Iterative Refinement

Precise retrieval of scientific information is fundamentally constrained by long-tailed concepts and high fact-sensitivity of scientific corpora. These challenges often limit the effectiveness of dense retrievers and hallucination-prone LLM augmentation. To address this, we present REPAIR, a self-evolving data augmentation framework for scientific dense retrievers. REPAIR iteratively synthesizes training data to address knowledge gaps by cycling through diagnosis of long-tail concepts, API-guided evidence expansion, and differentiation via hard negative mining. This process effectively grounds retrieval in factual reality to resolve fine-grained distinctions. Extensive experiments demonstrate that REPAIR significantly outperforms 19 strong baselines on nine materials science and biomedical benchmarks. Our work highlights that diagnosing and factually augmenting data to long-tail deficits is essential for robust scientific retrieval.

We study vector-valued binary affine refinement operators with finitely supported matrix masks and compactly supported continuous piecewise linear input and forcing data. We prove that every finite refinement iterate admits an exact ReLU realization of fixed width and depth linear in the number of iterations. No separation of the forcing profile from the binary cell seams is required. The main mechanism is universal reflection doubling. Pairing each residual profile with its reflection replaces the two binary transition matrices by one fixed block matrix together with a fixed swap involution. The cell-seam identity makes the two branch candidates agree at the tent fold, while their swap-odd component is bounded linearly by the distance to the fold. This permits exact branch selection by a fixed continuous piecewise linear cone switch, without multiplication by a variable selector. The resulting primal recursion requires the residual orbit in reverse order. We obtain exact backward replay from the residual memory controller developed previously for affine refinement, interpreted here through the reflection quotient of circle doubling. The construction propagates the full vectorized profiles rather than decomposing the input and forcing into reference atoms. We also treat stage-dependent forcing from a fixed finite-dimensional family and show that genuine reflection equivariance reduces the doubled cascade to a single parity sector.

Understanding the temporal progression of symptoms in clinical narratives is critical for disease monitoring, safety surveillance, and causality assessment. Clinical narratives, however, rarely provide explicit temporal anchors. Current approaches to temporal information reasoning focus predominantly on pairwise relation classification across multi-visit and timestamp-rich records, leaving the reconstruction of structured symptom trajectories from individual anchor-sparse reports largely unaddressed. We propose CRAFT, an LLM framework that pairs a generator with a constraint-based verifier to iteratively produce and refine stage-wise symptom timelines through targeted feedback. We conduct evaluation on MedTempo, a new benchmark of 5,347 vaccine adverse-event narratives spanning three COVID-19 vaccine types, with expert-validated temporal stage annotations for 3,166 reports. Experiments across four LLM backbones demonstrate that CRAFT consistently improves temporal ordering accuracy, with ablation analysis isolating the contribution of generator and verifier components across model capability levels.

As collaborative robots have entered domains such as manufacturing, agriculture, and healthcare, programming or adapting robot behavior typically requires robotic expertise that most end users lack. Natural language lowers this barrier. Recent advancements in large language models (LLMs) have made it feasible to translate natural language into robot task plans. However, language-based task specification suffers from semantic ambiguity, and generative models lack transparency for how language instructions become robot actions, making it difficult for users to validate the plan before execution. To address these issues, we introduce SHRIMP, a system that allows users to automatically generate a hierarchical robot primitive plan using natural language and iteratively revise their plan through re-prompting and explicit correction. At each revision, SHRIMP allows users to validate their plan in simulation, and once satisfied, execute it on the physical robot. Through a user study involving participants planning tabletop kitchen tasks (n=35), we validate that SHRIMP improves perceived control and enhances robot transparency. System videos and source code are available at https://wisc-hci.github.io/SHRIMP.

