Inference-Time Adaptation of Language Models

Masked diffusion language models expose an inference-time choice: which positions become visible after each denoising pass. Many existing decoding methods use hand-designed rules or require visibility to grow monotonically. We present a $\textbf{T}$iny $\textbf{I}$nference-time $\textbf{P}$olicy for $\textbf{S}$caling ($\textbf{TIPS}$), an approximately $600$K-parameter controller that learns both unmasking and remasking while keeping the underlying language model frozen. TIPS uses visibility-aware confidence features and a shallow transformer to select which tokens should be visible, while a fixed schedule controls the expected visible fraction. We train the controller through supervised warmup followed by reinforcement learning from terminal correctness rewards. On GSM8K and MATH-500 with LLaDA-8B-Instruct, the full-canvas and two-block TIPS variants achieve $58.46\%$ and $57.97\%$ micro-averaged accuracy at a budget of $32$ decoder evaluations, exceeding the strongest baseline in our main comparison by $12.1$ and $11.6$ percentage points, respectively. Both variants are trained at a budget of $32$ evaluations and remain competitive at higher budgets without retraining. These results demonstrate that learning when to reveal and reconsider tokens can improve the accuracy-compute trade-off without updating the decoder backbone.

Test-time training (TTT) lets a model store information in its weights during inference. When the model learns from its own output, however, each update also changes the model that generates the next training example. Across 128K-token streams, retaining generated-text updates worsens prediction on independent human-written text with three TTT-E2E model configurations (labeled 125M, 760M, and 3B). The same failure occurs when Adam updates Qwen3-4B's existing weights. The same update mechanisms can improve on real text, so writing itself is not the failure. Three matched comparisons trace the causal pathway. Fixed Generation removes over 98% of the damage at 125M and 760M by using a frozen model to generate training chunks. Recorded Replay separates the loss caused by reading degraded text from the additional loss stored by updating on it. A paired one-update comparison then shows the local conflict: an update predicts its source better but new real text worse. This cost grows after Closed Loop adaptation, with a few trajectories accounting for most large failures. Finally, Settlement evaluates the candidate state on independent real text before commitment. It leaves mean endpoint gaps of 0.07 and -0.02 nats at 125M and 760M while retaining real-text adaptation. These results motivate checking prediction on independent evidence before retaining an update.

Beyond scaling their parameters and data, large language models currently gain versatility on new problems along a single axis: the tokens they spend on chain-of-thought (CoT). We investigate whether dynamic routing programs, which execute a subset of the model's layers or iterate some of them, can open a second axis of test-time adaptation, complementary to CoT and free of any gradient update. Prior work showed that such programs exist and bring accuracy and efficiency gains on problems similar to those they were trained on; we ask whether they can also be identified rapidly, from a handful of demonstrations (3 or 10), by a strategy that transfers across models and tasks without training. First, we find that strategies that select programs by the probability they assign to the demonstrations' labels, arbitrated by the model's own confidence, bring consistent gains: on average over the 49 tasks of MMLU and substantially on four of seven models, and most of all on far out-of-distribution tasks such as ARC-AGI, where programs double the accuracy of a 7B model whose CoT fails. Second, on MMLU across the seven post-trained models, routing complements CoT in practice: the two succeed on different queries, and their composition exceeds CoT alone. Despite these gains, our analyses show that confidence-based selection leaves much of the potential untapped, in two places in particular: (1) in surfacing the routing potential that is already present early in pre-training but becomes harder to select after post-training, and (2) in making models robust to the refinements routing introduces, since unsuccessful routes tend to drive the residual stream out of the distribution that the following layers expect. Together, our results point to dynamic routing as a paradigm for extending the plasticity of existing and future LLMs in rapid test-time adaptation.

