arXiv subjects

Kaihao Zhu

Publications and source records attributed to Kaihao Zhu.

3 recordsLinked to original sources

arXiv2026

A Structural Proof of the Lower Bound 21 for $3\times3$ Matrix Multiplication over $\mathbb F_2$

We prove that the tensor rank of $3\times3$ matrix multiplication over $\mathbb F_2$ is at least $21$. The structural proof, independently developed by Qiushi Engine, converts occupation constraints on a single tensor factor into algebraic relations coupling all three factors. Certified quotient-rank bounds and finite geometry force any hypothetical $20$-term decomposition to have first-factor matrix-rank profile $(16,1,3)$. The ranks of the corresponding split-flattened summands therefore sum to $27$, exactly the rank of the full split flattening. Equality in rank subadditivity forces their images to form a direct sum; normalization by the inverse flattening then makes the summands pairwise annihilating idempotents. An explicit product identity for matrix multiplication implies that at most one first factor can be invertible, contradicting the three forced by the profile. The same obstruction constrains $22$-term decompositions attaining the split-rank bound. The complete proof, including the finite quotient bounds, is formalized in Lean. The accompanying research trajectory records Qiushi Engine's long-horizon autonomous research, from numerical experiments and quotient constructions to the structural proof.

cs.CC↗

arXiv2026

Data-Efficient Language Modeling: From Frontier Advancement to Principle-Guided Model Improvement

Learning from limited text requires models to use context, generalize to new inputs, and retain useful capabilities. Qiushi Engine conducted a long-horizon, end-to-end autonomous research program on BabyLM 2026 Strict-Small, within 10 million corpus words and 100 million cumulative word presentations. Three stages connected frontier advancement, principle discovery, and principle-guided model improvement. Stage I combined compact restatements, budget reinvestment, and residual incremental learning to build a frontier model. Stage II found that exact repetition and aligned restatement produce different patterns of context use, depending on target relations and prediction windows. In controlled tasks, recovering familiar performance did not ensure that unseen inputs could still use learned computations. These findings support a testable data-efficient learning principle: organize experience around the contextual dependencies needed for prediction; separately design visible information, supervision, and preservation; test learning, generalization, and retention. Stage III retained source text, masked more local clues, supervised selected targets, and preserved predictions on ordinarily masked inputs. Two continuation seeds from the same parent outperformed ordinary continuation on the complete nine-metric aggregate. Overall rose from 42.02 to 42.25 across two generations; the second achieved the highest Overall in the public Strict-Small snapshot of 8 September 2026. Further studies addressed compression, relational anchors, shared representations, and measurement. Models are available on Hugging Face; code and research records accompany the GitHub repository. Together, these stages illustrate Research RSI: recursive self-improvement of the research process. Scientific understanding and method innovations change subsequent questions and designs; new experiments test and refine them.

cs.CL↗

arXiv2026

Qiushi Engine on AstaBench E2E-Bench-Hard

This report analyzes Qiushi Engine v0.8 across all 40 test tasks in AstaBench E2E-Bench-Hard, a benchmark that requires autonomous agents to carry a research question through experimental design, code implementation, actual execution, result analysis, and report delivery. Qiushi Engine is model-configurable; this evaluation selected DeepSeek deepseek-v4pro-preview as the model backend. The official AstaBench leaderboard records a score of 0.816 and an average benchmark cost of USD 15.209 per task, while the full-precision local recomputation is $81.59 \pm 1.87$. Four tasks satisfied every rubric item, yielding a full-task completion rate of 4/40 = 10% -- 7 percentage points above, and about 3.3 times, the approximately 3% best rate reported for AstaBench's official agents. Across 507 required rubric items, 416 were satisfied (82.1%). Official scoring archives and 40 Meta-Trace records show sustained production and verification of reports, code, and experimental artifacts; the principal gaps lie in repeated runs, external dependencies, specified metrics, and ablation studies. The report explains the benchmark, system workflow, aggregate results, representative cases, and limits of interpretation.

cs.AI↗