Personalizing large language models (LLMs) to individual users is essential for improving user experience, yet existing approaches typically rely on explicit preference supervision such as pairwise comparisons or demographic attributes, limiting their applicability in natural interaction settings. We propose IRIS, a framework that learns dynamic user personas directly from implicit interaction streams by extracting behavioral signals from everyday conversations and iteratively refining persona representations through a prediction-driven closed loop without requiring explicit feedback. We introduce an evaluation protocol based on behavior prediction, persona stability, and decision prediction. A proof-of-concept study on a synthetic interaction stream derived from public-domain autobiographical text shows that IRIS produces stable personas and distinguishes individual users while revealing limitations of memory-only approaches on recall-oriented metrics. We then validate IRIS on anonymized real-world Reddit r/AmItheAsshole (AITA) data, with personas built solely from each author's historical interactions. Across 100 authors, IRIS achieves the highest decision prediction accuracy among all evaluated methods (61.0%), outperforming static personas, memory-only retrieval, and no-personalization baselines. These results suggest that implicit behavioral modeling provides a scalable alternative to explicit preference learning for personalized LLMs and offers a practical foundation for adaptive conversational systems and embodied agents that require continuously evolving models of their users.

We study vector-valued affine refinement operators of the form [ (Wγ)(t)=\sum_{j\in\mathbb{Z}} A_jγ(Mt-j)+B(t), ] with finitely supported matrix mask and compactly supported continuous piecewise linear input and forcing data. Building on the homogeneous realization theorem for (B\equiv 0), we prove that, for (M\ge 3), every finite affine iterate (W^nγ) admits an exact fixed-width ReLU realization whose depth is (O(n)). The main new ingredient is a residual memory controller. It replaces the noninvertible residual dynamics by an injective skew-product and permits exact backward replay of the residual states required by a Horner-type evaluation of the affine forcing sum. Offset frames align the forcing atoms away from residual seams, allowing complementary loop readouts to recover their values exactly. The remaining branch-selection ambiguity occurs only where the accumulated affine state has already vanished. For (M\ge 3), the result applies to arbitrary compactly supported continuous piecewise linear forcing terms. For (M=2), the same construction applies to ordinary-frame seam-separated forcing. We also prove a stage-dependent extension for forcing terms in a fixed finite-dimensional continuous piecewise linear span and record the resulting linear-depth upgrade for open-curve, finite-state, and Hilbert- and Morton-type recursive constructions.

Large language model (LLM) agents now perform well on correctness-oriented repository-level tasks, including SWE-Bench issue resolution and feature implementation in real codebases. However, they still struggle with repository-level code optimization, which requires preserving behavior while improving runtime performance. Passing tests is not enough in this setting; a patch must preserve behavior, implement code optimization, and approach expert speedups. Current agents often miss bottlenecks hidden behind abstraction layers and native extensions, stop after shallow speedups, or insufficiently test the code patches that thus may silently break edge cases. We present PerfAgent, a profiler-guided, verifier-in-the-loop workflow that gives an off-the-shelf coding agent the feedback needed to find real hotspots, improve beyond the first passing patch, and use profiler evidence rather than timing alone to decide what to optimize next. On two challenging optimization benchmarks, GSO and SWE-fficiency-Lite, PerfAgent more than doubles the rate of expert-matching patches over OpenHands with GPT-5.1, improving from 19.6% to 39.2% on GSO and from 26% to 74% on SWE-fficiency-Lite. It also surpasses an oracle best-of-five baseline at substantially lower cost, showing that the gains come from better feedback rather than additional test-time sampling.

Refinement operators generate many functions used in wavelet constructions, subdivision schemes, and geometric modeling. Their finite iterates can develop rapidly increasing numbers of linear pieces, making them a natural test case for the expressive power of deep neural networks. Earlier work showed that, for scalar binary refinement with a finitely supported mask, every compactly supported continuous piecewise linear seed has finite refinement iterates that admit exact ReLU realizations of fixed width and depth growing linearly with the number of refinement steps. The present paper gives a new construction of this known theorem. The difficulty is that the refinement cascade is driven by discontinuous binary digit choices, whereas ReLU networks produce continuous piecewise linear maps. We represent the residual dynamics on a polygonal model of the circle and describe each residual position in two overlapping coordinate systems, one ordinary and one shifted by one half. Their discontinuities occur at different points. The network switches between the two descriptions only where both are valid and the corresponding fixed linear cascade updates agree, so the switch is exact and requires no multiplication by a variable selector. The construction also gives exact readout of every continuous piecewise linear circle function satisfying the natural endpoint compatibility condition. Localized seeds are handled by a two-pass network, and translation covariance, finite decomposition, and gluing extend the result to arbitrary compactly supported continuous piecewise linear seeds in a preserved support window.

