# The Cost of a Physics Prior Is Bounded by the Ablation Gap

arXiv: https://arxiv.org/abs/2608.21059 · HTML: https://mlsanity.com/paper/2608.21059/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 35 references that are in the map.
- First posted on arXiv 21 Aug 2026.

## Builds on (most cited first, 20 of 20)

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- [Shortcut Learning in Deep Neural Networks](https://mlsanity.com/paper/2004.07780/) (2020)
- [Characterizing possible failure modes in physics-informed neural networks](https://mlsanity.com/paper/2109.01050/) (2021)
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- [Integrating Scientific Knowledge with Machine Learning for Engineering and Environmental Systems](https://mlsanity.com/paper/2003.04919/) (2020)
- [Deep Lattice Networks and Partial Monotonic Functions](https://mlsanity.com/paper/1709.06680/) (2017)
- [Certified Monotonic Neural Networks](https://mlsanity.com/paper/2011.10219/) (2020)
- [Monotonic Calibrated Interpolated Look-Up Tables](https://mlsanity.com/paper/1505.06378/) (2015)
- [Predicting into unknown space? Estimating the area of applicability of spatial prediction models](https://mlsanity.com/paper/2005.07939/) (2020)
- [Importance of spatial predictor variable selection in machine learning applications -- Moving from data reproduction to spatial prediction](https://mlsanity.com/paper/1908.07805/) (2019)
- [Monotonic classification: an overview on algorithms, performance measures and data sets](https://mlsanity.com/paper/1811.07155/) (2018)
- [Deontological Ethics By Monotonicity Shape Constraints](https://mlsanity.com/paper/2001.11990/) (2020)
- [ELENA: Epigenetic Learning through Evolved Neural Adaptation](https://mlsanity.com/paper/2501.05735/) (2025)
- [Advancing Eurasia Fire Understanding Through Machine Learning Techniques](https://mlsanity.com/paper/2502.17023/) (2025)
- [MorphBoost: Self-Organizing Universal Gradient Boosting with Adaptive Tree Morphing](https://mlsanity.com/paper/2511.13234/) (2025)
- [POSEIDON: Physics-Optimized Seismic Energy Inference and Detection Operating Network](https://mlsanity.com/paper/2601.02264/) (2026)
- [DeepSupp: Attention-Driven Correlation Pattern Analysis for Dynamic Time Series Support and Resistance Levels Identification](https://mlsanity.com/paper/2507.01971/) (2025)
- [Hybrid Physics-ML Framework for Pan-Arctic Permafrost Infrastructure Risk at Record 2.9-Million Observation Scale](https://mlsanity.com/paper/2510.02189/) (2025)
- [ORCA -- Online Regime Correlation Analyzer](https://mlsanity.com/paper/2604.17251/) (2026)
- [Artificial Adaptive Intelligence: The Missing Stage Between Narrow and General Intelligence](https://mlsanity.com/paper/2605.16844/) (2026)

## Abstract (arXiv)

Shape-constrained and physics-informed learning reports an accuracy cost of enforcing a prior and treats it as a property of the prior. We show it is mostly a property of the free features and the validation split. Let P be the excess risk of restricting a hypothesis class to functions with a shape constraint on features S, and D the excess risk of the ablated model that ignores S. Because a function constant in x_j is both non-decreasing and non-increasing in x_j, the ablated class is contained in the constrained class, so 0 <= P <= D for every risk functional, with no convexity, smoothness, or realizability assumption. Empirically the bound is a sign test: a constrained model must never be beaten by its own ablation. We instantiate it on an ordinal wildfire-severity task (N = 26,681, K = 3) with hard monotone constraints on four meteorological drivers, coordinates left free, and a validation ladder from i.i.d. resampling to 2-degree spatial blocking. Coordinates act as a shield: alone they recover 92.9% of the full model's macro-F1 under spatial blocking, collapsing D from 0.1288 to 0.0427; the same prior costs 0.0473 shielded and 0.3470 unshielded, a ratio of 7.3 with identical physics. Because D is protocol-dependent it does not transfer: coarsening blocks from 1 to 10 degrees drives D from 0.0942 to 0.0050, leaving two configurations unidentifiable a priori. Inversions of the certified nesting bound the pipeline's additive resolution: over 318 comparisons they give a self-calibrating floor of 0.0220 macro-F1, below which no reported price is interpretable, including four cells in our own headline grid. Cost and compliance are independent: the unconstrained model violates the prior at rate 0.48-0.49 while enforcing it costs 0.0473. We give a two-fit screen that rejects unidentifiable experiments before a constrained model is trained.