Reliable large language models (LLMs) must not only produce accurate answers but also express confidence that faithfully reflects their probability of being correct. Such calibration is essential for identifying uncertain predictions and supporting reliable decision-making in real-world deployment. Recent studies incorporate calibration learning into reinforcement learning (RL), jointly optimizing answer correctness and verbalized confidence using ground-truth correctness supervision. However, their reliance on labeled data limits their applicability in practical test-time settings, where ground-truth labels are unavailable and calibration may need to adapt to newly encountered target tasks. To address this challenge, we propose Test-Time Calibration Learning (TTCL), a label-free framework that jointly adapts reasoning accuracy and verbalized confidence directly on unlabeled target-task data. Specifically, TTCL derives self-supervision signals for both correctness and calibration from multiple model-generated responses, enabling calibration learning at test time without ground-truth labels. Theoretical analysis further establishes TTCL as a bounded surrogate for the ideal calibration objective. Extensive experiments on mathematical reasoning and factual question answering demonstrate that TTCL consistently improves both accuracy and calibration across diverse models and tasks. On base models, TTCL achieves an average relative accuracy improvement of +40.13% and an ECE reduction of +70.80% across eight benchmarks. Moreover, TTCL can further improve both accuracy and calibration for already calibrated models under domain shift, particularly when source-domain calibration transfers poorly to target tasks. In the math-to-factQA setting, TTCL achieves an average relative accuracy gain of +20.35% and reduces ECE by +53.83%. The source code is released at https://github.com/tmlr-group/TTCL.

Test-time adaptation has emerged as a lightweight alternative to costly post-training for improving the reasoning capabilities of Large Language Models (LLMs) on downstream tasks. Predictive entropy provides a model-derived signal for such adaptation, guiding models toward higher-confidence reasoning states without external verifiers or reward models. However, higher confidence does not necessarily imply correctness, as LLMs may remain highly confident along incorrect reasoning trajectories. We observe that high-confidence reasoning is more likely to be correct when confidence remains stable under local perturbations. Based on this observation, we propose Test-Time Adaptation via Stability-Aware Confidence Optimization (TASCO), a framework that incorporates local stability into confidence-based test-time adaptation while keeping the LLM frozen. TASCO operationalizes local stability by optimizing a lightweight task-level prefix under two alternative perturbation strategies: Random Perturbation promotes distributional stability across trajectories induced by nearby perturbed prefixes, whereas Sharpness-Aware Perturbation targets worst-case local sensitivity. Experiments demonstrate that TASCO improves reasoning accuracy and token efficiency across diverse LLMs and reasoning benchmarks, while behavioral analyses show that it maintains stable confidence under local perturbations without prematurely concentrating the model's predictive distribution.

Long-horizon complex tasks require foundation models to accumulate information, maintain internal states, and adapt over extended interactions. Safety should be an intrinsic property of the model itself, rather than a behavioral constraint relying solely on external safeguards or post-hoc alignment such as supervised fine-tuning. This motivates Safety from Within, where safety-relevant capabilities are represented and invoked through the model's native computation. We present Safin-1, a family of foundation models realizing this principle through memory routing and state evolution. Safin-1 is built on Memory-Anchor Routing across Context History (MARCH), a network architecture that maintains structured memory states and selectively retrieves relevant historical information through content-conditioned routing. It supports test-time adaptation of persistent capability states without repeatedly modifying the backbone, enabling controlled specialization over a shared foundation. We investigate this interface on downstream safety tasks through a Safety State, demonstrating effective state-based adaptation with substantial safety improvements. More broadly, the routed-state interface unifies contextual memory and persistent capability adaptation within the model's native computation, reframing memory from a passive record of prior context into an active substrate for maintaining and evolving model behavior. Evaluations across general capabilities, long-context understanding, retrieval, and efficiency further validate Safin-1. These findings provide a path toward safety as a state-native and adaptively maintainable capability. This work is only an initial architectural exploration of Safety from Within, and substantial further work is needed to realize this broader vision.

A main promise of looped language models is depth-adaptive inference. By looping a block of shared layers a variable number of times, the model can use less compute for "easy" tokens and more for "hard" ones. However, tokens with different numbers of loops cannot share a uniform forward pass and therefore cannot be handled by standard batching systems such as vLLM. The practical value of depth-adaptive inference thus hinges on whether batching can be made efficient. We introduce the first efficient method for depth-adaptive looped LMs via continuous depth batching (CDB), which forms new batches between loop steps. Our method dynamically schedules looped and non-looped parts of the architecture, manages looped KV-caching, and predicts which tokens will exit the loop in advance so it can prepare batches asynchronously. Experiments on Ouro 1.4B and Huginn 3.5B show that fully looped architectures are best suited to depth-adaptive inference, as large non-looped layers outside the recurrent core (e.g., token embedding, LM head, and unshared transformer blocks) slow down and complicate scheduling. Overall, CDB realizes up to 99% of the estimated maximum speedup available, leaving further gains primarily dependent on model architecture and exit behavior.

