The Anatomy of Implicit Bias: Information Allocation in Neural Network Training

Abstract

Implicit bias is usually explained as the preference of an optimization process for certain final solutions and their geometry. This view helps explain where a model finally stops. It gives less direct explanation of how this bias is formed during training. This paper proposes a training-time information allocation view. Under this view, optimization forms a writing pattern for error signals across parameter paths, coordinate channels, and sample regions. This paper builds a set of observable allocation diagnostics. These diagnostics include gradient demand, actual update injection, coordinate gain induced by exponential moving averages, channel-level update ratios, and sample-wise loss distributions. To separate training progress from internal allocation, this paper introduces a collapse--persistence analysis. Under matched training loss, if external loss statistics collapse but internal allocation ratios remain separated, then the factor changes the internal allocation of the training signal. Overall, this paper extends the analysis of implicit bias from final-solution geometry to training-time signal allocation. The main claim is that implicit bias is not only reflected by the final solution. It is also reflected by which parameter paths, coordinate channels, and sample regions receive the error signal first and more strongly during training. Based on this view, this paper places different training factors into a unified information-allocation diagnostic framework. The framework gives a mechanism-level explanation of training-time implicit bias. It also provides a basis for future optimization methods that control training progress and signal allocation separately.