# Cognitive Training for Language Models: Towards General Capabilities via Cross-Entropy Games

arXiv: https://arxiv.org/abs/2603.22479 · HTML: https://mlsanity.com/paper/2603.22479/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 42 references that are in the map.
- First posted on arXiv 23 Mar 2026.

## Builds on (most cited first, 29 of 29)

- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [A Survey on Evaluation of Large Language Models](https://mlsanity.com/paper/2307.03109/) (2023)
- [Chatbot Arena: An Open Platform for Evaluating LLMs by Human Preference](https://mlsanity.com/paper/2403.04132/) (2024)
- [On-Policy Distillation of Language Models: Learning from Self-Generated Mistakes](https://mlsanity.com/paper/2306.13649/) (2023)
- [Contrastive Decoding: Open-ended Text Generation as Optimization](https://mlsanity.com/paper/2210.15097/) (2022)
- [Policy Distillation](https://mlsanity.com/paper/1511.06295/) (2015)
- [TextWorld: A Learning Environment for Text-based Games](https://mlsanity.com/paper/1806.11532/) (2018)
- [Automated Curriculum Learning for Neural Networks](https://mlsanity.com/paper/1704.03003/) (2017)
- [ARC-AGI-2: A New Challenge for Frontier AI Reasoning Systems](https://mlsanity.com/paper/2505.11831/) (2025)
- [Security and Privacy Challenges of Large Language Models: A Survey](https://mlsanity.com/paper/2402.00888/) (2024)
- [DataSentinel: A Game-Theoretic Detection of Prompt Injection Attacks](https://mlsanity.com/paper/2504.11358/) (2025)
- [Human-Timescale Adaptation in an Open-Ended Task Space](https://mlsanity.com/paper/2301.07608/) (2023)
- [AgentGym: Evolving Large Language Model-based Agents across Diverse Environments](https://mlsanity.com/paper/2406.04151/) (2024)
- [Automatic and Universal Prompt Injection Attacks against Large Language Models](https://mlsanity.com/paper/2403.04957/) (2024)
- [If beam search is the answer, what was the question?](https://mlsanity.com/paper/2010.02650/) (2020)
- [A Tutorial on Meta-Reinforcement Learning](https://mlsanity.com/paper/2301.08028/) (2023)
- [AI-GAs: AI-generating algorithms, an alternate paradigm for producing general artificial intelligence](https://mlsanity.com/paper/1905.10985/) (2019)
- [SPICE: Self-Play In Corpus Environments Improves Reasoning](https://mlsanity.com/paper/2510.24684/) (2025)
- [A Comprehensive Survey on Data Augmentation](https://mlsanity.com/paper/2405.09591/) (2024)
- [Reinforcement Pre-Training](https://mlsanity.com/paper/2506.08007/) (2025)
- [RLP: Reinforcement as a Pretraining Objective](https://mlsanity.com/paper/2510.01265/) (2025)
- [Compositional game theory](https://mlsanity.com/paper/1603.04641/) (2016)
- [PretrainZero: Reinforcement Active Pretraining](https://mlsanity.com/paper/2512.03442/) (2025)
- [When does a predictor know its own loss?](https://mlsanity.com/paper/2502.20375/) (2025)
- [Smart Proofs via Smart Contracts: Succinct and Informative Mathematical Derivations via Decentralized Markets](https://mlsanity.com/paper/2102.03044/) (2021)
- [Meta-Diversity Search in Complex Systems, A Recipe for Artificial Open-Endedness ?](https://mlsanity.com/paper/2312.00455/) (2023)
- [Cross-Entropy Games for Language Models: From Implicit Knowledge to General Capability Measures](https://mlsanity.com/paper/2506.06832/) (2025)

## Built on by (most cited first, 2 of 2)

- [Cross-Entropy Games and Frost Training](https://mlsanity.com/paper/2605.27701/) (2026)
- [The Missing Piece in Pre-trained Model Evaluation: Reward-Guided Decoding Unlocks Task-Oriented Behavior Without Parameter Updates](https://mlsanity.com/paper/2605.28020/) (2026)

## Abstract (arXiv)

Defining a constructive process to build general capabilities for language models in an automatic manner is considered an open problem in artificial intelligence. Towards this, we consider the problem of building a curriculum of tasks that grows a model via relevant skill discovery. We provide a concrete framework for this task, using a family of tasks called Cross-Entropy Games, which we postulate is universal in a suitable sense. We show that if it is possible to grow the curriculum for relevant skill discovery by iterating a greedy optimization algorithm, then, under natural assumptions, there is essentially only one meta-objective possible (up to a few hyper-parameters). We call the resulting process cognitive training. We postulate that, given sufficiently capable language models as players and meta-samplers, cognitive training provides a principled way to relevant skill discovery; and hence to the extent general capabilities are achievable via greedy curriculum learning, cognitive training would be a solution.