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Language Is an Insufficient Substrate for Quantitative Reasoning, and Consequential Domains Need Large Quantitative Models

arXiv:2609.12105v1 Announce Type: new Abstract: The prevailing assumption in applied machine learning is that progress on consequential quantitative decisions such as pricing risk, allocating capital, triaging patients, or containing a network intrusion will follow from progress in large language models (LLMs). A language model is trained on a representation of the world that was produced by human description; description is a lossy encoding of the quantitative record, and the loss is irreversible: no downstream model, at any scale, can recover from a description what the description did not encode. We formalize this as a property of the representation on which a model is trained rather than of the model capacity, and we identify three further properties that consequential settings demand of a model and that a language substrate cannot supply by construction: reproducibility, lineage from every output back to the source records that produced. it, and calibrated uncertainty. We argue that these properties define a distinct model class, which we call the Large Quantitative Model (LQM).

Robust Prototypical Networks for Few-Shot Sensor Fault Diagnosis

arXiv:2609.12287v1 Announce Type: new Abstract: Industrial fault diagnosis often operates with only a handful of labeled fault examples, making few-shot learning attractive for sensor monitoring. Standard prototypical networks are simple and effective; however, their class prototypes may become unstable in the very-low-shot regime because each decision relies on a small support set. We propose \emph{Multi-Episode Prototypical Networks} (MEPN), which aggregate prototypes from multiple disjoint support episodes and use their mean as the final class representative, reducing prototype variance without changing the encoder architecture. We evaluate MEPN on the DeFACTO sensor dataset using five-way fault classification with synthetic bias, drift, spike, and noise faults injected into real industrial measurements. Over 100 independent runs, MEPN reaches \textbf{\SensorOneShotGcpn\%} in the per-episode one-shot setting ($K\!=\!1$ shot, aggregated over $N_{\text{agg}}\!=\!10$ support episodes), substantially above single-episode baselines. Under an equal 10-sample support budget, MEPN and ProtoNet at $K\!=\!10$ are statistically indistinguishable, confirming prototype accumulation as the mechanism rather than superior fixed-budget learning.

AIM: A Privacy-Aware Interoperable Memory Framework for Multi-Agent Multi-User LLM Systems

arXiv:2609.12320v1 Announce Type: new Abstract: Traditional large language models (LLMs) are scoped to individual user sessions, limiting their knowledge to a single conversation and preventing them from learning user preferences that evolve over time. Existing agentic memory systems address this limitation but generally operate at the individual-user level, restricting the public knowledge that could be shared across users to improve downstream responses. We introduce AIM (Agentic Interoperable Memory), a unified, privacy-aware memory framework that enables multi-agent, multi-user LLM systems to persistently manage private and shared memory. AIM dynamically classifies information as private, scoped to one user and inaccessible to others, or public, accessible to all users. It enforces index-level access controls so that private memories are retrievable only by their owner, protecting sensitive data while allowing beneficial shared knowledge to improve coordination and consistency. We also introduce MUMBench (Multi-User Memory Benchmark), a dataset of multi-user interactions containing private and shareable information across four domains. To our knowledge, MUMBench is the first public dataset designed to evaluate multiple memory operations, including retrieval, creation, update, and deletion, in a multi-user environment. Across three independent runs on MUMBench, AIM achieves 96.0% visibility classification accuracy, 58.8% strict operation accuracy, and 70.5% state-aware operation accuracy.

Affective Agent: On-Device Personalized Intervention Reasoning for Wearable Systems

arXiv:2609.12322v1 Announce Type: new Abstract: Affective computing has advanced wearable state inference, but on-device reasoning about whether, when, and how to intervene remains challenging. We present Affective Agent, a three-layer reference architecture for personalized intervention reasoning under uncertainty on wearable-class hardware. It combines a compact sub-billion-parameter language model with physiological evidence, context, and user history to decide whether, when, and how to intervene, without cloud dependency or per-user retraining. The architecture is organized into three interacting layers (perception, personalization, and reasoning), adapting to individual users through host-managed structured memory evolution rather than per-user weight updates. We instantiate Affective Agent in indoor environmental quality control and evaluate it on held-out, simulator-generated longitudinal scenarios spanning physiological variation, context, signal quality, and intervention history. Results show that memory-driven personalization and two-pass structured reasoning improve intervention decisions within this synthetic evaluation. By moving the decision layer on-device, this work demonstrates a path from wearable state inference toward closed-loop, personalized intervention on wearable-class hardware.
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  • LoRA-RC: Reservoir Computing with Low-Rank Adaptation Wenbin Wan
    arXiv:2609.12327v1 Announce Type: new Abstract: Reservoir computing (RC) trains only a linear readout over a fixed recurrent layer, making it fast and data-efficient for online prediction. However, a static reservoir degrades under system drift, readout-only adaptation is then insufficient, and unconstrained reservoir adaptation can destroy the echo-state and incremental stability properties that make RC reliable. This paper proposes LoRA-RC, which adapts the recurrent matrix through a low-rank
     

