{ "schema_version": 1, "builder_plan": { "scenario": "You already need task-specific training and want to reduce its memory or compute cost.", "change": "Change only the training technique on a small controlled run after checking prerequisites.", "baseline": "Your current training recipe with the same model, data split, and evaluation.", "steps": [ "Locate the paper's implementation and check its license, model support, data needs, and hardware requirements. Stop here if you cannot obtain the required artifacts.", "Save a small set of representative product tasks and expected outcomes. Keep evaluation tasks out of any training or tuning, and choose quality and cost limits before running.", "Run the baseline and the proposed change on identical inputs. Keep other settings fixed and repeat paired runs to expose variation.", "Save per-task outputs, failures, timings, and all usage costs. Review regressions before expanding the test." ], "measure": "Held-out quality, peak memory, training time, and full compute cost to the target quality.", "decision": "Keep the change only if it meets your preselected quality and latency limits and improves the metric you care about after setup and operating costs. Otherwise retain the baseline. This is an exploration plan, not a validated recommendation." }, "builder_review": null, "arxiv_id": "2609.15643", "title": "Principal-timestep Restricted Init via Sparse Matrix-decomposition in Flow-matching", "summary": "Prism-LoRA replaces standard LoRA initialization (and PiSSA-style spectral initialization) in flow-matching diffusion fine-tuning by restricting the initialization gradient to dominant timesteps and filtering task-irrelevant channels before performing the sparse matrix decomposition. 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(9) using the standard flow-matching objective, without any further modification to the timestep distribution:", "headline": "", "explanation": "", "objective": "", "symbols": {}, "evidence": "", "evidence_url": "", "source_url": "" }, { "anchor": "S3.E9", "label": "(9)", "section": "3 Method", "role": "proposed_method", "latex": "A_{0}=\\sqrt{\\gamma}\\,\\bigl[U_{G^{\\natural}}\\bigr]_{[:,\\,1:r]}\\bigl[S_{G^{\\natural}}^{1/2}\\bigr]_{[1:r]},\\quad B_{0}=\\sqrt{\\gamma}\\,\\bigl[S_{G^{\\natural}}^{1/2}\\bigr]_{[1:r]}\\bigl[V_{G^{\\natural}}\\bigr]_{[:,\\,1:r]}^{\\top},", "mathml": "A0=γ[UG♮][:, 1:r][SG♮1/2][1:r],B0=γ[SG♮1/2][1:r][VG♮][:, 1:r]⊤,", "context": "In the second stage, we apply the golden-channel sparse SVD to G♮ and initialize the LoRA factors from its leading spectral components:", "headline": "", "explanation": "", "objective": "", "symbols": {}, "evidence": "", "evidence_url": "", "source_url": "" } ], "equations_status": "selected", "core_kind": "formula", "equations_fetched_at": "2026-10-08", "equations_source_url": "", "equations_source_sha256": "", "exposures_reviewed_at": "", "exposures_source_sha256": "" }