\varepsilon)$ via bisection. We prove an $O(δ^2)$ transfer regret bound showing that source-domain allocations remain near-optimal on target tasks when curvature scores drift by $δ$, with explicit constants tied to the condition number of the target program. Together, these results elevate layer-wise capacity optimization from an empirical heuristic to a theoretically grounded, computationally efficient framework with provable optimality and generalization guarantees. |
| title | Curvature-Weighted Capacity Allocation: A Minimum Description Length Framework for Layer-Adaptive Large Language Model Optimization |
| topic | Information Theory Artificial Intelligence Machine Learning |
| url | https://arxiv.org/abs/2603.00910 |