# Large language models implicitly learn to straighten neural sentence trajectories to construct a predictive representation of natural language

arXiv: https://arxiv.org/abs/2311.04930 · HTML: https://mlsanity.com/paper/2311.04930/

## Key facts

- Cited by 32 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 52 references that are in the map.
- First posted on arXiv 5 Nov 2023.

## Builds on (most cited first, 15 of 15)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [DistilBERT, a distilled version of BERT: smaller, faster, cheaper and lighter](https://mlsanity.com/paper/1910.01108/) (2019)
- [HuggingFace's Transformers: State-of-the-art Natural Language Processing](https://mlsanity.com/paper/1910.03771/) (2019)
- [Aligning Books and Movies: Towards Story-like Visual Explanations by Watching Movies and Reading Books](https://mlsanity.com/paper/1506.06724/) (2015)
- [GPT-NeoX-20B: An Open-Source Autoregressive Language Model](https://mlsanity.com/paper/2204.06745/) (2022)
- [DeepSpeed Inference: Enabling Efficient Inference of Transformer Models at Unprecedented Scale](https://mlsanity.com/paper/2207.00032/) (2022)
- [Interpreting and improving natural-language processing (in machines) with natural language-processing (in the brain)](https://mlsanity.com/paper/1905.11833/) (2019)
- [The geometry of hidden representations of large transformer models](https://mlsanity.com/paper/2302.00294/) (2023)
- [Classification and Geometry of General Perceptual Manifolds](https://mlsanity.com/paper/1710.06487/) (2017)
- [Neural population geometry: An approach for understanding biological and artificial neural networks](https://mlsanity.com/paper/2104.07059/) (2021)
- [Emergence of Separable Manifolds in Deep Language Representations](https://mlsanity.com/paper/2006.01095/) (2020)
- [Predictive information in a sensory population](https://mlsanity.com/paper/1307.0225/) (2013)

## Built on by (most cited first, 30 of 32)

- [Layer by Layer: Uncovering Hidden Representations in Language Models](https://mlsanity.com/paper/2502.02013/) (2025)
- [LoopFormer: Elastic-Depth Looped Transformers for Latent Reasoning via Shortcut Modulation](https://mlsanity.com/paper/2602.11451/) (2026)
- [Temporal Straightening for Latent Planning](https://mlsanity.com/paper/2603.12231/) (2026)
- [Does Representation Matter? Exploring Intermediate Layers in Large Language Models](https://mlsanity.com/paper/2412.09563/) (2024)
- [AI-Generated Video Detection via Perceptual Straightening](https://mlsanity.com/paper/2507.00583/) (2025)
- [Tracing the Traces: Latent Temporal Signals for Efficient and Accurate Reasoning](https://mlsanity.com/paper/2510.10494/) (2025)
- [Context Structure Reshapes the Representational Geometry of Language Models](https://mlsanity.com/paper/2601.22364/) (2026)
- [A quantitative analysis of semantic information in deep representations of text and images](https://mlsanity.com/paper/2505.17101/) (2025)
- [Adaptive Context Length Optimization with Low-Frequency Truncation for Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2510.26389/) (2025)
- [Semantic Tube Prediction: Beating LLM Data Efficiency with JEPA](https://mlsanity.com/paper/2602.22617/) (2026)
- [Brain-Language Model Alignment: Insights into the Platonic Hypothesis and Intermediate-Layer Advantage](https://mlsanity.com/paper/2510.17833/) (2025)
- [Dynamics of the Transformer Residual Stream: Coupling Spectral Geometry to Network Topology](https://mlsanity.com/paper/2605.14258/) (2026)
- [Analyzing Stream Collapse in Hyper-Connections: From Diagnosis to Mitigation](https://mlsanity.com/paper/2606.03483/) (2026)
- [Rhetorical Questions in LLM Representations: A Linear Probing Study](https://mlsanity.com/paper/2604.14128/) (2026)
- [DepthKV: Layer-Dependent KV Cache Pruning for Long-Context LLM Inference](https://mlsanity.com/paper/2604.24647/) (2026)
- [Automatic Layer Selection for Hallucination Detection](https://mlsanity.com/paper/2605.26366/) (2026)
- [Compression Hacking: A Supplementary Perspective on Informatics Properties of Language Models from Geometric Distortion](https://mlsanity.com/paper/2505.17793/) (2025)
- [Towards Inference-time Scaling for Continuous Space Reasoning](https://mlsanity.com/paper/2510.12167/) (2025)
- [Reasoning Models Don't Just Think Longer, They Move Differently](https://mlsanity.com/paper/2605.15454/) (2026)
- [Pseudo-Unification: Entropy Probing Reveals Divergent Information Patterns in Unified Multimodal Models](https://mlsanity.com/paper/2604.10949/) (2026)
- [Shallow Prefill, Deep Decoding: Efficient Long-Context Inference via Layer-Asymmetric KV Visibility](https://mlsanity.com/paper/2605.06105/) (2026)
- [Layer-wise Representation Dynamics: An Empirical Investigation Across Embedders and Base LLMs](https://mlsanity.com/paper/2605.12714/) (2026)
- [Representation Without Reward: A JEPA Audit for LLM Fine-Tuning](https://mlsanity.com/paper/2605.15394/) (2026)
- [Task-Induced Representational Invariances Depend on Learning Objective in Deep RL](https://mlsanity.com/paper/2606.01868/) (2026)
- [Multi Attribute Bias Mitigation via Representation Learning](https://mlsanity.com/paper/2509.03616/) (2025)
- [Training-Driven Representational Geometry Modularization Predicts Brain Alignment in Language Models](https://mlsanity.com/paper/2602.07539/) (2026)
- [Representational Curvature Modulates Behavioral Uncertainty in Large Language Models](https://mlsanity.com/paper/2604.23985/) (2026)
- [TAPIOCA: Why Task- Aware Pruning Improves OOD model Capability](https://mlsanity.com/paper/2605.14738/) (2026)
- [MENTIS: What Belief Changes Under Alignment? Measuring Multi-Scale Latent Torsion in Language Models](https://mlsanity.com/paper/2606.01060/) (2026)
- [Information-Regularized Attention for Visual-Centric Reasoning](https://mlsanity.com/paper/2607.00434/) (2026)

## Abstract (arXiv)

Predicting upcoming events is critical to our ability to interact with our environment. Transformer models, trained on next-word prediction, appear to construct representations of linguistic input that can support diverse downstream tasks. But how does a predictive objective shape such representations? Inspired by recent work in vision (Henaff et al., 2019), we test a hypothesis about predictive representations of autoregressive transformers. In particular, we test whether the neural trajectory of a sentence becomes progressively straighter as it passes through the network layers. The key insight is that straighter trajectories should facilitate prediction via linear extrapolation. We quantify straightness using a 1-dimensional curvature metric, and present four findings in support of the trajectory straightening hypothesis: i) In trained models, the curvature decreases from the early to the deeper layers of the network. ii) Models that perform better on the next-word prediction objective exhibit greater decreases in curvature, suggesting that this improved ability to straighten sentence trajectories may be the driver of better language modeling performance. iii) Given the same linguistic context, the sequences that are generated by the model have lower curvature than the actual continuations observed in a language corpus, suggesting that the model favors straighter trajectories for making predictions. iv) A consistent relationship holds between the average curvature and the average surprisal of sentences in the deep model layers, such that sentences with straighter trajectories also have lower surprisal. Importantly, untrained models do not exhibit these behaviors. In tandem, these results support the trajectory straightening hypothesis and provide a possible mechanism for how the geometry of the internal representations of autoregressive models supports next word prediction.