Ivan Pasichnyk

Ivan Pasichnyk

Standard neural network training uses constant momentum (typically 0.9), a convention dating to 1964 with limited theoretical justification for its optimality. We derive a time-varying momentum schedule from the critically damped harmonic oscillator: mu(t) = 1 - 2*sqrt(alpha(t)), where alpha(t) is the current learning rate. This beta-schedule requires zero free parameters beyond the existing learning rate schedule. On ResNet-18/CIFAR-10, beta-scheduling delivers 1.9x faster convergence to 90% accuracy compared to constant momentum. More importantly, the per-layer gradient attribution under this schedule produces a cross-optimizer invariant diagnostic: the same three problem layers are identified regardless of whether the model was trained with SGD or Adam (100% overlap). Surgical correction of only these layers fixes 62 misclassifications while retraining only 18% of parameters. A hybrid schedule -- physics momentum for fast early convergence, then constant momentum for the final refinement -- reaches 95% accuracy fastest among five methods tested. The main contribution is not an accuracy improvement but a principled, parameter-free tool for localizing and correcting specific failure modes in trained networks.

Ivan Pasichnyk

Designing environments that maximize the rate of emergent behavior development in AI agents remains an open problem. We present the first systematic study of stress-performance relationships in large language model (LLM) multi-agent systems, drawing an explicit parallel to the Yerkes-Dodson law from cognitive psychology. Using a grid-world survival arena, we conduct 22 experiments across four phases, varying environmental pressure through resource scarcity (upkeep cost) and reproductive competition (sexual selection). Our key finding is that cooperative behavior follows an inverted-U curve: trade interactions peak at 29 under medium pressure (upkeep=5), while both low and extreme pressure produce 8--12 trades. Under extreme pressure, behavioral repertoire collapses to movement-only within 5--12 turns. We further show that sexual selection -- a softer pressure mechanism where all agents survive but not all reproduce -- eliminates inter-agent aggression entirely and produces communicative behavior absent under survival pressure. These results suggest that environmental pressure calibration is a viable curriculum design strategy for LLM agent development, analogous to the inverted-U relationship between arousal and performance in biological systems.