# A Latent Space Theory for Emergent Abilities in Large Language Models

arXiv: https://arxiv.org/abs/2304.09960 · HTML: https://mlsanity.com/paper/2304.09960/

## Key facts

- Cited by 43 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 31 references that are in the map.
- First posted on arXiv 19 Apr 2023.

## Builds on (most cited first, 22 of 22)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [PaLM: Scaling Language Modeling with Pathways](https://mlsanity.com/paper/2204.02311/) (2022)
- [Finetuned Language Models Are Zero-Shot Learners](https://mlsanity.com/paper/2109.01652/) (2021)
- [Scaling Instruction-Finetuned Language Models](https://mlsanity.com/paper/2210.11416/) (2022)
- [Emergent Abilities of Large Language Models](https://mlsanity.com/paper/2206.07682/) (2022)
- [Multitask Prompted Training Enables Zero-Shot Task Generalization](https://mlsanity.com/paper/2110.08207/) (2021)
- [Rethinking the Role of Demonstrations: What Makes In-Context Learning Work?](https://mlsanity.com/paper/2202.12837/) (2022)
- [What Makes Good In-Context Examples for GPT-3?](https://mlsanity.com/paper/2101.06804/) (2021)
- [An Explanation of In-context Learning as Implicit Bayesian Inference](https://mlsanity.com/paper/2111.02080/) (2021)
- [Learning To Retrieve Prompts for In-Context Learning](https://mlsanity.com/paper/2112.08633/) (2021)
- [Are Transformers universal approximators of sequence-to-sequence functions?](https://mlsanity.com/paper/1912.10077/) (2019)
- [Data Distributional Properties Drive Emergent In-Context Learning in Transformers](https://mlsanity.com/paper/2205.05055/) (2022)
- [Impact of Pretraining Term Frequencies on Few-Shot Reasoning](https://mlsanity.com/paper/2202.07206/) (2022)
- [The Learnability of In-Context Learning](https://mlsanity.com/paper/2303.07895/) (2023)
- [A Theory of Emergent In-Context Learning as Implicit Structure Induction](https://mlsanity.com/paper/2303.07971/) (2023)
- [Why Do Pretrained Language Models Help in Downstream Tasks? An Analysis of Head and Prompt Tuning](https://mlsanity.com/paper/2106.09226/) (2021)
- [Entailment Semantics Can Be Extracted from an Ideal Language Model](https://mlsanity.com/paper/2209.12407/) (2022)
- [On Approximation Capabilities of ReLU Activation and Softmax Output Layer in Neural Networks](https://mlsanity.com/paper/2002.04060/) (2020)
- [Why Learning of Large-Scale Neural Networks Behaves Like Convex Optimization](https://mlsanity.com/paper/1903.02140/) (2019)

