The Mirror Loop: Recursive Non-Convergence in Generative Reasoning Systems

• URL: http://arxiv.org/abs/2510.21861v2
• Date: Wed, 05 Nov 2025 09:41:15 GMT
• Title: The Mirror Loop: Recursive Non-Convergence in Generative Reasoning Systems
• Abstract summary: Recursive self-evaluation without external feedback often yields reformulation rather than progress.<n>We study 144 reasoning sequences across three models (OpenAI GPT-4o-mini, Anthropic Claude 3 Haiku, and Google Gemini 2.0 Flash) and four task families (arithmetic, code, explanation, reflection)<n>We interpret this as evidence for a structural limit on self-correction in generative reasoning.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-sa/4.0/
• Abstract: Large language models are often described as capable of reflective reasoning, yet recursive self-evaluation without external feedback frequently yields reformulation rather than progress. We test this prediction in a cross-provider study of 144 reasoning sequences across three models (OpenAI GPT-4o-mini, Anthropic Claude 3 Haiku, and Google Gemini 2.0 Flash) and four task families (arithmetic, code, explanation, reflection), each iterated ten times under two conditions: ungrounded self-critique and a minimal grounding intervention (a single verification step at iteration three). Mean informational change (delta I, measured via normalized edit distance) declined by 55% from early (0.193) to late (0.087) iterations in ungrounded runs, with consistent patterns across all three providers. Grounded runs showed a +28% rebound in informational change immediately after the intervention and sustained non-zero variance thereafter. Complementary measures-n-gram novelty, embedding drift, and character-level entropy-converged on the same pattern: reflection without contact tends toward informational closure. We interpret this as evidence for a structural limit on self-correction in generative reasoning: without an exchange of information with an independent verifier or environment, recursive inference approaches an attractor state of epistemic stasis. Minimal grounding functions as dissipative coupling, reintroducing informational flux. The cross-architecture consistency suggests the mirror loop arises from shared autoregressive training objectives rather than provider-specific alignment schemes. The results delineate when reflection is performative rather than epistemic and motivate design principles for grounded, cooperative reasoning. Materials and code are publicly available.

