# Hadamax Encoding: Elevating Performance in Model-Free Atari

arXiv: https://arxiv.org/abs/2505.15345 · HTML: https://mlsanity.com/paper/2505.15345/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Placed in Deep RL algorithms and representations, one of 15 directions in Deep reinforcement learning methods.
- Builds on 48 of its 61 references that are in the map.
- First posted on arXiv 21 May 2025.

## Placed in

- Deep reinforcement learning methods / [Deep RL algorithms and representations](https://mlsanity.com/deeprl/deep-rl-algorithms-and-representations/)

## Builds on (most cited first, 30 of 48)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [Playing Atari with Deep Reinforcement Learning](https://mlsanity.com/paper/1312.5602/) (2013)
- [Deep Reinforcement Learning with Double Q-learning](https://mlsanity.com/paper/1509.06461/) (2015)
- [Mastering Atari, Go, Chess and Shogi by Planning with a Learned Model](https://mlsanity.com/paper/1911.08265/) (2019)
- [Learning Latent Dynamics for Planning from Pixels](https://mlsanity.com/paper/1811.04551/) (2018)
- [Mastering Diverse Domains through World Models](https://mlsanity.com/paper/2301.04104/) (2023)
- [Soft Actor-Critic Algorithms and Applications](https://mlsanity.com/paper/1812.05905/) (2018)
- [Mastering Atari with Discrete World Models](https://mlsanity.com/paper/2010.02193/) (2020)
- [IMPALA: Scalable Distributed Deep-RL with Importance Weighted Actor-Learner Architectures](https://mlsanity.com/paper/1802.01561/) (2018)
- [Rainbow: Combining Improvements in Deep Reinforcement Learning](https://mlsanity.com/paper/1710.02298/) (2017)
- [Dueling Network Architectures for Deep Reinforcement Learning](https://mlsanity.com/paper/1511.06581/) (2015)
- [A Distributional Perspective on Reinforcement Learning](https://mlsanity.com/paper/1707.06887/) (2017)
- [CURL: Contrastive Unsupervised Representations for Reinforcement Learning](https://mlsanity.com/paper/2004.04136/) (2020)
- [Brax -- A Differentiable Physics Engine for Large Scale Rigid Body Simulation](https://mlsanity.com/paper/2106.13281/) (2021)
- [Temporal Difference Learning for Model Predictive Control](https://mlsanity.com/paper/2203.04955/) (2022)
- [Data-Efficient Reinforcement Learning with Self-Predictive Representations](https://mlsanity.com/paper/2007.05929/) (2020)
- [Diffusion for World Modeling: Visual Details Matter in Atari](https://mlsanity.com/paper/2405.12399/) (2024)
- [Randomized Ensembled Double Q-Learning: Learning Fast Without a Model](https://mlsanity.com/paper/2101.05982/) (2021)
- [Noisy Networks for Exploration](https://mlsanity.com/paper/1706.10295/) (2017)
- [Mastering Atari Games with Limited Data](https://mlsanity.com/paper/2111.00210/) (2021)
- [An Introduction to Deep Reinforcement Learning](https://mlsanity.com/paper/1811.12560/) (2018)
- [ViZDoom: A Doom-based AI Research Platform for Visual Reinforcement Learning](https://mlsanity.com/paper/1605.02097/) (2016)
- [The Dormant Neuron Phenomenon in Deep Reinforcement Learning](https://mlsanity.com/paper/2302.12902/) (2023)
- [Training Very Deep Networks](https://mlsanity.com/paper/1507.06228/) (2015)
- [Bigger, Better, Faster: Human-level Atari with human-level efficiency](https://mlsanity.com/paper/2305.19452/) (2023)

## Built on by (most cited first, 7 of 7)

- [Simplicial Embeddings Improve Sample Efficiency in Actor-Critic Agents](https://mlsanity.com/paper/2510.13704/) (2025)
- [Mind the GAP! The Challenges of Scale in Pixel-based Deep Reinforcement Learning](https://mlsanity.com/paper/2505.17749/) (2025)
- [Modularized Reinforcement Learning on LLMs: From MDP Creation to Exploration and Learning](https://mlsanity.com/paper/2606.21943/) (2026)
- [Higher Resolution, Better Generalization: Unlocking Visual Scaling in Deep Reinforcement Learning](https://mlsanity.com/paper/2605.10546/) (2026)
- [Representation Learning Enables Scalable Multitask Deep Reinforcement Learning](https://mlsanity.com/paper/2606.05555/) (2026)
- [A Progressive Design Study of Visual Encoders and Value Estimation for Replay-Free Parallelized Q-Learning](https://mlsanity.com/paper/2608.07335/) (2026)
- [V-Simba: Unleashing the Architectural Potential of RL in Visual Continuous Control](https://mlsanity.com/paper/2608.07870/) (2026)

## Abstract (arXiv)

Neural network architectures have a large impact in machine learning. In reinforcement learning, network architectures have remained notably simple, as changes often lead to small gains in performance. This work introduces a novel encoder architecture for pixel-based model-free reinforcement learning. The Hadamax (Hadamard max-pooling) encoder achieves state-of-the-art performance by max-pooling Hadamard products between GELU-activated parallel hidden layers. Based on the recent PQN algorithm, the Hadamax encoder achieves state-of-the-art model-free performance in the Atari-57 benchmark. Specifically, without applying any algorithmic hyperparameter modifications, Hadamax-PQN achieves an 80% performance gain over vanilla PQN and significantly surpasses Rainbow-DQN. For reproducibility, the full code is available on hrefhttps://github.com/Jacobkooi/HadamaxGitHub.