Recent advances in Large Language Models (LLMs) and Vision-Language Models (VLMs) enable the automatic generation of parametric 3D designs from natural-language specifications. This chapter presents an empirical study of foundation models for automatic Computer-Aided Design (CAD) generation of mechanical parts, using a unified evaluation pipeline and a curated benchmark of 97 engineering design problems. We introduce LLMForge, a multi-model text-to-CAD framework integrating JSON-schema validation, analytic feature scoring, mesh synthesis, and multi-round iterative refinement, studied under two critique regimes. IterTracer uses a Phong-shaded ray-trace renderer with analytic visual metrics (silhouette IoU, hole visibility, edge clearance, aspect-ratio conformance) for lightweight geometry-aware feedback across rounds. IterVision replaces the analytic scorer with a VLM semantic critic (Qwen2.5-VL-72B) that evaluates rendered views via chain-of-thought visual reasoning, assessing spatial coherence and design intent. On a benchmark spanning four canonical geometry families (plates with holes and bolt circles, multi-feature boxes, flanged cylinders, and L-brackets), we evaluate seven foundation models: DeepSeek-V3.2, Qwen3-235B-A22B, Llama-3.3-70B, Gemma-3-27B, GLM-4.5, MiniMax-M2.1, and INTELLECT. Under IterTracer, the four highest-ranked models form a tight cluster (overall mean in [0.885, 0.890]) with 98.97% mesh success, showing that compact instruction-tuned models can match substantially larger systems. VLM-based critique in IterVision yields 100% watertight mesh generation on the leading model while surfacing systematic difficulty on rotationally symmetric geometries such as cylinders, where visual and semantic scoring diverge most. We discuss benchmark design, failure modes, CAD-oriented prompting, and implications for industrial workflows and scalable automated mechanical design.

Learning visuomotor policies for long-horizon manipulation remains a fundamental challenge. Recent skill-based imitation learning methods based on discrete quantization have shown promising results by representing complex behaviors as temporally extended skills. However, most existing approaches primarily encode action trajectories into latent skills, yielding weak visual-semantic grounding and limiting the ability to leverage visual observations for skill selection. Moreover, discrete tokenization inevitably incurs precision errors during continuous action generation. To alleviate these issues, we propose Aligned Refinement Policy (ARP), a discrete-skill framework that couples semantic grounding with execution-level refinement. Specifically, ARP introduces (i) a visual--action alignment objective that contrastively aligns visual embeddings with pre-quantized action representations in a shared latent space while preserving a state-independent skill decoder, and (ii) a lightweight Iterative Residual Head (IRH) that performs a two-step refinement to recover fine-grained control for precise execution. Extensive experiments show that ARP achieves state-of-the-art performance on the LIBERO and Meta-World benchmarks. Moreover, real-robot experiments on the Kuavo 4 Pro humanoid platform further validate its effectiveness, yielding consistent performance gains over several baselines on two challenging manipulation tasks.

Large Language Models have shown remarkable capabilities in code generation. However, most existing evaluations focus only on single-attempt accuracy and overlook the iterative refinement process that is central to real-world programming. This study presents a systematic investigation of LLMs' ability to rectify their own code through execution feedback. Using real-world programming problems across four models and two major programming languages, this study evaluates performance using iterative refinement framework where LLMs receive compiler error messages and testcase feedback after each attempt. This study introduces metrics to evaluate code failures, analyze rectification patterns, and compare the effectiveness of reasoning and non-reasoning models, offering actionable insights into both the understanding and practical application of feedback loops in LLM-driven code generation systems. Results show that reasoning models consistently improve over iterations, substantially outperforming non-reasoning models in leveraging feedback, while syntactic and runtime errors are far more tractable than logical or algorithmic failures.