LoRA-RC: Reservoir Computing with Low-Rank Adaptation

14 September 2026 at 12:00
arXiv:2609.12327v1 Announce Type: new Abstract: Reservoir computing (RC) trains only a linear readout over a fixed recurrent layer, making it fast and data-efficient for online prediction. However, a static reservoir degrades under system drift, readout-only adaptation is then insufficient, and unconstrained reservoir adaptation can destroy the echo-state and incremental stability properties that make RC reliable. This paper proposes LoRA-RC, which adapts the recurrent matrix through a low-rank correction driven by streaming prediction errors. The base reservoir and adaptation bases are fixed offline; a small core matrix is adapted online, projected onto a spectral-norm ball, and low-pass filtered at each step. The projection guarantees that every applied recurrent matrix remains within a certified contraction set, and an incremental input-to-state stability bound is established for the reservoir along each online adaptation path, with path-independent rate and gain. On a Lorenz system with an abrupt parameter drift, LoRA-RC cuts post-drift prediction error by 56% versus a fixed RC and 51% versus readout-only adaptation; ablations over 20 seeds show that removing the projection inflates this error by more than a factor of 40.

What Drives Recovery in Agentic Text-to-Cypher? LAST-CQ: An LLM Agent Self-Refinement Framework

arXiv:2609.12746v1 Announce Type: new Abstract: Agentic pipelines for structured-query generation are rapidly expanding, but it is unclear which part of the loop produces the gain. We use LAST-CQ -- a five-agent, training-free, execution-grounded Text-to-Cypher framework -- as an instrumented testbed, running three counterfactuals over 2,471 live-database queries and six backbones spanning three vendor scale tiers. Removing correction is worth between 3.1% aggregate execution-BLEU against the single-pass system and 12.3% against a no-refinement counterfactual (up to 80.7% for the weakest backbone). Replacing schema-grounded, LLM-synthesised feedback with raw database error strings costs almost nothing (20.9% vs. 19.9% naive exact match;

Diffusion Models and Concept Formation

arXiv:2609.13047v1 Announce Type: new Abstract: Humans organize knowledge into a taxonomy of concepts with nested levels of abstraction and a \emph{basic level} at which people recognize and name objects with the least cognitive effort. Cobweb is a classic cognitive account of this ability, an incremental learner that builds a probabilistic concept hierarchy by maximizing category utility. We argue that diffusion models, although designed for image synthesis, implicitly perform the same computation. The noisy marginals of a diffusion model are Gaussian smoothings of the data distribution, and the modes of these marginals form a hierarchy that corresponds to a Cobweb tree of probabilistic prototypes in four respects. Both are hierarchical density models, both are hierarchical-Bayesian models with Gaussian prototypes, both treat categorization as score-following that reduces uncertainty, and in both a basic level emerges. We locate this basic level for a diffusion model at an intermediate noise level, where recent analyses show that the reverse process commits to the class identity of a sample. The two models differ mainly in how they represent and learn the taxonomy. Cobweb learns a discrete tree incrementally, whereas a diffusion model encodes a continuous, interpolable hierarchy in a single learned score field fit to the data distribution. We test the correspondence on MNIST and Fashion-MNIST by recovering the diffusion hierarchy through mode-finding and comparing the basic levels of the two models. This reframes diffusion as a cognitive model of concept formation and offers Cobweb a continuous, scalable instantiation.