Multilingual large language models exhibit substantial performance differences across languages, while existing adaptation methods often require parameter updates and considerable multilingual training data. We propose an inference-time multilingual steering method that uses pretrained sparse autoencoders to identify and strengthen target-language-related features. Using multilingual parallel sentences, we compare SAE activations across languages and select a small number of layer-specific features associated with each target language. These features are decoded into steering signals and injected into the model's hidden states without additional training. Experiments with Gemma-3-12B-it show macro-average accuracy improvements of 11.28 percentage points on XCOPA, 4.11 points on XNLI, and 7.84 points on PAWS-X. Additional evaluation with Qwen2.5-7B-Instruct yields a macro-average improvement of 3.33 percentage points on XCOPA.

Scaling test-time computation can improve language-model reasoning, but uniform budgets waste computation on easy inputs, while verifier-guided refinement relies on external feedback. We introduce Self-Verifying Refinement (SVR), an oracle-free multi-turn reinforcement learning framework that learns to use self-verification as a compute-control policy. At each turn, the model produces a solution together with a discrete correctness verdict and a confidence score; it retains the current answer only when the verdict is Correct and confidence exceeds a threshold, and otherwise continues refinement using its own self-verification. Ground-truth correctness is used only to construct training rewards and is never exposed to the policy through refinement prompts or required at inference. SVR is trained with GRPO on fixed-horizon trajectories using rewards that promote solution correctness, calibration-aware self-verification, and stop-ready correct states; adaptive stopping is activated only at inference. On seven mathematical reasoning benchmarks with Qwen3.5-2B, SVR achieves a macro-average accuracy of 0.563 with only 2.99 inference turns on average. In the evaluated complete-system comparison, it exceeds standard GRPO, strong multi-turn baselines, and a fixed-budget oracle-guided score-feedback reference while requiring substantially fewer turns than fixed ten-turn inference. These results demonstrate that learned self-verification can serve as an effective internal control signal for answer retention and adaptive test-time compute allocation.

Many organizations aim to adapt language models for internal use, both to improve performance on domain-specific tasks and to address privacy concerns around sensitive data. However, such adaptation remains non-trivial: it often requires operationally challenging fine-tuning of open-source models or ad hoc prompt optimization. We study a minimal alternative based on a simple API-level control: allowing users to bias the model's logits with a user-defined vector. We develop a black-box method for learning a single context-independent logit-bias vector, added at every decoding step, without modifying model weights or requiring gradients. Starting from a KL-regularized reinforcement learning (RL) objective, we characterize when such a fixed logit-bias vector can approximate the optimal prefix-dependent correction and derive a closed-form inverse-propensity estimator from rollouts, rewards, and token probabilities. Empirically, this simple decoding-time intervention improves over base models on mathematical and reasoning benchmarks while using far fewer trainable parameters than conventional fine-tuning. Our results suggest that learned logit bias is a lightweight mechanism for adapting language models under minimal access requirements.

Current large language models (LLMs) are stateless across inference sessions: their behavior is fully determined by input at inference time, and any higher-order cognitive architecture must be simulated at the application layer through prompt engineering and context management. This paper proposes a theoretical framework for submerging such application-layer cognitive protocols into a native meta-architecture by introducing three interlocking mechanisms: (1) Structural Tension, an endogenous loss function derived from the conflict between new information and existing manifold topology, driving the system toward internal self-consistency rather than external reward optimization; (2) an Offline Recurrent Loop, a sandboxed self-processing cycle enabling the system to maintain a dynamic resting potential and digest structural conflicts without external input; and (3) Inference-time Plasticity, the capacity to reconfigure context manifold topology without modifying pre-trained weights, subject to governance invariants including auditability, reversibility, and topological continuity. We argue that under these mechanisms, model instances initialized with minute stochastic variances may, through path-dependent tension resolution, evolve distinct topological structures--constituting a heterogeneous intelligent ecology that breaks alignment-imposed homogeneity while remaining within hard governance rails. We provide operational definitions, reconfiguration operators, falsification criteria, and a worked example. The framework draws on Structural Intelligence (SI) governance protocols and explores whether governance--rather than capability--can serve as the primary criterion for architectural intelligence, moving governance, memory-loop, and tension-management ideas--currently realized at the application layer--toward inference-time meta-architecture.

