Gradient-Based Optimization Analysis and Subspace Trajectory Profiling for Low-Rank Adaptation in Edge-Constrained Models

Resource information

Format

ipynb, zip

Original repository

23091418

DOI

10.5281/zenodo.23091418

Credit basis

Creators in Zenodo record metadata

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Open files available from the original Zenodo deposit

Last checked

Nov 5, 2026

License

cc-by-4.0

Last record update

Nov 5, 2026

About this resource

This optimization artifact establishes an advanced diagnostic framework and tensor-level computational audit of gradient dynamics, subspace trajectories, and optimization stability in Low-Rank Adaptation (LoRA) mechanics across edge-constrained transformer models. Rather than treating low-rank adapter updates as decoupled black-box heuristics, this codebase isolates the mathematical, structural, and runtime challenges governing gradient-based PEFT optimization on resource-limited hardware. By analyzing how gradient update paths deviate from full-rank trajectories grad_W(L), this repository examines how subspace alignment, singular value decay, and gradient projection mechanics dictate convergence efficiency, parameter capacity, and memory overhead in sub-billion parameter regimes. The study provides modular, reproducible analysis and diagnostic pipelines designed for layer-wise tensor inspection, subspace tracking, and memory profiling. Core methodological and architectural investigations include: Gradient Alignment & Grassmann Distance Trajectory Profiling: Quantifies the structural divergence between low-rank adapter updates (Delta W = B * A) and full-weight gradient trajectories across training epochs. It tracks principal angles (theta_i = arccos(sigma_i(U_dW^T U_full)) to measure how effectively gradient information is preserved and projected into low-rank adapter subspaces without alignment collapse. SVD Spectral Decay & Rank Collapse Detection: Evaluates singular value decomposition (SVD) spectrum entropy and Frobenius norm retention across adapter bottleneck layers ( r = {4, 8, 16, 32} ). It audits how spectral energy distribution shifts during gradient-based updates, identifying precursors to premature rank collapse in sub-billion parameter transformers (e.g., SmolLM2, Qwen2.5). Gradient Variance & Parameter-Scale Optimization Dynamics: Analyzes the numerical stability of gradient optimization loops under edge-constrained execution. The suite audits empirical covariance matrices and gradient trace dynamics across adapter parameters to assess variance reduction and convergence stability relative to vanilla SGD or Adam baselines. Memory-Optimized VRAM Allocation & Backpropagation Profiling: Executes detailed CUDA memory profiling tailored for edge and consumer hardware configurations (such as 16GB VRAM environments). It tracks exact operational VRAM footprints during backward passes, ensuring that custom gradient hooks, projection matrices, and metric logging operate within strict hardware bounds without triggering out-of-memory (OOM) failures. Subspace-Aware Integration & Zero-Latency Weight Merging: Examines floating-point precision dynamics (FP16, BF16, and FP32) during gradient-informed adapter integration ( W_eff = W_0 + (alpha/r) (B . A) ) . It quantifies numerical drift and quantization stability, validating zero-latency inference serving for edge-deployed models. By bridging theoretical tensor analysis with strict edge-hardware constraints, this framework introduces a rigorous diagnostic paradigm for isolating gradient optimization bottlenecks and subspace trajectories in parameter-efficient fine-tuning architectures.