# Playing the network backward: A Game Theoretic Attribution Framework

arXiv: https://arxiv.org/abs/2605.06212 · HTML: https://mlsanity.com/paper/2605.06212/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Circuits and mechanistic analysis, one of 13 directions in Mechanistic interpretability.
- Builds on 9 of its 72 references that are in the map.
- First posted on arXiv 7 May 2026.

## Placed in

- Mechanistic interpretability / [Circuits and mechanistic analysis](https://mlsanity.com/mechinterp/circuits-and-mechanistic-analysis/)

## Builds on (most cited first, 9 of 9)

- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [Deep Inside Convolutional Networks: Visualising Image Classification Models and Saliency Maps](https://mlsanity.com/paper/1312.6034/) (2013)
- [SmoothGrad: removing noise by adding noise](https://mlsanity.com/paper/1706.03825/) (2017)
- [Captum: A unified and generic model interpretability library for PyTorch](https://mlsanity.com/paper/2009.07896/) (2020)
- [AtP*: An efficient and scalable method for localizing LLM behaviour to components](https://mlsanity.com/paper/2403.00745/) (2024)
- [Software for Dataset-wide XAI: From Local Explanations to Global Insights with Zennit, CoRelAy, and ViRelAy](https://mlsanity.com/paper/2106.13200/) (2021)
- [DAVE: Distribution-aware Attribution via ViT Gradient Decomposition](https://mlsanity.com/paper/2602.06613/) (2026)
- [Relu and softplus neural nets as zero-sum turn-based games](https://mlsanity.com/paper/2512.20582/) (2025)

## Abstract (arXiv)

Attribution methods explain which input features drive a model's prediction, making them central to model debugging and mechanistic interpretability. Yet backward attribution methods, including gradients, LRP, and transformer-specific rules, lack a shared framework in which to compare the underlying backward calculations. We introduce such a framework by recasting backward attribution as a two-player game on an extended network graph, building on Gaubert and Vlassopoulos' ReLU Net Game. Gradients and the full alpha-beta-LRP family arise as integrals over game trajectories under specific equilibria, so attribution maps become projections of trajectory distributions rather than the primary object. Desired explanation properties, such as localisation focus, robustness to input noise, or stable attention routing, can be specified as game-theoretic concepts, including policy regularization, risk aversion, and extended action sets, and translate directly into novel adaptations of the well-known backward rules. On ViT-B/16, one such selected adaptation of alpha-beta-LRP outperforms prior transformer-specific backward methods across all considered localisation metrics.