Autonomous Research for Open-Ended Problems: A Case Study on Telecom Ticket Retrieval

arXiv:2609.13073v1 Announce Type: new Abstract: Recent breakthroughs in LLM-based systems and their abilities in problem solving and coding have allowed progress in the AI for Science paradigm, potentially replacing human roles in machine learning (ML) research. However, while several frameworks of fully autonomous end-to-end ML research have been proposed, successful implementations of them are often limited to problems with narrow search spaces, like language modeling or biomedical ML benchmarks. In this paper, we explore how autonomous research can be adapted to solve open-ended, industry-grade ML problems, by considering a case study: telecom ticket retrieval, an open-ended task with degrees of freedom in representation, architecture, and training data generation. We discover that autonomous research for open-ended problems with commercial and open-source agents shows both promise and limitations: while autonomous research can excel in narrow hyperparameter optimization, it lacks human-like intuition and creativity and requires operational overhead. Even with minimal human supervision, autonomous research can reach $90\%$ of state-of-the-art performance (0.34 vs. 0.38 Recall@1) in a much shorter time period (10 weeks vs. 10 months of human work) at a modest cost (up to \$200 per Cursor campaign). Our empirical evidence recommends that human researchers and autonomous research frameworks work together for best results in ML research.

Can We Trust LLM Judges: A Study of Capability-Dependent Biases and Multi-Judge Ensemble for Bias Calibration

arXiv:2609.12002v1 Announce Type: cross Abstract: LLMs are increasingly used as automated judges for model training and evaluation, yet individual judges exhibit systematic biases that undermine reliability. Much of prior work has studied biases in pairwise LLM-as-a-judge settings; in this paper, we focus on absolute scoring tasks, which mirror more realistic use cases. Across four benchmarks and six models (36 judge-examinee pairs), we show that a model's task accuracy strongly predicts its judging accuracy (Pearson $r \geq 0.90$ on most models) and inversely predicts its directional bias ($r \leq -0.83$), but that accuracy alone does not ensure fair evaluation: more capable examinee models consistently receive more lenient judgments from all judges ($r \geq 0.83$). To address this, we propose calibrated weighted majority voting (WMV), an ensemble evaluation method that aggregates multiple LLM judges weighted by online estimates of their false-positive and false-negative rates. We introduce a disagreement-based estimator that derives these error rates purely from inter-judge agreement patterns, requiring no ground-truth labels or task metadata. In a simulated experiment with shifting task distributions, our label-free WMV tracks an oracle with perfect error-rate knowledge to within 0.5 percentage points on average, outperforming both individual judges and unweighted majority voting. These results demonstrate that principled multi-judge calibration can simultaneously improve accuracy and correct for systematic leniency without requiring labeled data, offering a scalable path to reliable automated evaluation as model capabilities increase.
  • ✇cs.AI, q-bio.NC updates on arXiv.org
  • Hierarchical Prototype Emergence in Modern Hopfield Models Aditya Cowsik · Adithya Sriram
    arXiv:2609.12079v1 Announce Type: cross Abstract: Hierarchical correlations are a universal feature of any realistic model of data, and the question of how associative memory models may learn these correlations and generalize beyond them to construct new sensible images is an important step towards understanding more complex modern architectures such as diffusion models. We consider a hierarchical model for memories which are sampled and stored in a dense Hopfield network with polynomial activa
     

Hierarchical Prototype Emergence in Modern Hopfield Models

arXiv:2609.12079v1 Announce Type: cross Abstract: Hierarchical correlations are a universal feature of any realistic model of data, and the question of how associative memory models may learn these correlations and generalize beyond them to construct new sensible images is an important step towards understanding more complex modern architectures such as diffusion models. We consider a hierarchical model for memories which are sampled and stored in a dense Hopfield network with polynomial activation. We analytically derive conditions for each level of this hierarchy to be locally stable - that is they are local energy minima. We use prototype reconstruction as a minimal model of generalization and we find that it takes only a quasi-polynomial amount of information to generalize beyond particular memories and even particular groups in the hierarchy. We observe a qualitatively analogous phase diagram in the number of memories, sharpness of the activation function (polynomial degree) for data from Fashion-MNIST.

Explanations-Driven Active Feature Acquisition for Algorithmic Recourse

arXiv:2609.12179v1 Announce Type: cross Abstract: Algorithmic recourse methods typically assume that a predictive model has access to all features of an individual. In practice, decisions are often made with partial information, because features are costly to acquire. Active feature acquisition addresses cost-constrained prediction, but existing methods are explanation-agnostic: prior work provides explanations only after acquiring additional features, rather than using explanations to drive acquisition. This work flips that and treats algorithmic recourse and feature acquisition jointly. We use Markov Blanket theory to unify counterfactual, semifactual, and alterfactual explanations and to characterize how available recourse grows as features are acquired. Building on this framework, we propose an Explanation-Driven Feature Acquisition (EDFA) method that selects features by explanatory value per unit cost. The framework is further extended with distribution-free validity guarantees for recourse issued from partial information, which signal trustworthy, lower-cost recourse, along with a lower bound on the calibration data required to certify them. Experiments on 7 publicly available datasets with neural network-based predictive models show that EDFA acquires substantially fewer features than state-of-the-art AFA baselines while maintaining comparable accuracy and yielding more decision-relevant, actionable recourse. The implementation is available on GitHub.

