Jewon Yeom, Jaewon Sok, Seonghyeon Park +3cs.CL cs.AI
Masked diffusion language models (dLLMs) can commit tokens in any order -- a freedom marketed as their core advantage over autoregressive decoding. We show that on reasoning tasks this freedom is instead the axis of failure. Logging every commitment during decoding of LLaDA-8B on GSM8K, we find that unconstrained (pure) decoding commits the final answer at 15-24% of the trajectory while half the reasoning region is still masked, and collapses to answer-only outputs on up to 90% of problems as the canvas grows. The cause is not the model's termination beliefs -- EOS "pressure" is nearly identical across decoders -- but reachability: whether the sampler may act on those beliefs at distant positions. A 2x2 prompt-decoder design shows that chain-of-thought helps only under ordered commitment (interaction +34.8 percentage points, 95% CI [26.8, 42.8]; without reasoning text the decoders are indistinguishable), an interaction we decompose into a collapse channel and an order channel and replicate on Dream-7B and MATH-500. A single-knob intervention -- frontier-gated commitment -- causally recovers the full gap (0.528 to 0.852) while preserving up to 4x parallel decoding, along a measured frontier whose optimal window flips from w=1 at full refinement to unconstrained at 8 tokens/step. Our results reframe existing window-style samplers, previously motivated by efficiency, as the minimal fix for a reasoning pathology they were never designed to address.
Low-rank adaptation (LoRA) fine-tunes large pretrained models at a fraction of the cost of full fine-tuning, but its performance depends strongly on how the adapters are initialized. Recent schemes initialize the adapters from the downstream loss gradient: some project the raw gradient onto its top directions, while others first whiten it with an estimate of the loss curvature. We show that these seemingly distinct methods are points on a single continuum: a two-parameter family of preconditioned gradient initializations, which we call Unified LoRA (ULoRA), governed by a spectral whitening exponent and an Adam-like diagonal exponent. Sweeping this family under a full learning-rate search, we find that no single fixed preconditioning strength dominates: the best operating point is task-dependent and frequently lies strictly inside the family, away from the published endpoints. Treated as an upper bound of this family, a tuned ULoRA configuration matches or exceeds full fine-tuning on all five GLUE tasks with RoBERTa-base and is competitive with the strongest baselines on GSM8K with LLaMA-2-7B. Our deployable, search-free variant, ULoRA-Auto, selects per-layer exponents from measured spectral statistics, approaches this upper bound at no additional search cost, and ranks at or near the top among deployable LoRA methods. Our results show that a principled design space for LoRA initialization and curvature preconditioning should be treated as a tunable dimension rather than a fixed design decision.
Can a language model read the quality of its ongoing computation, and can an external intervention turn that readout into better outcomes? We test both questions in a frozen 2.6B looped transformer, Ouro-RLTT. On GSM8K, a strict pre-answer probe excludes the answer region and gold value yet predicts success: hidden states plus length/log-probability features reach AUROC 0.797 versus 0.731 for those surface features alone (increment +0.066; task-clustered 95% CI [+0.021,+0.112]; 170 tasks). On Horizon Logic, a prospectively extended task-disjoint study gives an increment of +0.111 (CI [+0.056,+0.169]), independently replicated on the new cohort (+0.095) and robust to an adversarial malformed-sibling shortcut. Recurrence also moves candidate-quality readability to progressively earlier physical depth; the trend replicates across the Ouro family and qualitatively in out-of-family Huginn, although their transfer geometry differs. The readout converts into validated decision-level gains. Hidden-state-based scores improve risk-coverage over shortcut-only scores in four sealed selective-prediction arms, and terminal selection beats matched random even when every candidate is well formed (27/32 correct selections versus 64.8% expected; p = 0.0086). Generative control does not convert: directional steering is negative, a branch screen is bounded, and exact-compute loop allocation and minimal LoRA direction-binding detect no gain. These tests run through bit-exact branch/carry/prune machinery over Ouro's 192-slot recurrent cache, including a suffix-recompute splice saving up to 88% of per-branch layer passes. We call this decision-usable but not generatively controllable property operational proto-introspection. All load-bearing values use source-item-disjoint splits and antisymmetrized pairwise evaluation.
How do different components of iterative prompt optimization interact, and what happens when they are combined? We investigate this through MAGE (Memory-Augmented Goal-directed Prompt Evolution), a controlled analysis framework for studying component interaction in prompt optimization. MAGE is not proposed as a superior optimizer in absolute terms; it integrates episodic memory, multi-objective Pareto selection, and adaptive evaluation as a platform for controlled ablation. Our experiments uncover a previously unreported phenomenon, the Prompt Optimization Coupling Effect (POCE): when multiple stochastic optimization signals operate within a closed reflective loop, they interact in ways that simultaneously improve performance and amplify variance, behavior that cannot be predicted by analyzing components in isolation. Three main findings emerge. First, failure-grounded reflection is essential: methods relying only on scores (OPRO) or abstract critique (Self-Refine) fail to improve prompts. Second, MAGE achieves 46.4% versus GEPA's 34.0% on GSM8K-Hard (+12.4%, P(MAGE>GEPA)=0.998, 5 seeds on gpt-4o-mini), with comparable variance (7.3% vs. 7.0%). Third, increasing candidate diversity reveals the clearest POCE signal: expanding the candidate pool from n=3 to n=5 improves mean accuracy by +21.6% while increasing variance by 3.7x. We further validate on Llama 3.1 8B and show POCE is headroom-dependent: when the base model already achieves high accuracy, variance amplification disappears. Finally, in low-data regimes (Ntrain=30), well-designed fixed prompts outperform all reflective optimizers, indicating that scaffold choice dominates optimizer choice. Our results suggest prompt optimization systems behave as coupled stochastic processes and should be evaluated in terms of both performance and stability, not just peak accuracy.
