# More Data, Worse Decisions? Preference Reversals in Neural Networks under Gram Incompatibility

arXiv: https://arxiv.org/abs/2607.27255 · HTML: https://mlsanity.com/paper/2607.27255/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 23 references that are in the map.
- First posted on arXiv 28 Jul 2026.

## Builds on (most cited first, 16 of 16)

- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [Understanding Black-box Predictions via Influence Functions](https://mlsanity.com/paper/1703.04730/) (2017)
- [WILDS: A Benchmark of in-the-Wild Distribution Shifts](https://mlsanity.com/paper/2012.07421/) (2020)
- [Deep CORAL: Correlation Alignment for Deep Domain Adaptation](https://mlsanity.com/paper/1607.01719/) (2016)
- [This Looks Like That: Deep Learning for Interpretable Image Recognition](https://mlsanity.com/paper/1806.10574/) (2018)
- [Estimating Training Data Influence by Tracing Gradient Descent](https://mlsanity.com/paper/2002.08484/) (2020)
- [Representer Point Selection for Explaining Deep Neural Networks](https://mlsanity.com/paper/1811.09720/) (2018)
- [Whoever Started the Interference Should End It: Guiding Data-Free Model Merging via Task Vectors](https://mlsanity.com/paper/2503.08099/) (2025)
- [Domain Adaptation for Time Series Under Feature and Label Shifts](https://mlsanity.com/paper/2302.03133/) (2023)
- [Axioms for AI Alignment from Human Feedback](https://mlsanity.com/paper/2405.14758/) (2024)
- [Pareto Merging: Multi-Objective Optimization for Preference-Aware Model Merging](https://mlsanity.com/paper/2408.12105/) (2024)
- [Keep the Faith: Faithful Explanations in Convolutional Neural Networks for Case-Based Reasoning](https://mlsanity.com/paper/2312.09783/) (2023)
- [Learning How to Vote with Principles: Axiomatic Insights Into the Collective Decisions of Neural Networks](https://mlsanity.com/paper/2410.16170/) (2024)
- [M-Loss: Quantifying Model Merging Compatibility with Limited Unlabeled Data](https://mlsanity.com/paper/2602.08564/) (2026)
- [Do Neural Networks Preserve Case Structure? Case-Based Decomposition, Interpretation, and Decision Consistency](https://mlsanity.com/paper/2607.11347/) (2026)

## Abstract (arXiv)

Neural networks increasingly combine data across populations, time periods, and operating conditions to improve generalization. This raises a reliability question: whether a model refitted on pooled data preserves an action ordering supported by both sources. Case-Based Decision Theory (CBDT) formalizes this requirement through its composition axiom, which requires source-supported preferences to survive their union. We study when this property holds for fixed-representation neural networks with ordinary least squares (OLS) output heads. First, we show that pooled refitting recomputes the inverse-Gram geometry used to weight source evidence, which can reverse shared preferences, and derive exact and approximate preservation conditions. Next, we introduce a scale-invariant Gram mismatch measure for prioritizing candidate pools and geometry-oriented regularization for shaping source geometry during training. Finally, we develop a three-stage audit that traces strict pairwise reversals through decision changes to task-defined utility loss. Experiments spanning a load-based bidding proxy and medical and financial decision proxies reveal stable and reversal-prone pooling regimes: the load audit identifies a measurable nonzero class of source-consensus-relative harmful decisions under the proxy utility, while cross-domain audits show that comparable mismatch can correspond to sharply different preservation rates. Geometry-oriented objectives occupy distinct descriptive accuracy-consistency-geometry-harm operating points. Together, the framework makes compositional reliability measurable and operational through screening, analytic certification, geometry-oriented training, and decision-consequence auditing.