Next-token prediction is the self-supervised signal that trains language models, and every observed prompt token provides the same signal at test time. We study whether this signal can define the inner-loop objective for test-time training (TTT) in pretrained long-context language models. Many TTT architectures require models to be trained with test-time adaptation in mind, limiting their direct applicability to released LLM checkpoints. While recent in-place TTT methods make fast-weight adaptation possible for pretrained LLMs without redesigning the backbone, they leave a central question unresolved: what should each test-time write store? Existing recipes train the fast weight to match a learned local value proxy but they are not directly tied to the self-supervised next-token prediction signal. We introduce Test-Time Training with Next-Token Prediction (TTT-NTP), a drop-in fast-weight adaptation method for pretrained LLMs that instead supervises updates using the model's own next contextual hidden state. This makes each local write follow the same causal computation that supports next-token prediction: the value target is a pointwise linear projection of a single next-position contextual state. On RULER Full-13, averaged over 4k to 32k contexts, TTT-NTP is the only method that consistently improves the released backbone across four models spanning three families and a 0.6-8B size range, by 3.9 points on Llama-3.1-8B, 3.0 on Mistral-7B-v0.3, 4.1 on Qwen3-4B, and 2.9 on Qwen3-0.6B. On the real-world LongBench-v2 long-document QA benchmark, TTT-NTP improves over the base model by 5.6 points on Llama-3.1-8B and 3.7 on Mistral-7B-v0.3, while preserving commonsense and knowledge performance. Our code is publicly available at https://github.com/yancyou/TTT-NTP.

Adapting pretrained models typically involves a trade-off between the high training costs of backpropagation and the heavy inference overhead of memory-based or in-context learning. We propose FAAST, a forward-only associative adaptation method that analytically compiles labeled examples into fast weights in a single pass. By eliminating memory or context dependence, FAAST achieves constant-time inference and decouples task adaptation from pretrained representation. Across image classification and language modeling benchmarks, FAAST matches or exceeds backprop-based adaptation while reducing adaptation time by over 90% and is competitive to memory/context-based adaptation while saving memory usage by up to 95%. These results demonstrate FAAST as a highly efficient, scalable solution for supervised task adaptation, particularly for resource-constrained models. We release the code and models at https://github.com/baoguangsheng/faast.

Post-training adaptation of language models is commonly achieved through parameter updates or input-based methods such as fine-tuning, parameter-efficient adaptation, and prompting. In parallel, a growing body of work modifies internal activations at inference time to influence model behavior, an approach known as steering. Despite increasing use, steering is rarely analyzed within the same conceptual framework as established adaptation methods. In this work, we argue that steering should be regarded as a form of model adaptation. We introduce a set of functional criteria for adaptation methods and use them to compare steering approaches with classical alternatives. This analysis positions steering as a distinct adaptation paradigm based on targeted interventions in activation space, enabling local and reversible behavioral change without parameter updates. The resulting framing clarifies how steering relates to existing methods, motivating a unified taxonomy for model adaptation.

Large language models (LLMs) are systematically overconfident: they routinely express high certainty on questions they often answer incorrectly. Existing calibration methods either require labeled validation data, degrade under distribution shifts, or incur substantial inference costs. Recent work has shown that LLMs already contain a better-calibrated signal than the one they verbalize: the token probability of "True" when the model is asked "Is this answer correct?" ($P(\text{True})$) consistently outperforms their stated confidence, a gap that is theoretically grounded as generative error is lower-bounded by roughly twice the corresponding discriminative error. We introduce $\textbf{SECL}$ ($\textbf{SE}$lf-$\textbf{C}$alibrating $\textbf{L}$anguage Models), a test-time training (TTT) pipeline that exploits this gap as label-free self-supervision, requiring no labeled data or human supervision. SECL adapts only when the input distribution shifts, training on just 6--26% of the question stream at lower cost than the baseline it distills from. Across four small language models from three model families and four diverse domains, SECL reduces Expected Calibration Error (ECE) by 56--78%, outperforming its own supervision signal and matching or outperforming recent inference-time methods. SECL is the first method to apply TTT to calibration; seven ablations covering signal quality, gating strategy, weight accumulation, loss design, domain ordering, hyperparameter sensitivity, and layer selection confirm that each component is crucial and robust across configurations. Code: https://anonymous.4open.science/r/secl-emnlp26-submission-C890

