Same Error, Different Function: The Optimizer as an Implicit Prior in Financial Time Series

• URL: http://arxiv.org/abs/2603.02620v1
• Date: Tue, 03 Mar 2026 05:47:19 GMT
• Title: Same Error, Different Function: The Optimizer as an Implicit Prior in Financial Time Series
• Authors: Federico Vittorio Cortesi, Giuseppe Iannone, Giulia Crippa, Tomaso Poggio, Pierfrancesco Beneventano,
• Abstract summary: We show that different model-training-pipeline pairs with identical test loss learn qualitatively different functions.<n>We conclude that in underspecified settings, optimization acts as a consequential source of inductive bias.
• Score: 0.5405981353784005
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Neural networks applied to financial time series operate in a regime of underspecification, where model predictors achieve indistinguishable out-of-sample error. Using large-scale volatility forecasting for S$\&$P 500 stocks, we show that different model-training-pipeline pairs with identical test loss learn qualitatively different functions. Across architectures, predictive accuracy remains unchanged, yet optimizer choice reshapes non-linear response profiles and temporal dependence differently. These divergences have material consequences for decisions: volatility-ranked portfolios trace a near-vertical Sharpe-turnover frontier, with nearly $3\times$ turnover dispersion at comparable Sharpe ratios. We conclude that in underspecified settings, optimization acts as a consequential source of inductive bias, thus model evaluation should extend beyond scalar loss to encompass functional and decision-level implications.

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