Заседание семинара «Компьютерная алгебра»

21 октября в 16:30 состоится очередное заседание семинара «Компьютерная алгебра». Руководитель семинара – д.ф.-м.н. С.А. Абрамов.

На заседании семинара будет представлен доклад на тему:

«Motion Compression Does Not Certify Local-Response Adequacy»

Автор доклада:

Min Wu (Software Engineering Institute, East China Normal University, Shanghai, P.R.China)

Аннотация доклада

Does nearly rank-one optimization motion imply that a rank-one response is sufficient to predict what comes next? We show that it need not. Across four LLM families under controlled fixed-driver SGD, one direction captures 99.75--99.998% of adjacent-update energy at family medians, yet both a gradient-aligned rank-one response and the leading prefix-SVD rank-one response are less accurate than the matched unrestricted local model in all 32 conditions. Adding the first curvature-generated transverse direction improves the gradient-aligned response in every condition. For a smooth fixed loss with nonzero gradient and transverse curvature, we prove that small-step gradient descent exhibits quadratic motion nonoccupancy but linear normalized restriction of the gradient-aligned rank-one response, with explicit leading coefficients. Thus the standard energy-based compression statistic approaches rank one quadratically while normalized gradient-aligned rank-one restriction decays linearly. Nonlinear Qwen and Llama scaling studies support this separation.

In a separate disjoint Qwen3-8B confirmation using full-FP32 computation and exact selected-space HVPs, the median exponents are 2.010, 1.005, and 0.501, versus the predicted 2, 1, and 1/2, while the leading coefficients agree with theory to within 0.6%.

The empirical separation also persists in a same-anchor shuffled-minibatch AdamW bridge. Together, these results show that near-perfect trajectory-energy compression can still fail to identify an adequate predictive response order. Compression describes what moved; predictive response order should be validated against the update operator rather than inferred from trajectory energy alone.

Заседание семинара будет проходить в дистанционном режиме через Zoom. Ссылка для подключения будет направлена участникам семинара по электронной почте. По вопросу участия в семинаре просьба обращаться по электронной почте: moscowcaconf@gmail.com