Agentic TCAD Calibration Workflow for Oxide Semiconductor Transistors

arXiv:2609.12184v1 Announce Type: cross Abstract: Experimental TCAD calibration is essential for predictive technology modeling of emerging oxide semiconductor transistors. However, it remains time-consuming and expert dependent because of model ambiguity. Multiple physical models and parameter sets can reproduce the same measured transfer characteristics, while local fitting alone cannot uniquely identify the underlying device physics. We present the first demonstration of an agentic TCAD calibration workflow for a fabricated bottom-gate In--W--O (BG-IWO) transistor. Starting from the measured transfer curve and device information, the workflow uses measurement--TCAD residuals and local sensitivity tests to select bounded parameter corrections or evaluate additional physical models, and accept only updates that improve device metrics. The LLM agent orchestrates the workflow, while Sentaurus governs the device physics. For the 2\%-W reference device, five agent-suggested updates yield a fixed calibrated model, reducing the multi-metric device objective $J$ by 14.3$\times$. Maximum $V_{\mathrm{th}}$/$I_{\mathrm{on}}$ errors are 36.1~mV/0.022 decade for varying-drain-bias tests and 46.2~mV/0.062 decade for varying-channel-length tests, demonstrating model transferability across bias and geometry rather than a local parameter fit. W-composition tests provide process-sensitive insight. This agentic workflow provides a faster route to model development for emerging device technologies.

QuPAINT: Physics-Aware Multimodal Reasoning for Quantum Material Characterization

arXiv:2609.12202v1 Announce Type: cross Abstract: Characterizing two-dimensional (2D) quantum materials by optical microscopy requires localizing exfoliated flakes and determining their layer thickness from subtle optical contrast and interference color to select suitable flakes for device fabrication. However, models face synthetic-to-real domain shifts and variation across materials, substrates, laboratories, and imaging conditions. We present QuPAINT, a physics-aware multimodal framework for transferable quantum flake characterization. The Synthetic Materials Framework (Synthia) generates diverse synthetic microscopy images while preserving layer-dependent optical behavior. Using these images, we construct QMat-Instruct, a multimodal instruction dataset with image-specific reasoning traces generated from verified annotations and constrained to observable optical cues. QuPAINT integrates these signals through Physics-Informed Attention (PIA), which injects substrate-relative optical priors into the visual representation to support grounded multimodal reasoning. For evaluation, we introduce QF-Bench, to our knowledge, the largest real-world benchmark for this problem, spanning diverse microscopy and substrate conditions. Using its verified annotations, we study counting, visual grounding, reasoning quality, confidence calibration, and transfer to an unseen material. QuPAINT-8B substantially outperforms prior methods and establishes state-of-the-art performance for both general and monolayer flake detection. Additional experiments show that image-grounded supervision improves strict spatial grounding and confidence calibration while preserving robust general flake detection on the unseen material.

Predicting Collision Cross Sections with GRACE: Geometric Residual Adduct Conditioning via Early-fusion

arXiv:2609.12223v1 Announce Type: cross Abstract: Collision cross section (CCS), derived from ion mobility mass spectrometry, is a common descriptor for molecular annotation. Prediction is challenging for machine learning models because it reflects the size, shape, and ionization state of a gas-phase molecular ion. Most predictors either ignore explicit 3D structure or treat adduct identity as a late categorical feature, which limits their ability to capture adduct-dependent geometric effects. We present GRACE (Geometric Residual Adduct Conditioning via Early-fusion), a 3D CCS predictor that adapts a pretrained molecular geometry encoder using geometric residual adduct conditioning via early fusion. GRACE combines two inductive biases: a residual objective relative to an adduct-aware physical descriptor baseline and adduct conditioning within the encoder via a learned adduct token and low-rank attention adapters. We evaluate the model on a curated set of over 9,000 experimental molecule-adduct CCS records with random, scaffold, and adduct-sensitive splits designed to separate interpolation, scaffold generalization, and adduct-driven generalization. GRACE achieves the best mean percentage difference among the evaluated learned models on all three splits: 1.67% on the random split, 2.11% on the scaffold split, and 2.36% on the adduct-sensitive split. Diagnostic analyses suggest that residual learning stabilizes training by removing the dominant mass-CCS trend, while early fusion improves adduct-sensitive prediction relative to late fusion. Across four independent external test sets, GRACE shows consistently lower error than the other evaluated models. On a held-out set, GRACE also attains the lowest mean percent difference when compared with four previously reported physics-based workflows. These results support residual learning and encoder-level adduct conditioning as practical inductive biases for fast, accurate CCS prediction.