## Built on by (most cited first, 30 of 43)

- [What and How does In-Context Learning Learn? Bayesian Model Averaging, Parameterization, and Generalization](https://mlsanity.com/paper/2305.19420/) (2023)
- [In-Context Convergence of Transformers](https://mlsanity.com/paper/2310.05249/) (2023)
- [Are Emergent Abilities in Large Language Models just In-Context Learning?](https://mlsanity.com/paper/2309.01809/) (2023)
- [Still No Lie Detector for Language Models: Probing Empirical and Conceptual Roadblocks](https://mlsanity.com/paper/2307.00175/) (2023)
- [Demystifying Chains, Trees, and Graphs of Thoughts](https://mlsanity.com/paper/2401.14295/) (2024)
- [Is In-Context Learning in Large Language Models Bayesian? A Martingale Perspective](https://mlsanity.com/paper/2406.00793/) (2024)
- [In-Context Learning Learns Label Relationships but Is Not Conventional Learning](https://mlsanity.com/paper/2307.12375/) (2023)
- [Reason for Future, Act for Now: A Principled Framework for Autonomous LLM Agents with Provable Sample Efficiency](https://mlsanity.com/paper/2309.17382/) (2023)
- [In-Context Learning with Representations: Contextual Generalization of Trained Transformers](https://mlsanity.com/paper/2408.10147/) (2024)
- [Do LLM Agents Have Regret? A Case Study in Online Learning and Games](https://mlsanity.com/paper/2403.16843/) (2024)
- [Efficient Reinforcement Learning with Large Language Model Priors](https://mlsanity.com/paper/2410.07927/) (2024)
- [Unveiling the Statistical Foundations of Chain-of-Thought Prompting Methods](https://mlsanity.com/paper/2408.14511/) (2024)
- [Mind the Inconspicuous: Revealing the Hidden Weakness in Aligned LLMs' Refusal Boundaries](https://mlsanity.com/paper/2405.20653/) (2024)
- [Multi-Agent Debate for LLM Judges with Adaptive Stability Detection](https://mlsanity.com/paper/2510.12697/) (2025)
- [BookGPT: A General Framework for Book Recommendation Empowered by Large Language Model](https://mlsanity.com/paper/2305.15673/) (2023)
- [Estimating the Hallucination Rate of Generative AI](https://mlsanity.com/paper/2406.07457/) (2024)
- [Bayesian scaling laws for in-context learning](https://mlsanity.com/paper/2410.16531/) (2024)
- [Trainable Transformer in Transformer](https://mlsanity.com/paper/2307.01189/) (2023)
- [From Words to Actions: Unveiling the Theoretical Underpinnings of LLM-Driven Autonomous Systems](https://mlsanity.com/paper/2405.19883/) (2024)
- [Why Can Large Language Models Generate Correct Chain-of-Thoughts?](https://mlsanity.com/paper/2310.13571/) (2023)
- [Training Language Models via Neural Cellular Automata](https://mlsanity.com/paper/2603.10055/) (2026)
- [Video Latent Flow Matching: Optimal Polynomial Projections for Video Interpolation and Extrapolation](https://mlsanity.com/paper/2502.00500/) (2025)
- [Towards Semantic Communication Protocols for 6G: From Protocol Learning to Language-Oriented Approaches](https://mlsanity.com/paper/2310.09506/) (2023)
- [The Role of Diversity in In-Context Learning for Large Language Models](https://mlsanity.com/paper/2505.19426/) (2025)
- [JAM: Controllable and Responsible Text Generation via Causal Reasoning and Latent Vector Manipulation](https://mlsanity.com/paper/2502.20684/) (2025)
- [Amplifying Limitations, Harms and Risks of Large Language Models](https://mlsanity.com/paper/2307.04821/) (2023)
- [Why is prompting hard? Understanding prompts on binary sequence predictors](https://mlsanity.com/paper/2502.10760/) (2025)
- [Knowledge Distillation from Language-Oriented to Emergent Communication for Multi-Agent Remote Control](https://mlsanity.com/paper/2401.12624/) (2024)
- [Towards Auto-Regressive Next-Token Prediction: In-Context Learning Emerges from Generalization](https://mlsanity.com/paper/2502.17024/) (2025)
- [From Drift to Coherence: Stabilizing Beliefs in LLMs](https://mlsanity.com/paper/2606.17832/) (2026)

## Abstract (arXiv)

Languages are not created randomly but rather to communicate information. There is a strong association between languages and their underlying meanings, resulting in a sparse joint distribution that is heavily peaked according to their correlations. Moreover, these peak values happen to match with the marginal distribution of languages due to the sparsity. With the advent of LLMs trained on big data and large models, we can now precisely assess the marginal distribution of languages, providing a convenient means of exploring the sparse structures in the joint distribution for effective inferences. In this paper, we categorize languages as either unambiguous or ε-ambiguous and present quantitative results to demonstrate that the emergent abilities of LLMs, such as language understanding, in-context learning, chain-of-thought prompting, and effective instruction fine-tuning, can all be attributed to Bayesian inference on the sparse joint distribution of languages.