Computer-Aided Design is pivotal in modern manufacturing, yet existing automated methods predominantly rely on open-loop, one-shot generation, creating a mismatch with iterative real-world practices. In this paper, we present IterCAD, a unified multimodal agent framework for closed-loop, interactive CAD generation and editing. We formulate the task as a multi-turn interaction between a multimodal agent and an executable CAD sandbox, covering three tasks: Drawing-to-Code, Text-to-Code, and Interactive Editing. To support this, we develop a data synthesis pipeline incorporating advanced industrial manufacturing features to generate standard-compliant multi-view engineering drawings, complex code-editing tasks, and high-fidelity interaction trajectories. We optimize the agent via progressive SFT followed by geometry-aware reinforcement learning with viable-prefix masking to enhance code executability and geometric fidelity. Finally, we introduce the IterCAD-Bench evaluation suite and propose the Chamfer Distance Tolerance-Recall (CD-TR) curve alongside its AUC-TR metric, establishing a survivor-bias-free standard that unifies code validity and geometric precision. Extensive experiments demonstrate that IterCAD achieves highly competitive performance across multiple benchmarks, significantly outperforming existing approaches in both code executability and geometric precision, while exhibiting superior capabilities in closed-loop iterative refinement.

Literary translation poses unique challenges due to the scarcity of high-quality annotated data and the need to balance expression fluency with literary effect. We present a multi-aspect iterative refinement framework that generates high-quality translation references and preference data through specialized LLM translators, each targeting a distinct quality dimension. We leverage the generated data for supervised fine-tuning and reinforcement learning. Experiments show that our generated references outperform the original ground truth for SFT by 8.65 CEA100 points. For reinforcement learning, we find that DPO leads to performance degradation in this setting, while leveraging an explicit reward model for GRPO yields an additional 1.51 point improvement. We attribute this to the stability of two-stage training and GRPO's online exploration capability. Our resulting models, LitMT-8B and LitMT-14B, achieve 67.25 and 69.07 CEA100 respectively on the MetaphorTrans English-to-Chinese literary translation benchmark, competitive with Claude Sonnet 4.5 at 68.43, and demonstrate strong generalization to out-of-domain literary work (i.e., O. Henry).

Generating executable tool plans requires selecting appropriate subsets from tool libraries, a combinatorial search problem with an exponentially large solution space. However, we identify a critical misalignment in predominant approaches: standard autoregressive (AR) decoding suffers from early commitment, where initial token choices rigidly constrain the search trajectory. A controlled study shows that masked denoising raises Pass@10 solution coverage from 0.320 to 0.943 over AR sampling under matched compute. Motivated by this, we propose DiG-Plan, a framework that decouples combinatorial exploration from structural refinement. DiG-Plan employs a diffusion-based proposer to generate diverse tool sets via iterative refinement, followed by an AR refiner for dependency prediction. On TaskBench, DiG-Plan improves over AR baselines by a 10% relative margin, with the largest gains on complex compositional tasks; API-Bank results show that the propose-refine-select design remains effective across domains. Code is available at https://github.com/puddingyeah/DiG-Plan.

We introduce the Image Reconstruction Game, a fully automated benchmark in which a vision-language model issues corrective instructions to an image generator across multiple turns, making accumulated common ground directly observable as a rendered image. Benchmarking two Describer models crossed with two Generator models across seven image categories, we find that the describer is the dominant factor in reconstruction quality, while the generator determines whether iterative refinement helps or hurts. Mathematical and geometric images pose the greatest challenge. The describer's token budget strongly affects convergence: shorter budgets yield sparser first renderings with more room for visible improvement, while longer budgets raise absolute quality but leave less to fix. Stronger describers use a richer correction vocabulary spanning spatial, numeric, and structural categories, while weaker describers concentrate on surface properties and tend to stop after a few turns. Human validation shows that the best automated judge reaches only slight-to-fair agreement with human preferences, and automated scores require human recalibration to be used reliably.

Accurate precipitation nowcasting is vital for disaster mitigation, but deep learning methods face a key trade-off: regression models produce over-smoothed, spectrally decaying predictions that blur convective details and violate turbulence power laws; diffusion models generate realistic yet unanchored hallucinations lacking physical grounding. We propose Spectral-Decoupled Iterative Refinement (SDIR), a deterministic framework that reformulates nowcasting as progressive frequency-decoupled refinement. SDIR first extracts a stable low-frequency synoptic skeleton, then iteratively refines high-frequency textures under physical constraints, eliminating both blurring and hallucinations. It features a dual-path design: the Synoptic Frequency-Guided Former (SFG-Former) with Scale-Adaptive Transformers for global structure, and the Fourier Residual Refiner (FR-Refiner) with Scale-Conditioned Fourier Neural Operators for fine residuals. A Physically Consistent Power Spectral Density (PCPSD) loss with dynamic masking enforces a turbulence-consistent spectral distribution. Experiments on three benchmarks show SDIR significantly outperforms SOTA methods in spatial accuracy while achieving spectral fidelity competitive with diffusion-based methods, enabling reliable high-resolution operational nowcasting. Code link: https://github.com/RuntimeWarning/SDIR.