Reinforcement Learning over Patient Trajectories for Clinical Reasoning in EHR Foundation Models

arXiv:2609.12277v1 Announce Type: cross Abstract: Electronic health record (EHR) foundation models trained on longitudinal patient trajectories have demonstrated strong performance across diverse clinical prediction tasks. However, their clinical reasoning capabilities remain constrained by next-token prediction on limited and incomplete EHR data. To address this, we propose a reinforcement learning (RL) fine-tuning framework that treats EHR foundation models as generative policies over patient trajectories. We formulate common clinical prediction problems (e.g., hospital readmission) as event-conditioned, time-windowed reasoning tasks. We then design time-aware, rollout-sensitive rewards to account for finite rollout lengths and temporally inconclusive outcomes. We find that RL fine-tuning consistently improves over pre-trained backbones and strong baselines. Notably, it enables smaller models to surpass larger pre-trained models in data-limited regimes and induces positive transfer across tasks. Further analysis shows that RL fine-tuned models generate trajectories with stronger structural and semantic alignment to ground truth and greater downstream utility.

Amortized Low-Rank Adaptation for Model-Based Reinforcement Learning

arXiv:2609.12278v1 Announce Type: cross Abstract: World models let agents plan by predicting the consequences of their actions, but changes in the environment can make them inaccurate. We study the problem of adapting a world model to an unknown test-time environment, drawn from a known environment family, using only a few episodes of interaction. Existing approaches trade off computational cost against expressivity, i.e., the range of models a method can produce. For example, in-context learning is computationally cheap but limited in expressivity, and gradient-based adaptation is expressive but computationally expensive. We present CLAW (Context-conditioned Low-rank Adaptation of World models), which addresses this tradeoff by using a hypernetwork to generate low-rank (LoRA) adapters at test time. During pretraining, we simulate adaptation to a variety of environments and jointly train the hypernetwork and base world model. At test time, we freeze the base model and use a forward pass of the hypernetwork to generate adapters from a small batch of test-time transitions. We evaluate CLAW in locomotion and manipulation environment families that vary in dynamics, embodiment, and reward. We show that, using only seconds of test-time data, CLAW outperforms gradient-based adaptation and in-context learning during online adaptation. We also show that CLAW avoids overfitting in data-scarce regimes, that its advantage comes from the expressive adapters rather than context conditioning, and that pretraining the hypernetwork jointly with the base model outperforms training it post hoc.

Breaking the Token Ceiling: Distilling Smaller, Stronger Byte Models

arXiv:2609.12303v1 Announce Type: cross Abstract: Small models are made more capable through distillation from a larger one that shares their tokenization scheme. However, do distilled byte and token models behave similarly in terms of scaling trends as compute and data increases? To enable this comparison, we introduce two variants to efficiently convert token logits to Byte Logits: 1) approximate: Marginalize-It, and 2) exact: End-Of-Token. We then present the first large scale study of overtraining decoder-only dense transformer models varying two dimensions simultaneously: the tokenization scheme (Tokens, Bytes, Bytes w/ eot) and the training objective (Distillation vs. Cross-Entropy), sweeping layer-parameter-matched models with roughly 1 billion parameters up to 1 trillion bytes of data. Across eight benchmarks spanning three categories: Multiple Choice QA, Language Generation, and Machine Translation, we find that Token-1B models outperform byte models (End-Of-Token-1B and Bytes-1B) in the low-FLOP regime but eventually plateau; byte models start worse yet surpass Token-1B models with more compute, reaching a higher downstream task performance ceiling. Extrapolating the average top-1 error vs. validation BPB scaling laws predicts that, asymptotically, distilled End-Of-Token-1B outperforms distilled Token-1B by up to 4%. They are also far more data efficient, matching the performance of distilled Token-1B using only one-sixth of the training data. Moreover, by operating over a small vocabulary of 256 bytes instead of on the order of 100K tokens, they circumvent the need for top-k truncation during logit dumping, while also reducing logit storage costs to roughly one-fifth. Finally, our downstream performance scaling laws predict that our distilled End-Of-Token-1B models asymptotically surpass the Llama 3.2-1B, Gemma-3-1B-pt, and Gemma 2B models on averaged downstream tasks by up to 6.5%, 8.1%, and 2.1%, respectively.

