A Shared Subcircuit Lets LLMs Count Down Across Tasks

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).

Frontier LLMs can perform multi-step reasoning over content-free filler tokens like dots or counting sequences, producing correct answers with no visible chain-of-thought (CoT). This is a limit case for behavioral oversight, where surface tokens carry no information about the underlying reasoning. But hidden from the output is not the same as hidden from us. On four task families (fact retrieval, parallel numeric composition, string manipulation, and in-context computation), two open-weights frontier models (DeepSeek V3, Kimi K2) compute over filler tokens in a structured, legible way: attention routes the question through the filler region to the answer, logit-lens readouts show retrieved facts emerging early and their composition crystallizing in late layers, and KV-cache transplants at filler positions causally swap outputs between examples. We introduce an unsupervised decoding pipeline that takes only hidden states as input and recovers intermediate values with 80-95% accuracy (best LLM judge) across both models and all four tasks, without ground-truth labels or training. Hidden computation that defeats behavioral CoT monitoring is, on these tasks, directly readable from the residual stream, suggesting monitorability is a property of the model's full computational trace, not just its surface tokens.

Large language models fail at counting repeated tokens despite strong performance on broader reasoning benchmarks. These failures are commonly attributed to limitations in internal count tracking. We show this attribution is wrong. Linear probes on the residual stream decode the correct count with near-perfect accuracy at every post-embedding layer, across all model depths. This holds even at the exact layers where the wrong answer crystallizes while the model simultaneously outputs an incorrect count. Attention patterns show no evidence of collapse over repeated tokens and tokenization artifacts account for none of the failure. Instead, a format-triggered multi-layer perceptron (MLP) block overwrites the correctly-encoded count with a fixed wrong answer at roughly 88--93,% network depth. This prior fires for repeated word-tokens in space-separated list format and is absent for repeated digit-tokens. It is suppressed by comma-separated delimiters in larger models but persists in smaller ones. The finding holds across Llama-3.2 (1B and 3B) and Qwen2.5 (1.5B, 3B and 7B) at consistent relative depth. Counting failure is a failure of routing not of representation and the two require different interventions.