# On the Predictive Power of Representation Dispersion in Language Models

arXiv: https://arxiv.org/abs/2506.24106 · HTML: https://mlsanity.com/paper/2506.24106/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 30 references that are in the map.
- First posted on arXiv 30 Jun 2025.

## Builds on (most cited first, 23 of 23)

- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [Axiomatic Attribution for Deep Networks](https://mlsanity.com/paper/1703.01365/) (2017)
- [Probing Classifiers: Promises, Shortcomings, and Advances](https://mlsanity.com/paper/2102.12452/) (2021)
- [Generalization through Memorization: Nearest Neighbor Language Models](https://mlsanity.com/paper/1911.00172/) (2019)
- [How Contextual are Contextualized Word Representations? Comparing the Geometry of BERT, ELMo, and GPT-2 Embeddings](https://mlsanity.com/paper/1909.00512/) (2019)
- [Mechanistic Interpretability for AI Safety -- A Review](https://mlsanity.com/paper/2404.14082/) (2024)
- [The Vendi Score: A Diversity Evaluation Metric for Machine Learning](https://mlsanity.com/paper/2210.02410/) (2022)
- [Supervised Contrastive Learning for Pre-trained Language Model Fine-tuning](https://mlsanity.com/paper/2011.01403/) (2020)
- [Representation Degeneration Problem in Training Natural Language Generation Models](https://mlsanity.com/paper/1907.12009/) (2019)
- [All-but-the-Top: Simple and Effective Postprocessing for Word Representations](https://mlsanity.com/paper/1702.01417/) (2017)
- [The Geometry of Categorical and Hierarchical Concepts in Large Language Models](https://mlsanity.com/paper/2406.01506/) (2024)
- [Signal Propagation in Transformers: Theoretical Perspectives and the Role of Rank Collapse](https://mlsanity.com/paper/2206.03126/) (2022)
- [The geometry of hidden representations of large transformer models](https://mlsanity.com/paper/2302.00294/) (2023)
- [Intrinsic Dimension Estimation for Robust Detection of AI-Generated Texts](https://mlsanity.com/paper/2306.04723/) (2023)
- [Efficient Nearest Neighbor Language Models](https://mlsanity.com/paper/2109.04212/) (2021)
- [Neuro-Symbolic Language Modeling with Automaton-augmented Retrieval](https://mlsanity.com/paper/2201.12431/) (2022)
- [Why do Nearest Neighbor Language Models Work?](https://mlsanity.com/paper/2301.02828/) (2023)
- [What Happened in LLMs Layers when Trained for Fast vs. Slow Thinking: A Gradient Perspective](https://mlsanity.com/paper/2410.23743/) (2024)
- [Bridging Information-Theoretic and Geometric Compression in Language Models](https://mlsanity.com/paper/2310.13620/) (2023)
- [ContraCLM: Contrastive Learning For Causal Language Model](https://mlsanity.com/paper/2210.01185/) (2022)
- [The Intrinsic Dimension of Prompts in Internal Representations of Large Language Models](https://mlsanity.com/paper/2501.10573/) (2025)
- [How Instruction and Reasoning Data shape Post-Training: Data Quality through the Lens of Layer-wise Gradients](https://mlsanity.com/paper/2504.10766/) (2025)

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

- [Seeing without Looking: Do Vision-Language Benchmarks Really Test Vision?](https://mlsanity.com/paper/2605.22903/) (2026)
- [An LLM-based Agentic Framework for Accessible Network Control](https://mlsanity.com/paper/2509.20600/) (2025)
- [Dispersion Loss Counteracts Embedding Condensation and Improves Generalization in Small Language Models](https://mlsanity.com/paper/2602.00217/) (2026)
- [The Geometric Canary: Predicting Steerability and Detecting Drift via Representational Stability](https://mlsanity.com/paper/2604.17698/) (2026)
- [Contrastive Regularization for Accent-Robust ASR](https://mlsanity.com/paper/2605.03297/) (2026)
- [Global Divergence, Local Convergence: Representation Geometry in SSMs and Transformers](https://mlsanity.com/paper/2609.08692/) (2026)
- [Before Attention Sinks Form: Hidden-State Geometry Reveals and Modulates Their Formation](https://mlsanity.com/paper/2610.16745/) (2026)

## Abstract (arXiv)

We show that a language model's ability to predict text is tightly linked to the breadth of its embedding space: models that spread their contextual representations more widely tend to achieve lower perplexity. Concretely, we find that representation dispersion--the average pairwise cosine distance among hidden vectors--strongly and negatively correlates with perplexity across diverse model families (LLaMA, Qwen, and others) and domains (Wikipedia, news, scientific abstracts). Beyond illustrating this link, we show how dispersion can be leveraged for a range of practical tasks--without requiring labeled data. First, measuring dispersion on unlabeled text allows us to rank examples by difficulty and identify hard slices in new domains, offering a data-efficient tool for screening and prioritizing models before full evaluation. Next, we find that identifying layers with higher dispersion pinpoints the best representations for retrieval-based methods such as kNN-LM, bypassing exhaustive layer-by-layer searches. Finally, we integrate a simple "push-away" objective into training, which increases dispersion in both single-domain and cross-domain scenarios and directly improves perplexity in each. Code is available at https://github.com/yanhong-lbh/rep_dispersion.