How Much is Left? LLMs Linearly Encode Their Remaining Output Length
Not on the map. Why?
Abstract (arXiv)
Large language models generate one token at a time, yet their responses show remarkably consistent length structure: step-by-step solutions converge in predictable token counts, retrievals stop after a few sentences, retractions extend responses by measurable amounts. We ask whether the model carries an internal estimate of how much response remains. Training minimal-capacity linear probes on frozen hidden states of three open-weight 7-8B models across seven completion-style datasets, we find three converging pieces of evidence. First, total response length is linearly decodable from the prompt's last hidden state alone, before any output is emitted. Second, probe directions trained on natural-language datasets transfer broadly, including to controlled synthetic completions never seen in training, outperforming a statistical baseline; the converse direction generally fails, and this asymmetry is itself informative. Third, on curated high-loss completions, the probe's per-position estimate shifts upward at the moment the model retracts and restarts a partial solution, a directional behavior no position-only predictor can reproduce (qualitative, not aggregate). We frame this as approximate estimation of remaining generation length, distinct from exact-counting impossibility results for transformers, and interpret it as evidence that LLMs maintain a plan-like internal representation of output length (decodable, not necessarily used causally).
Key facts. Cited by 2 papers in the map (data through 14 Oct 2026). Builds on 39 of its 76 references that are in the map. First posted on arXiv 6 Jul 2026.
Builds on
39 of 76 references.
References · 39
- 2016Optimization Methods for Large-Scale Machine Learningcited by 1,150
- 2015Deep Learning with Limited Numerical Precisioncited by 376
- 2014RAPPOR: Randomized Aggregatable Privacy-Preserving Ordinal Responsecited by 272
- 2016Minimax Optimal Procedures for Locally Private Estimationcited by 107
- 2016Statistical Inference for Model Parameters in Stochastic Gradient Descentcited by 71
- 2019Collecting and Analyzing Multidimensional Data with Local Differential Privacycited by 49
- 2015Local, Private, Efficient Protocols for Succinct Histogramscited by 36
- 2022Optimal Algorithms for Mean Estimation under Local Differential Privacycited by 36
- 2017Optimal Schemes for Discrete Distribution Estimation under Locally Differential Privacycited by 29
- 2021Fast and Robust Online Inference with Stochastic Gradient Descent via Random Scalingcited by 28
- 2018Hadamard Response: Estimating Distributions Privately, Efficiently, and with Little Communicationcited by 26
- 2021Differentially Private Quantilescited by 23
27 more
- 2019Estimating Numerical Distributions under Local Differential Privacycited by 17
- 2020Empirical Risk Minimization in the Non-interactive Local Model of Differential Privacycited by 16
- 2018Locally Private Mean Estimation: Z-test and Tight Confidence Intervalscited by 15
- 2023Fast Optimal Locally Private Mean Estimation via Random Projectionscited by 14
- 2018HiGrad: Uncertainty Quantification for Online Learning and Stochastic Approximationcited by 13
- 2019On Constructing Confidence Region for Model Parameters in Stochastic Gradient Descent via Batch Meanscited by 13
- 2018Answering Range Queries Under Local Differential Privacycited by 12
- 2021Differentially Private Approximate Quantilescited by 12
- 2022Differentially Private Bootstrap: New Privacy Analysis and Inference Strategiescited by 10
- 2019Estimating Smooth GLM in Non-interactive Local Differential Privacy Model with Public Unlabeled Datacited by 9
- 2021Communication-Constrained Distributed Quantile Regression with Optimal Statistical Guaranteescited by 8
- 2022Bounded Space Differentially Private Quantilescited by 8
- 2024Online Quantile Regressioncited by 7
- 2023Unbounded Differentially Private Quantile and Maximum Estimationcited by 6
- 2016Divide and Conquer in Non-standard Problems and the Super-efficiency Phenomenoncited by 5
- 2023Online Local Differential Private Quantile Inference via Self-normalizationcited by 5
- 2023Private Statistical Estimation of Many Quantilescited by 3
- 2018Locally Differentially-Private Randomized Response for Discrete Distribution Learningcited by 2
- 2024Locally Private Histograms in All Privacy Regimescited by 2
- 2025Lightweight Protocols for Distributed Private Quantile Estimationcited by 2
- 2025Online differentially private inference in stochastic gradient descentcited by 2
- 2025Differentially Private Quantiles with Smaller Errorcited by 2
- 2025Federated Learning of Quantile Inference under Local Differential Privacycited by 2
- 2022One-bit Submission for Locally Private Quasi-MLE: Its Asymptotic Normality and Limitationcited by 1
- 2024Uncertainty quantification by block bootstrap for differentially private stochastic gradient descentcited by 1
- 2025Versatile Differentially Private Learning for General Loss Functionscited by 1
- 2025High-Dimensional Differentially Private Quantile Regression: Distributed Estimation and Statistical Inferencecited by 1
Built on by
Citing papers per year: 2026: 2.
2 papers.
- 2026TokenCast: Forecasting Token Consumption During LLM Agent Execution28 Sep 2026
- 2026A Shared Subcircuit Lets LLMs Count Down Across Tasks14 Jul 2026
Similar, not cited
Close in wording, no citation either way
- 2025How Do LLMs Use Their Depth?
- 2025Length Representations in Large Language Models
- 2025The Illusion of Diminishing Returns: Measuring Long Horizon Execution in LLMs
- 2025LIFEBench: Evaluating Length Instruction Following in Large Language Models
- 2024Keep Guessing? When Considering Inference Scaling, Mind the Baselines
- 2026Encoded but Not Decoded: Layer-Localized Evidence for a Three-Level Gap in LLM Syntax
- 2025Beyond Exponential Decay: Rethinking Error Accumulation in Large Language Models
- 2024The CAP Principle for LLM Serving: A Survey of Long-Context Large Language Model Serving