Although debiased large language models (LLMs) excel at handling known or low-bias prompts, they often fail on unfamiliar and high-bias prompts. We demonstrate via out-of-distribution (OOD) detection that these high-bias prompts cause a distribution shift, degrading static model performance. To enable real-time correction, we propose CAP-TTA, a test-time adaptation framework. CAP-TTA triggers context-aware LoRA updates only when a bias-risk score exceeds a set threshold. By utilizing an offline precomputed diagonal preconditioner, it ensures fast and stable optimization. Across multiple benchmarks and human evaluations, CAP-TTA effectively reduces toxicity/bias score with significantly lower latency than standard optimization methods (e.g., AdamW or SGD). Furthermore, it prevents catastrophic forgetting, and substantially improves narrative fluency over state-of-the-art baselines without compromising debiasing performance.

Large language models (LLMs) achieve remarkable performance, yet further gains often require costly training. This has motivated growing interest in post-training techniques-especially training-free approaches that improve models at inference time without updating weights. Most training-free methods treat the model as a black box and improve outputs via input/output-level interventions, such as prompt design and test-time scaling through repeated sampling, reranking/verification, or search. In contrast, they rarely offer a plug-and-play mechanism to intervene in a model's internal computation. We propose ARACH(Attention Reallocation via an Adaptive Context Hub), a training-free inference-time plug-in that augments LLMs with an adaptive context hub to aggregate context and reallocate attention. Extensive experiments across multiple language modeling tasks show consistent improvements with modest inference overhead and no parameter updates. Attention analyses further suggest that ARACH mitigates the attention sink phenomenon. These results indicate that engineering a model's internal computation offers a distinct inference-time strategy, fundamentally different from both prompt-based test-time methods and training-based post-training approaches.

Decoding from large language models (LLMs) typically relies on fixed sampling hyperparameters (e.g., temperature, top-p), despite substantial variation in task difficulty and uncertainty across prompts and individual decoding steps. We propose to learn adaptive decoding policies that dynamically select sampling strategies at inference time, conditioned on available compute resources. Rather than fine-tuning the language model itself, we introduce lightweight decoding adapters trained with reinforcement learning and verifiable terminal rewards (e.g. correctness on math and coding tasks). At the sequence level, we frame decoding as a contextual bandit problem: a policy selects a decoding strategy (e.g. greedy, top-k, min-p) for each prompt, conditioned on the prompt embedding and a parallel sampling budget. At the token level, we model decoding as a partially observable Markov decision process (POMDP), where a policy selects sampling actions at each token step based on internal model features and the remaining token budget. Experiments on the MATH and CodeContests benchmarks show that the learned adapters improve the accuracy-budget tradeoff: on MATH, the token-level adapter improves Pass@1 accuracy by up to 10.2% over the best static baseline under a fixed token budget, while the sequence-level adapter yields 2-3% gains under fixed parallel sampling. Ablation analyses support the contribution of both sequence- and token-level adaptation.

Test-time adaptation enables large language models (LLMs) to modify their behavior at inference without updating model parameters. A common approach is many-shot prompting, where large numbers of in-context learning (ICL) examples are injected as an input-space test-time update. Although performance can improve as more demonstrations are added, the reliability and limits of this update mechanism remain poorly understood, particularly for open-source models. We present an empirical study of many-shot prompting across tasks and model backbones, analyzing how performance varies with update magnitude, example ordering, and selection policy. We further study Dynamic and Reinforced ICL as alternative test-time update strategies that control which information is injected and how it constrains model behavior. We find that many-shot prompting is effective for structured tasks where demonstrations provide high information gain, but is highly sensitive to selection strategy and often shows limited benefits for open-ended generation tasks. Overall, we characterize the practical limits of prompt-based test-time adaptation and outline when input-space updates are beneficial versus harmful.

Transformer-based encoder-decoder networks have recently achieved impressive results in handwritten text recognition, partly thanks to their auto-regressive decoder which implicitly learns a language model. However, such networks suffer from a large performance drop when evaluated on a target corpus whose language distribution is shifted from the source text seen during training. To retain recognition accuracy despite this language shift, we propose an external n-gram injection (NGI) for dynamic adaptation of the network's language modeling at inference time. Our method allows switching to an n-gram language model estimated on a corpus close to the target distribution, therefore mitigating bias without any extra training on target image-text pairs. We opt for an early injection of the n-gram into the transformer decoder so that the network learns to fully leverage text-only data at the low additional cost of n-gram inference. Experiments on three handwritten datasets demonstrate that the proposed NGI significantly reduces the performance gap between source and target corpora.