For sparse, structured reinforcement-learning tasks with semantic reward-function interfaces, LLM-generated reward shaping is better framed as debugging than one-shot generation. We study PPO-trained agents using MiniGrid as core evaluation and MuJoCo as boundary stress test. Our audit finds two dominant one-shot failure modes -- reward flooding and semantic/API misunderstanding -- plus a rarer weak-shaping case. We propose diagnostic-driven iterative refinement, where training diagnostics and a failure-mode taxonomy guide targeted reward-function revision. Refinement improves DoorKey-8x8 from 2.3% to 97.6% and KeyCorridor from 31.2% to 86.7% with high seed-to-seed variance. Controls show these gains are not from retrying or extra training: metrics-only re-prompting yields large drops, while a static-vocabulary control recovers much of the gap (87.6%; 70.7%), showing the taxonomy prompt is a major mechanism and dynamic labels provide only partially isolated incremental evidence. Budget-matched and Best-of-3 comparisons separate refinement from selection and training-time effects. Component-removal tests, sensitivity analyses, and an audit against author labels provide converging evidence for the debugging interpretation while revealing calibration limits. Continuous-control results show the boundary: success-based diagnostics can misfire in dense-reward locomotion, and return-trend feedback removes one false-positive mechanism without robust gains. The low-call protocol is a cost contrast with population-based reward search, not a benchmark comparison. In four crossed-variance-design environments, point estimates suggest larger gains when LLM reward-function variance dominates but bootstrap intervals are wide. The method is bounded to sparse structured tasks with reliable interfaces under PPO; fields like event_text may help, hurt, or be neutral.

Symbolic regression (SR) seeks closed-form mathematical expressions that fit observed data. Neural SR methods amortize the search by training an encoder to map observations directly to expressions in a single pass, but this amortized inference leaves a residual amortization gap between its one-shot prediction and the true posterior. We propose Latent Equation Embedding (LEE), a framework that closes this gap through iterative amortized inference in a functionally grounded latent space. LEE learns a shared latent space Z equipped with three components: an encoder f_theta that jointly embeds symbolic tokens and numerical observations into a single latent vector z; an expression decoder g_expr that reconstructs formulas from z; and an evaluation decoder g_eval that predicts function values from z, explicitly grounding the latent space in functional behavior. At inference, LEE performs iterative refinement by re-encoding decoded expressions jointly with observations, progressively improving the latent estimate. LEE uses the encoder itself as a learned inference optimizer: each re-encoding step implicitly computes the mismatch between the candidate and the data. Because g_eval is differentiable in z, we additionally interleave continuous gradient descent with discrete re-encoding, yielding a hybrid iterative and gradient refinement procedure. On SRBench across three noise levels, against 19 baselines spanning genetic programming, symbolic-neural hybrids, and pre-trained Transformers, LEE produces expressions 2--10x simpler than the strongest accuracy-oriented baselines, including Operon, GP-GOMEA, TPSR, RAG-SR, and GenSR, with complexity 8--11 versus 20--90. These results advance the low-complexity region of the accuracy-complexity Pareto frontier and show graceful degradation as noise increases.

We present an image-conditioned point cloud completion approach that treats images as the primary geometric source rather than a secondary guide. To this end, we introduce an Image-to-Point (I2P) module that can reconstruct complete point clouds directly from a single RGB image, with no need for 3D inputs. Additionally, we introduce a transformer-based Point-to-Point (P2P) refinement module that uses self- and cross-attention between point tokens and image features to iteratively refine the coarse I2P output. The I2P module enables the image encoder to learn rich geometric representations, while the P2P module progressively recovers fine-grained details. Unlike existing multimodal methods that rely on auxiliary losses or fusion modules, our explicit I2P task provides a strong, geometry-aware prior based on images alone. Extensive experiments on ShapeNet-ViPC demonstrate state-of-the-art completion performance with a 12.3% relative Chamfer Distance improvement over prior methods. Code is available at: https://github.com/AzharSindhi/I2PRef.git