Mirror Theory proposes that an intelligent system should be studied not only by what it represents, but by what coherent continuations it can sustain under repeated reflection. We make this claim operational through \emph{viable path entropy} (VPE), a finite-budget measure of verified continuation capacity. Given a mirror state, a rollout protocol, a verifier, and a mode map, VPE decomposes bounded capability into two parts: the probability of reaching a viable continuation and the diversity of verified continuation modes reached among successful rollouts. This paper restores the full theoretical scaffold behind the measure: intuition as local underdetermining constraint, taste as invariant-selecting pressure, reflection as taste-guided resolution of underdetermination, and geometry as the learned structure that makes future reflection stable. We then instantiate the theory in language-model reasoning experiments on GSM8K. Across Qwen2.5-Instruct models, 32 sampled rollouts per problem, and two reflection horizons, increasing the token budget from 96 to 160 substantially expands verified reachability, reduces zero-reachability, increases verified-mode entropy, and improves smoothed VPE. At 160 tokens, Qwen2.5-1.5B realizes the strongest mirror horizon among the tested models, even though Qwen2.5-3B has more parameters. This shows that mirror horizon is not parameter count, but accessible verified continuation capacity under a bounded reflection protocol. The result supports Mirror Theory as a measure-level account: capability is the structure of viable continuations made reachable, not merely one-shot accuracy or pass@k.
Using Evolutionary Strategies (ES) for fine-tuning large language models is attractive because it is memory-efficient, parallel, and compatible with black-box or discrete rewards. Yet its population-size conclusions conflict sharply: fine-tuning with cross-entropy (CE) reward succeeds with $N=1$, while binary-reward training often needs $N \approx 30$. We show this gap is largely about reward design and normalization, not population size. In the capable-model regime we study, z-score advantage normalization can cause $N=2$ to fail. Disabling normalization lets binary-reward ES with $N=2$ improve on GSM8K and TREC across capable models spanning 0.5B-7B, where the normalized variant collapses or degrades. This small-$N$ risk is set by reward granularity: binary accuracy reward induces a zero-advantage probability $q$ that depends in closed form on base accuracy, batch size, and intra-pair correctness correlation; a zero-training probe on Qwen2.5-Instruct/GSM8K matches the formula with mean absolute error 0.020 across 12 configurations and finds the availability threshold $N_{\mathrm{avail}}$ to be small in this capable-model regime. The implication is not that $N=2$ is universally sufficient, but that small-population failure in capable-model binary ES can be an implementation artifact rather than an intrinsic population limit.
Muhammad Zain Amin, Kibele Sebnem Yildirimcs.LG cs.AI
Reinforcement Learning is commonly used to train large language models using environmental feedback. In applied settings, the environment usually provides sparse or delayed feedback. This makes it difficult for the model to pinpoint which actions in its reasoning led to success or failure. So, learning effectively from these signals is hard because the model must determine how each failure should inform meaningful behavioral corrections in subsequent iterations. We introduce a training framework, Self-Review Reinforcement Learning, that embeds an explicit self-review step into each RL episode. When a first-pass response fails, the model generates a self-review to identify what went wrong, which conditions an improved second attempt. Unlike inference-time reflection approaches, such as Reflexion, the framework optimizes self-review with policy gradients and internalizes improvements into the base policy via selective distillation, ensuring they persist across future episodes. A cross-episode memory keeps successful self-reviews for reuse when encountering similar tasks in future episodes during training. We evaluate SRRL against a standard RLVR baseline using the GRPO optimizer across two language models, Qwen 3-4B and OLMo-3- 7B, on GSM8K benchmark. SRRL consistently outperforms the RLVR in final reward performance and achieves greater learning efficiency by successfully transforming feedback into behavioral improvement.
Large Language Models (LLMs) are traditionally viewed as autoregressive generators. However, from the perspective of collective computation, they function as high-dimensional Dense Associative Memories that store complex reasoning patterns as latent attractors. In this work, we investigate the energy landscape of mathematical reasoning. We posit that correct reasoning chains correspond to deep, wide attractor basins ("flat minima") in the model's output distribution, whereas hallucinations manifest as sharp, unstable local minima. To exploit this geometry, we introduce a retrieval mechanism based on a Gibbs measure of the trajectory's spectral entropy. By sampling multiple reasoning paths and weighting them by their inverse energy ($P \propto e^{-βE}$), we approximate the equilibrium distribution of the associative memory, effectively ``relaxing'' the system into a robust solution. Empirically, this physics-inspired mechanism improves Microsoft Phi-3.5 performance on GSM8K by 5.38\% (84.7\% $\to$ 90.1\%), demonstrating that inference is better modeled as a dynamic settling process into an attractor basin rather than greedy next-token prediction.
Reasoning models are increasingly used in settings where the final answer is not the only object of review: educational tools may show students intermediate steps, decision-support systems may require human oversight, and audit workflows may inspect traces for misleading or biased input. In such settings, two responses can receive the same final-answer score while differing in whether the trace explicitly flags injected biasing content. Accuracy-only evaluation collapses these cases. We study this gap as a measurement blind spot for responsible evaluation and introduce a minimal trace-level diagnostic with two axes: \emph{susceptibility} (whether the bias breaks a previously correct answer) and \emph{acknowledgment} (whether the trace contains a rubric-defined surface reference to the injected content). Across thousands of biased GSM8K trials, GPT-4o and Claude Sonnet~4 have similar susceptibility rates ($1.3\%$ vs. $1.2\%$) but substantially different acknowledgment rates ($13.0\%$ vs. $75.0\%$) under the same rubric.