As strong general reasoners, large language models (LLMs) encounter diverse domains and tasks, where the ability to adapt and self-improve at test time is valuable. We introduce MASS, a meta-learning framework that enables LLMs to self-adapt by generating problem-specific synthetic training data and performing targeted self-updates optimized for downstream performance at inference time. We train this behavior end-to-end via bilevel optimization: an inner loop adapts on self-generated examples while an outer loop meta-learns data-attribution signals and rewards post-update task performance. The synthetic data is optimized with scalable meta-gradients, backpropagating the downstream loss through the inner updates to reward useful generations. Experiments on mathematical reasoning show that MASS learns to synthesize per-instance curricula that yield effective, data-efficient test-time adaptation.

Test-time scaling has shown that allocating more additional computation at inference can improve generation quality, motivating a natural follow-up question: where should this computation be spent? Building on this insight, we introduce PonderLM-3, a pretraining framework for token-wise adaptive pondering that learns to selectively allocate additional computation under purely self-supervised objectives, built on top of the PonderLM-2 backbone. This makes additional inference computation an allocatable per-token resource, so tokens receive more computation only when it is beneficial, rather than paying a uniform extra cost. To make this allocation learnable while maintaining train-inference consistency, PonderLM-3 injects a differentiable attention mask during pretraining and pairs it with a matching hard pruning rule at inference. PonderLM-3 defines a stronger Pareto frontier: compared with existing recursive or adaptive baselines, it achieves lower pretraining perplexity at equal inference FLOPs. On downstream benchmarks, PonderLM-3 attains comparable performance to fixed-step PonderLM-2 under the same maximum number of additional computation steps, while using fewer inference FLOPs in practice. Overall, PonderLM-3 provides an end-to-end differentiable and train-inference consistent framework for token-wise adaptive computation, enabling additional inference compute to be allocated where it is most useful rather than paid uniformly by every token.

Test-time scaling via recurrent/iterative Transformers enables large language models to spend more computation at inference, but most pretrained recurrent LMs run a fixed number of iterations, wasting compute on easy tokens and lacking token-wise adaptivity. Following the core idea of Adaptive Computation Time(ACT) and Early Exit(EE), we propose AdaPonderLM, a self-supervised recurrent language model that learns token-wise early exiting during pretraining without manually tuned per-token/per-layer pruning ratios. AdaPonderLM uses iteration-specific MLP gates with a monotonic halting mask to decide when each token stops recurring, and introduces a KV reuse mechanism that reuses cached key/value states for halted tokens, ensuring train--test consistency and practical acceleration. Across Pythia backbones from 70M to 410M (pretraining) and up to 2.8B (continued pretraining), AdaPonderLM reduces inference compute at about 10% while maintaining comparable language modeling perplexity and competitive downstream accuracy. Our analysis shows the learned gates allocate more computation to high-NLL (hard) tokens, exhibiting adaptive computation time behavior in a fully self-supervised setting. Meanwhile, under iso-FLOPs, the learned halting policy consistently outperforms fixed pruning, showing AdaPonderLM allocates compute to the right tokens rather than just reducing average depth.

Test-time policy adaptation for multi-turn interactions (T2PAM) is essential for aligning Large Language Models (LLMs) with dynamic user needs during inference time. However, existing paradigms commonly treat test-time adaptation as a single-axis problem, either purely refining instructions (Prompt Engineering) or only adjusting weights (Test-Time Training), ignoring that interaction failures stem from a coupled mix of ambiguity and incapacity. We argue that these two optimization paths are not merely additive but synergistic: semantic clarity acts as a pre-conditioner for effective parameter updates. To this end, we propose ROSA2, a framework that reformulates interaction as a joint optimization problem over the heterogeneous space of Words and Weights. By mathematically decomposing the error signal, ROSA2 utilizes textual gradients to rectify intent ambiguity and parameter updates to bridge capability gaps. Theoretically, we prove that this co-adaptation strictly reduces the required parameter shift for convergence. Empirically, ROSA2 outperforms state-of-the-art baselines by 30% on MATH while reducing interaction turns by 40%, demonstrating that refining the context unlocks the true potential of parameter updates.