Recovering Input Text from Hidden States: Study of Gradient-Based Inversion of Decoder-Only Language Models

• URL: http://arxiv.org/abs/2607.00852v1
• Date: Wed, 01 Jul 2026 12:18:12 GMT
• Title: Recovering Input Text from Hidden States: Study of Gradient-Based Inversion of Decoder-Only Language Models
• Abstract summary: We study the hidden-state inversion problem as a continuous embedding-space optimisation.<n>We analyse which tokens break the reconstructions and find a sharp categorical asymmetry.<n>Last-layer hidden states of GPT-2 are as sensitive as original text.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: This work studies the hidden-state inversion problem: recovering the original input token sequence of a decoder-only language model from its last-layer hidden states. Rather than treating inversion as a one-shot reconstruction, we study it as a continuous embedding-space optimisation in which a soft proxy is driven towards the leaked target without any hard-token projection during the search, and a token is committed only once, at the end of the inner loop. This design choice has two consequences which are the main focus of this paper. First, keeping the optimisation entirely in continuous space exposes a rich set of internal signals: rank trajectories of the ground-truth token, per-position loss curves, and a discrete loss measured at commit time. Second, the discrete loss allows assessing the correctness of recovery via cumulative discrete loss. We further analyse which tokens break the reconstructions and find a sharp categorical asymmetry: space-prefixed, high-frequency function words in dense regions of the embedding matrix dominate the failures, while content-bearing tokens are recovered almost perfectly. On 10-token C4 prompts the exact-match rate rises from 66.9% to 97.5% (mean similarity 0.994) as the candidate window is widened, confirming that most errors are recoverable near-misses rather than genuine ambiguities. A comparison with the released SIPIT reference situates these findings: per-step hard projection is faster, but the continuous formulation is what makes the optimisation observable and its failures detectable. The results show that last-layer hidden states of GPT-2 are as sensitive as the original text.

Related papers

• GradCuit: Credit-Assigned Gradient Flow Enables Robust and Interpretable Test-Time Latent Reasoning [61.67411833252235]
  We introduce GradCuit, which inserts optimizable latent states at a selected Transformer layer between the hidden representations of the prompt and the generated continuation.<n>Across five instruction-tuned backbones, three reasoning benchmarks, and two answer formats, GradCuit achieves an average accuracy of 64.5%.<n>For interpretability, token-level gradient attribution reveals that latent influence concentrates on reasoning-connector tokens, while layer analysis identifies early-to-middle Transformer layers as the most effective optimization space.
  arXiv  Detail & Related papers  (2026-08-03T17:55:24Z)
• Escaping Confidence Trap: Evolutionary Decoding for Mathematical Reasoning in Diffusion LLMs [69.52853771994451]
  We analyze the decoding trajectories of LLaDA 2.0 and identify a recurring diffusion confidence trap.<n>We propose Evolutionary Decoding, a training-free test-time scaling framework that views diffusion decoding as an evolutionary process.
  arXiv  Detail & Related papers  (2026-08-01T11:48:25Z)
• Progressive Cramming: Reliable Token Compression and What It Reveals [5.7789316833104225]
  Token cramming compresses sequences into learned embeddings with near-perfect reconstruction.<n>We introduce progressive cramming, which grows the target prefix token-by-token, stopping only when reconstruction is no longer achievable.
  arXiv  Detail & Related papers  (2026-07-23T11:46:36Z)
• Deeper is Not Always Better: Mitigating the Alignment Tax via Confident Layer Decoding [92.1521161575198]
  We introduce Confident Decoding, a training-free decoding strategy that dynamically selects the most reliable near-final layer.<n> Experiments across dense and Mixture-of-Experts LLMs demonstrate consistent gains on challenging reasoning benchmarks.
  arXiv  Detail & Related papers  (2026-06-20T07:03:26Z)
• When Probing Accuracy Saturates, Fragility Resolves: A Complementary Metric for LLM Pre-Training Analysis [1.0829694003408499]
  Linear probing declares a property "encoded" when a classifier on hidden states achieves high accuracy.<n>Standard linear probing saturates within the first few thousand steps, leaving most of training invisible to the instrument.<n>We introduce fragility, a complementary per-layer metric defined as the activation-noise level at which probe accuracy collapses.
  arXiv  Detail & Related papers  (2026-06-09T19:00:23Z)
• Continuous Language Diffusion as a Decoder-Interface Problem [9.603960937964183]
  Continuous diffusion language models can generate fluent text from Gaussian-corrupted sentence embeddings.<n>We study this puzzle through Embedded Language Flows (ELF) and identify a decoder-basin mechanism.<n>We introduce a diagnostic protocol for denoisability, semantic recoverability, order sensitivity, decoder compatibility, and trajectory reliability.
  arXiv  Detail & Related papers  (2026-06-07T20:00:33Z)
• Measuring Temporal Linguistic Emergence in Diffusion Language Models [0.0]
  Diffusion language models expose an explicit denoising trajectory.<n>We study three independent 32-step runs of LLaDA-8B-Base on WikiText-103 text.
  arXiv  Detail & Related papers  (2026-04-25T10:17:47Z)
• CORE: Context-Robust Remasking for Diffusion Language Models [51.59514489363897]
  We propose Context-Robust Remasking (CORE), a training-free framework for inference-time revision.<n>Rather than trusting static token probabilities, CORE identifies context-brittle tokens by probing their sensitivity to targeted masked-context perturbations.<n>On LLaDA-8B-Base, CORE delivers consistent improvements across reasoning and code benchmarks, outperforming compute-matched baselines and improving MBPP by up to 9.2 percentage points.
  arXiv  Detail & Related papers  (2026-02-04T00:12:30Z)
• CLUE: Non-parametric Verification from Experience via Hidden-State Clustering [64.50919789875233]
  We show that correctness of a solution is encoded as a geometrically separable signature within the trajectory of hidden activations.<n>ClUE consistently outperforms LLM-as-a-judge baselines and matches or exceeds modern confidence-based methods in reranking candidates.
  arXiv  Detail & Related papers  (2025-10-02T02:14:33Z)
• The Remarkable Robustness of LLMs: Stages of Inference? [5.346230590800585]
  We investigate the robustness of Large Language Models (LLMs) to structural interventions by deleting and swapping adjacent layers during inference.<n>Surprisingly, models retain 72-95% of their original top-1 prediction accuracy without any fine-tuning.
  arXiv  Detail & Related papers  (2024-06-27T17:57:03Z)
• Robust Depth Completion with Uncertainty-Driven Loss Functions [60.9237639890582]
  We introduce uncertainty-driven loss functions to improve the robustness of depth completion and handle the uncertainty in depth completion. Our method has been tested on KITTI Depth Completion Benchmark and achieved the state-of-the-art robustness performance in terms of MAE, IMAE, and IRMSE metrics.
  arXiv  Detail & Related papers  (2021-12-15T05:22:34Z)
• Pseudo-Convolutional Policy Gradient for Sequence-to-Sequence Lip-Reading [96.48553941812366]
  Lip-reading aims to infer the speech content from the lip movement sequence. Traditional learning process of seq2seq models suffers from two problems. We propose a novel pseudo-convolutional policy gradient (PCPG) based method to address these two problems.
  arXiv  Detail & Related papers  (2020-03-09T09:12:26Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.