Gradient-Descent Steps to Success over Mean Accuracy: A Paradigm Shift for ML

Traditional evaluation of machine learning (ML) models typically focuses on achieving the maximum possible accuracy irrespective of the computational cost. In this article, we propose a paradigm shift towards evaluating performance based on computational effort-explicitly defined here as the total number of gradient descent steps required to reach an acceptable level of accuracy with high probability. Building upon the concept of computational effort originally introduced by Koza for Genetic Programming, we extend this metric to any ML model trained via gradient descent. Furthermore, we demonstrate that minimising this effort acts as a novel form of Automatic Machine Learning (AutoML). By evaluating it across 11 diverse ML models and five standard classification datasets, we uncover significant insights into the dynamics of gradient-based learning. Our findings reveal that optimal hyper-parameters consistently favour unusually large learning rates. Crucially, we demonstrate that the rapid, aggressive landscape traversal enabled by these large rates not only promotes generalisation-as seen in phenomena like superconvergence-but also statistically minimises the expected computational effort for training. Furthermore, we identify distinct phase transitions in the optimal search strategy: while a single training run suffices for lower accuracy targets, reaching a model's performance limit requires a dramatic shift towards conducting numerous independent, short restarts. Finally, we illustrate how this effort-based paradigm provides a robust framework for model selection, allowing practitioners to choose optimal algorithms based on the difficulty of a problem as perceived by different models for a given target accuracy, or to maximise the achievable accuracy for a fixed budget of gradient descent steps.

The Timing Dependencies of Trust: Speed, Accuracy, and cBCI Neuro-Decoupling in Human-AI Teams

The speed and accuracy of an artificial teammate fundamentally alter the failure states of Human-AI integration. While high-speed AI interventions risk inducing reflexive blind compliance, delayed interventions can induce ambiguous cognitive conflict. This study investigates how the fundamental characteristics of an in-task AI assistant, Fast/Less-Accurate (FLA-AI) versus Slow/Accurate (SA-AI) impact the synergy of Collaborative Brain-Computer Interface (cBCI) teams in a Virtual Reality drone task. Seventeen operators completed continuous search tasks under high cognitive workload while their spatial covariance was mapped using a 2D Adaptive Riemannian Oracle. The results mathematically demonstrate that AI timing dictates the mechanism of team failure. Fast AI induced instant, blind compliance; human accuracy under deception collapsed to 50.2%, and pure behavioural teams (N=8) failed to scale beyond 74.1%. In contrast, Slow AI induced delayed cognitive conflict; humans hesitated (61.1% accuracy), but N=8 behavioural teams eventually recovered to 100.0%. Crucially, the Riemannian Oracle mathematically adapted to these states: it heavily restricted temporal windows (< 0.8s) to intercept fast reflexive compliance, while widening windows (> 1.2s) to capture delayed cognitive conflict. Integrating these isolated veridical signals via Hybrid Fusion successfully rescued the Fast AI team (+7.6% at N=8) and significantly accelerated the recovery of smaller Slow AI teams (+6.9% at N=4). These findings prove that cBCI synergy is heavily contingent on the temporal dynamics of trust, providing a critical framework for designing dynamically gated Human-AI systems.