# Feedback Attribution and Representation Geometry: Metrics for Comparing Individual and Shared Rewards in MARL

arXiv: https://arxiv.org/abs/2607.16524 · HTML: https://mlsanity.com/paper/2607.16524/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 15 references that are in the map.
- First posted on arXiv 17 Jul 2026.

## Builds on (most cited first, 13 of 13)

- [The Surprising Effectiveness of PPO in Cooperative, Multi-Agent Games](https://mlsanity.com/paper/2103.01955/) (2021)
- [Counterfactual Multi-Agent Policy Gradients](https://mlsanity.com/paper/1705.08926/) (2017)
- [QMIX: Monotonic Value Function Factorisation for Deep Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/1803.11485/) (2018)
- [The Dormant Neuron Phenomenon in Deep Reinforcement Learning](https://mlsanity.com/paper/2302.12902/) (2023)
- [SMACv2: An Improved Benchmark for Cooperative Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2212.07489/) (2022)
- [DR3: Value-Based Deep Reinforcement Learning Requires Explicit Regularization](https://mlsanity.com/paper/2112.04716/) (2021)
- [Neural MMO: A Massively Multiagent Game Environment for Training and Evaluating Intelligent Agents](https://mlsanity.com/paper/1903.00784/) (2019)
- [System Neural Diversity: Measuring Behavioral Heterogeneity in Multi-Agent Learning](https://mlsanity.com/paper/2305.02128/) (2023)
- [Attention-Guided Contrastive Role Representations for Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2312.04819/) (2023)
- [Neural MMO 2.0: A Massively Multi-task Addition to Massively Multi-agent Learning](https://mlsanity.com/paper/2311.03736/) (2023)
- [MA2CL:Masked Attentive Contrastive Learning for Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2306.02006/) (2023)
- [Low-Rank Agent-Specific Adaptation (LoRASA) for Multi-Agent Policy Learning](https://mlsanity.com/paper/2502.05573/) (2025)
- [Prism: Spectral Parameter Sharing for Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2602.06476/) (2026)

## Abstract (arXiv)

Cooperative multi-agent RL systems routinely use team-averaged rewards, a feedback-attribution choice that gives each agent the team outcome regardless of its individual contribution. We ask whether this leaves a measurable signature, geometric or behavioral, on learned representations. We propose EffRank/n (effective rank normalized by agent count) and Dact (mean pairwise KL divergence between agents' action distributions) as low-overhead diagnostics for reward-attribution effects, then test them on competent MAPPO agents in SMACv2 textttprotoss5vs5, where unit type is encoded in the observation. In an observation × reward-attribution comparison (unit type observed vs. masked; individual damage-contribution reward vs. shared team reward), geometry follows observation rather than reward. With unit type observed, shared and individual rewards have similar EffRank/n (0.31±0.03 vs. 0.29±0.02) and probe accuracy (0.75±0.05 vs. 0.73±0.05, both gg 1/3 chance), while Dact leans higher under individual rewards (1.23±0.06 vs. 1.07±0.20). Masking unit type cuts the above-chance probe signal by more than half, to 0.49 in both reward arms. In short: individually rewarded agents are competent and separable by role, but on SMACv2 the observation explains the geometry and reward attribution shows up mainly in behavior. Thus geometric diagnostics must control for observed role information and test persistent roles that are not directly observed. EffRank/n and Dact add <5% overhead.