Self-Verifying Anomaly Detection using Explainable AI for Cybersecurity of DER Networks

arXiv:2609.12305v1 Announce Type: cross Abstract: The rapid growth of Distributed Energy Resources (DERs) has significantly expanded the cyber attack surface of modern power grids. Furthermore, increasing sophistication in attack techniques demands anomaly detection systems (ADS) that are accurate, interpretable, and reliable to support DER cybersecurity. While ML-based ADS provide strong detection capabilities, their black-box nature reduces operator trust and limits Security Operation Center's (SOC) ability to effectively interpret alerts and respond, highlighting the need for explainable Artificial Intelligence (XAI) to ensure transparency and operational confidence. This paper presents an XAI-based anomaly detection framework tailored for DER networks (ExCYDER). The proposed framework uses a self-verifying mechanism that validates ADS alerts to ensure trustworthy decision-making. ExCYDER combines LightGBM with SHAP to check whether each model decision aligns with its feature-attribution evidence, allowing the system to confirm that its internal reasoning is consistent and reliable. Experiments on a realistic DNP3 dataset achieved over 98% detection accuracy, an average rule--SHAP consistency of 44.6%, a SHAP latency of 14.5 ms per alert, and a confidence deviation within 5%, demonstrating stable verification behavior with minimal computational overhead. The framework distinguished between coherent and inconsistent alerts without compromising detection accuracy, demonstrating that integrated verification within XAI-based ADS enhances interpretability, auditability, and operational robustness for DER-focused SOCs.

ESTS at WMT26: Routing-Informed Expert Pruning for Model Compression

arXiv:2609.12310v1 Announce Type: cross Abstract: We describe six submissions under the team name ESTS to the unconstrained WMT26 Model Compression Shared Task for English--Simplified Chinese and English--Egyptian Arabic. We submit three compression operating points per translation direction, all derived from GPT-OSS-20B. We use task-specific routing mass to rank experts and cross-lingual routing divergence to allocate retained capacity across layers, then physically remove low-importance experts. The resulting specialists are recovery-tuned on GPT-5.1-generated synthetic translation data and further compressed by applying MXFP4 quantization to the retained expert projection weights. We additionally implement a robust inference system for the instruction-conditioned WMT26 setting, including category inference, output validation, retries, segmented fallback, and source-owned JSON reconstruction. Across our six submissions, parameter counts range from 4.186B to 7.770B and packed artifact sizes from 4.55 to 6.33~GiB. Internal xCOMET-XL evaluation using GPT-5.1 pseudo-references provides an internal comparison across the submitted compression operating points.

MInTRL: Off-policy Intervention can boost On-policy RL

arXiv:2609.12419v1 Announce Type: cross Abstract: Reinforcement learning with verifiable rewards is typically performed on-policy, keeping training data close to the current policy but limiting learning to trajectories that the policy can discover itself. Off-policy methods such as supervised fine-tuning, on the other hand, can leverage external knowledge beyond the base model's capabilities, but may suffer from large distribution shift. The key challenge is thus to expand exploration without sacrificing learnability. In this work, we introduce Minimal Intervention Reinforcement Learning (MInTRL), which expands the exploration frontier through sparse, local interventions in otherwise on-policy rollouts. During generation, a judge-intervention policy periodically reviews the current policy's output, replaces erroneous suffixes with short corrections, and immediately returns control to the policy. During training, MInTRL adopts a sequence-level advantage-regression objective that eliminates the need for importance sampling. We show that sparse, local interventions can substantially improve coverage beyond finite-budget on-policy sampling while preserving the overall on-policy nature of the resulting trajectories. Across math and code benchmarks, MInTRL consistently outperforms standard on-policy and off-policy baselines. Ablations show that MInTRL remains effective with self-intervention and across different judge policies, while performance peaks at moderate intervention intensity, highlighting the importance of intervening minimally. These results establish minimal intervention as an effective paradigm for enhancing on-policy RL.
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