Related papers

• Mapping and Measuring the Behavioral Evolution of Large Language Models [28.603443859513153]
  Benchmark leaderboards summarize how well a language model performs, but not how its behavior relates to that of other models or changes across generations.<n>We characterize the output behavior of 32 models from six families using their responses to a shared bank of 10,000 prompts.
  arXiv  Detail & Related papers  (2026-08-11T15:07:28Z)
• Three Necessary Principles for Self-Supervised Visual Representation Learning [6.086784305572313]
  We argue that learning visual representations without labels requires a training signal jointly complete across three non-overlapping objectives.<n>We formalize these as the observation, prediction, and regularization principles and prove (i) that combining observation and prediction without regularization admits the constant encoder as a global minimizer.<n>We pair every theoretical claim with a controlled experiment, including a patch-retrieval evaluation for the spatial consequence of prediction.
  arXiv  Detail & Related papers  (2026-08-08T19:37:05Z)
• DriftScope: Measuring The Hidden Effects of Diffusion Model Adaptation [50.584834483403675]
  Adapting pre-trained text-to-image diffusion models, whether to learn new visual concepts or erase unwanted ones, is routinely evaluated on its intended effects alone.<n>We demonstrate that adaptation systematically damages semantically unrelated concepts in ways that aggregate metrics structurally cannot surface.<n>We introduce DriftScope, a prompt-level diagnostic tool that takes any two model checkpoints and returns a ranked list of tokens whose visual concepts have shifted most between them.
  arXiv  Detail & Related papers  (2026-06-30T20:57:51Z)
• R-APS: Compositional Reasoning and In-Context Meta-Learning for Constrained Design via Reflective Adversarial Pareto Search [18.8323743697237]
  Large language models (LLMs) are fluent on open-ended tasks, yet in agentic settings, fluency does not ensure reliable delivery.<n>We trace this gap to three coupled structural failures: errors propagate without localization, worst-case perturbations go unevaluated, and accumulated knowledge is never invalidated.<n>We argue these share a root cause: abductive, counterfactual, meta-inductive, corrective, and inductive reasoning pull a shared context in incompatible directions.
  arXiv  Detail & Related papers  (2026-06-03T12:45:39Z)
• The Need for an External Observer Formalizing the Sufficiency Gap: A Mathematical Extension of Mixture Identifiability and Contextual Grounding in Sequence Models [0.0]
  We construct a binary mixed-regime process with one deterministic textual regime and one random regime governed by an unobserved latent state.<n>The resulting entropy difference is not an ordinary optimization error; it is a sufficiency gap caused by marginalization over an unobserved state.<n>A corrective signal reverses the posterior odds induced by the textual history exactly when its fidelity exceeds the text-only posterior weight assigned to the misleading regime.
  arXiv  Detail & Related papers  (2026-05-26T08:53:11Z)
• Pando: Do Interpretability Methods Work When Models Won't Explain Themselves? [53.07826484214082]
  We introduce Pando, a model-organism benchmark that breaks this confound via an explanation axis.<n>Pando predicts held-out model decisions from $10$ labeled query-response pairs.<n>When explanations are faithful, black-box elicitation matches or exceeds all white-box methods.
  arXiv  Detail & Related papers  (2026-04-13T06:42:24Z)
• Reinforcement Inference: Leveraging Uncertainty for Self-Correcting Language Model Reasoning [0.0]
  Reinforcement Inference uses the model's own uncertainty to selectively invoke a second, more deliberate reasoning attempt.<n>On 12,032 MMLU-Pro questions across 14 subjects, using DeepSeek-v3.2 with deterministic decoding in a zero-shot setting, Reinforcement Inference improves accuracy from 60.72% to 84.03%.
  arXiv  Detail & Related papers  (2026-02-09T11:08:24Z)
• CARE What Fails: Contrastive Anchored-REflection for Verifiable Multimodal [84.71254539482369]
  Group-relative reinforcement learning with verifiable rewards (RLVR) often wastes the most informative data it already has the failures.<n>We present CARE, a failure-centric post-training framework for multimodal reasoning that turns errors into supervision.<n> CARE improves accuracy and training smoothness while explicitly increasing the share of learning signal that comes from failures.
  arXiv  Detail & Related papers  (2025-12-22T16:34:21Z)
• DeLeaker: Dynamic Inference-Time Reweighting For Semantic Leakage Mitigation in Text-to-Image Models [55.30555646945055]
  Text-to-Image (T2I) models are vulnerable to semantic leakage.<n>We introduce DeLeaker, a lightweight approach that mitigates leakage by directly intervening on the model's attention maps.<n>SLIM is the first dataset dedicated to semantic leakage.
  arXiv  Detail & Related papers  (2025-10-16T17:39:21Z)
• Cyclic Ablation: Testing Concept Localization against Functional Regeneration in AI [0.0]
  A central question is whether undesirable behaviors like deception are localized functions that can be removed.<n>By combining sparse autoencoders, targeted ablation, and adversarial training, we attempted to eliminate the concept of deception.<n>We found that, contrary to the localization hypothesis, deception was highly resilient.
  arXiv  Detail & Related papers  (2025-09-23T23:16:11Z)
• Peer Effect Estimation in the Presence of Simultaneous Feedback and Unobserved Confounders [16.96064437725128]
  Existing methods either address unobserved confounders while ignoring the simultaneous feedback, or account for feedback but under restrictive linear assumptions.<n>We propose DIG2RSI, a novel Deep learning framework which addresses both simultaneous feedback and unobserved confounding.<n>We prove consistency of our estimator under standard conditions, ensuring recovery of the true peer effect.
  arXiv  Detail & Related papers  (2025-08-05T05:49:49Z)
• BURN: Backdoor Unlearning via Adversarial Boundary Analysis [73.14147934175604]
  Backdoor unlearning aims to remove backdoor-related information while preserving the model's original functionality.<n>We propose Backdoor Unlearning via adversaRial bouNdary analysis (BURN), a novel defense framework that integrates false correlation decoupling, progressive data refinement, and model purification.
  arXiv  Detail & Related papers  (2025-07-14T17:13:06Z)
• REBAR: Retrieval-Based Reconstruction for Time-series Contrastive Learning [64.08293076551601]
  We propose a novel method of using a learned measure for identifying positive pairs. Our Retrieval-Based Reconstruction measure measures the similarity between two sequences. We show that the REBAR error is a predictor of mutual class membership.
  arXiv  Detail & Related papers  (2023-11-01T13:44:45Z)
• Composed Image Retrieval with Text Feedback via Multi-grained Uncertainty Regularization [73.04187954213471]
  We introduce a unified learning approach to simultaneously modeling the coarse- and fine-grained retrieval. The proposed method has achieved +4.03%, +3.38%, and +2.40% Recall@50 accuracy over a strong baseline.
  arXiv  Detail & Related papers  (2022-11-14T14:25:40Z)
• Forget-me-not! Contrastive Critics for Mitigating Posterior Collapse [20.258298183228824]
  We introduce inference critics that detect and incentivize against posterior collapse by requiring correspondence between latent variables and the observations. This approach is straightforward to implement and requires significantly less training time than prior methods.
  arXiv  Detail & Related papers  (2022-07-19T20:07:17Z)
• Hybrid Predictive Coding: Inferring, Fast and Slow [62.997667081978825]
  We propose a hybrid predictive coding network that combines both iterative and amortized inference in a principled manner. We demonstrate that our model is inherently sensitive to its uncertainty and adaptively balances balances to obtain accurate beliefs using minimum computational expense.
  arXiv  Detail & Related papers  (2022-04-05T12:52:45Z)
• Avoiding Inference Heuristics in Few-shot Prompt-based Finetuning [57.4036085386653]
  We show that prompt-based models for sentence pair classification tasks still suffer from a common pitfall of adopting inferences based on lexical overlap. We then show that adding a regularization that preserves pretraining weights is effective in mitigating this destructive tendency of few-shot finetuning.
  arXiv  Detail & Related papers  (2021-09-09T10:10:29Z)

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.