# All or None: Identifiable Linear Properties of Next-token Predictors in Language Modeling

arXiv: https://arxiv.org/abs/2410.23501 · HTML: https://mlsanity.com/paper/2410.23501/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 46 of its 81 references that are in the map.
- First posted on arXiv 30 Oct 2024.

## Builds on (most cited first, 30 of 46)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Efficient Estimation of Word Representations in Vector Space](https://mlsanity.com/paper/1301.3781/) (2013)
- [Distributed Representations of Words and Phrases and their Compositionality](https://mlsanity.com/paper/1310.4546/) (2013)
- [Understanding intermediate layers using linear classifier probes](https://mlsanity.com/paper/1610.01644/) (2016)
- [Interpretability Beyond Feature Attribution: Quantitative Testing with Concept Activation Vectors (TCAV)](https://mlsanity.com/paper/1711.11279/) (2017)
- [Refusal in Language Models Is Mediated by a Single Direction](https://mlsanity.com/paper/2406.11717/) (2024)
- [Toy Models of Superposition](https://mlsanity.com/paper/2209.10652/) (2022)
- [Discovering Latent Knowledge in Language Models Without Supervision](https://mlsanity.com/paper/2212.03827/) (2022)
- [The Linear Representation Hypothesis and the Geometry of Large Language Models](https://mlsanity.com/paper/2311.03658/) (2023)
- [The Geometry of Truth: Emergent Linear Structure in Large Language Model Representations of True/False Datasets](https://mlsanity.com/paper/2310.06824/) (2023)
- [Variational Autoencoders and Nonlinear ICA: A Unifying Framework](https://mlsanity.com/paper/1907.04809/) (2019)
- [Emergent World Representations: Exploring a Sequence Model Trained on a Synthetic Task](https://mlsanity.com/paper/2210.13382/) (2022)
- [Trained Transformers Learn Linear Models In-Context](https://mlsanity.com/paper/2306.09927/) (2023)
- [Generating Wikipedia by Summarizing Long Sequences](https://mlsanity.com/paper/1801.10198/) (2018)
- [Emergent Linear Representations in World Models of Self-Supervised Sequence Models](https://mlsanity.com/paper/2309.00941/) (2023)
- [Language Models Represent Space and Time](https://mlsanity.com/paper/2310.02207/) (2023)
- [Nonlinear ICA Using Auxiliary Variables and Generalized Contrastive Learning](https://mlsanity.com/paper/1805.08651/) (2018)
- [Does Localization Inform Editing? Surprising Differences in Causality-Based Localization vs. Knowledge Editing in Language Models](https://mlsanity.com/paper/2301.04213/) (2023)
- [Linearity of Relation Decoding in Transformer Language Models](https://mlsanity.com/paper/2308.09124/) (2023)
- [Linear Representations of Sentiment in Large Language Models](https://mlsanity.com/paper/2310.15154/) (2023)
- [Improving Instruction-Following in Language Models through Activation Steering](https://mlsanity.com/paper/2410.12877/) (2024)
- [The Geometry of Categorical and Hierarchical Concepts in Large Language Models](https://mlsanity.com/paper/2406.01506/) (2024)
- [Interventional Causal Representation Learning](https://mlsanity.com/paper/2209.11924/) (2022)
- [CITRIS: Causal Identifiability from Temporal Intervened Sequences](https://mlsanity.com/paper/2202.03169/) (2022)
- [Future Lens: Anticipating Subsequent Tokens from a Single Hidden State](https://mlsanity.com/paper/2311.04897/) (2023)
- [Nonparametric Identifiability of Causal Representations from Unknown Interventions](https://mlsanity.com/paper/2306.00542/) (2023)
- [On Linear Identifiability of Learned Representations](https://mlsanity.com/paper/2007.00810/) (2020)
- [ICE-BeeM: Identifiable Conditional Energy-Based Deep Models Based on Nonlinear ICA](https://mlsanity.com/paper/2002.11537/) (2020)
- [Language Models Implement Simple Word2Vec-style Vector Arithmetic](https://mlsanity.com/paper/2305.16130/) (2023)
- [The Geometry of Multilingual Language Model Representations](https://mlsanity.com/paper/2205.10964/) (2022)

## Built on by (most cited first, 14 of 14)

- [I Predict Therefore I Am: Is Next Token Prediction Enough to Learn Human-Interpretable Concepts from Data?](https://mlsanity.com/paper/2503.08980/) (2025)
- [Position: An Empirically Grounded Identifiability Theory Will Accelerate Self-Supervised Learning Research](https://mlsanity.com/paper/2504.13101/) (2025)
- [What is causal about causal models and representations?](https://mlsanity.com/paper/2501.19335/) (2025)
- [Statistical and structural identifiability in representation learning](https://mlsanity.com/paper/2603.11970/) (2026)
- [Stop Probing, Start Coding: Why Linear Probes and Sparse Autoencoders Fail at Compositional Generalisation](https://mlsanity.com/paper/2603.28744/) (2026)
- [When Does Closeness in Distribution Imply Representational Similarity? An Identifiability Perspective](https://mlsanity.com/paper/2506.03784/) (2025)
- [Nonparametric Identification of Latent Concepts](https://mlsanity.com/paper/2510.00136/) (2025)
- [On the Blessing of Pre-training in Weak-to-Strong Generalization](https://mlsanity.com/paper/2605.05710/) (2026)
- [Not all solutions are created equal: An analytical dissociation of functional and representational similarity in deep linear neural networks](https://mlsanity.com/paper/2609.38998/) (2026)
- [Beyond the Black Box: Identifiable Interpretation and Control in Generative Models via Causal Minimality](https://mlsanity.com/paper/2512.10720/) (2025)
- [Concept Component Analysis: A Principled Approach for Concept Extraction in LLMs](https://mlsanity.com/paper/2601.20420/) (2026)
- [Logit Distance Bounds Representational Similarity](https://mlsanity.com/paper/2602.15438/) (2026)
- [Who Guards the Guardians? The Challenges of Evaluating Identifiability of Learned Representations](https://mlsanity.com/paper/2602.24278/) (2026)
- [Relational Linear Properties in Language Models: An Empirical Investigation](https://mlsanity.com/paper/2605.22532/) (2026)

## Abstract (arXiv)

We analyze identifiability as a possible explanation for the ubiquity of linear properties across language models, such as the vector difference between the representations of "easy" and "easiest" being parallel to that between "lucky" and "luckiest". For this, we ask whether finding a linear property in one model implies that any model that induces the same distribution has that property, too. To answer that, we first prove an identifiability result to characterize distribution-equivalent next-token predictors, lifting a diversity requirement of previous results. Second, based on a refinement of relational linearity [Paccanaro and Hinton, 2001; Hernandez et al., 2024], we show how many notions of linearity are amenable to our analysis. Finally, we show that under suitable conditions, these linear properties either hold in all or none distribution-equivalent next-token predictors.