We present $\textbf{Research Math Agents (RMA)}$, an agentic framework for automated reasoning on research-level mathematical problems. Unlike prior studies centered on competition mathematics or formal theorem proving, RMA targets research-level mathematical problems that require long-horizon reasoning, literature grounding, and iterative proof refinement. RMA decomposes research-level proof solving into specialized modules for problem analysis, literature search and understanding, fair comparison, knowledge-bank construction, and proof verification, all coordinated by initializer, proposer, and verifier agents through a shared structured memory. Within this unified framework, these agents operate in a multi-role, multi-round workflow, collaboratively generating, refining, and verifying candidate proofs through iterative feedback. We evaluate RMA on the First Proof benchmark, which consists of ten research-level problems contributed by expert mathematicians across diverse domains. Through comprehensive expert evaluation, RMA outperforms strong baselines on the First Proof benchmark, including GPT-5.2R and Aletheia, solving eight out of ten research problems and producing more logically sound and readable proofs. Our comprehensive ablation studies further show that performance gains arise from the interaction of structured reasoning modules, iterative refinement, and verifier-based feedback, rather than any single component. Our solutions and implementations will be made publicly available upon acceptance.

Inference-time scaling has emerged as a major approach for improving reasoning capabilities, and has been increasingly applied to diffusion models. However, existing inference-time scaling methods for diffusion models typically rely on external verifiers or reward models to rank and select samples, limiting their scalability to settings where such evaluators are available and reliable. Moreover, while recent diffusion models perform sequential inference with region-wise, mixed-noise conditioning, inference-time scaling tailored to this setting remains relatively underexplored. We propose Iterative Partial Refinement (IPR), an inference-time scaling method for sequential diffusion that requires no external verifier. Starting from an already-generated sample, IPR re-noises a subset of regions and regenerates them conditioned on the remaining regions, enabling the model to revise earlier decisions under a richer context than was available during the initial generation. This iterative partial refinement produces more globally consistent samples without external verification. On reasoning tasks requiring global constraint satisfaction, IPR consistently improves performance: on MNIST Sudoku, the valid solution rate increases from 55.8% to 75.0%. These results show that iterative partial refinement alone can serve as an effective inference-time scaling strategy for diffusion models in sequential, mixed-noise settings. Code is available at: https://github.com/ahn-ml/IPR

Multi-agent LLM workflows -- systems composed of multiple role-specific LLM calls -- often outperform single-prompt baselines, but they remain difficult to debug and refine. Failures can originate from subtle errors in intermediate outputs that propagate to downstream nodes, requiring developers to inspect long traces and infer which agent to modify. We present PROTEA, a unified interface for offline, test-driven improvement of multi-agent workflows. PROTEA executes a workflow, scores intermediate node outputs with configurable rubrics, and overlays per-node states and rationales on the workflow graph to localize likely bottlenecks. To support complex systems where final-answer references are the primary supervision, PROTEA performs backward node evaluation: it generates candidate node-level expectations from final-answer references and graph context, then compares them with observed node outputs. For selected nodes, PROTEA presents targeted prompt revisions as editable before/after comparisons, then automatically reruns and re-evaluates the workflow to show output changes and score trajectories within the same interface. In two production-adjacent workflows, PROTEA improved document-inspection accuracy from 64.3% to 83.9% and recommendation Hit@5 from 0.30 to 0.38. In a formative study with six experienced LLM developers, participants valued graph-level localization, per-node rationales, and editable before/after prompt revisions.

Recent progress in dense optical flow has been driven by increasingly complex architectures and multi-step refinement for test-time scaling. While these approaches achieve strong benchmark performance, they also require substantial computation during inference. This raises a fundamental question: Is scaling test-time computation the only way to improve dense optical flow accuracy? We argue that it is not. Instead, powerful visual semantic and geometric priors encoded in modern foundation models can reduce, if not overcome, the need for computationally expensive iterative refinement at test-time. In this paper, we present a framework that estimates dense optical flow in a single forward pass, leveraging pretrained foundation representations, while avoiding iterative refinement and additional inference-time computation, thus offering an alternative to test-time scaling. Our method extracts visual semantic features from a frozen DINO-v2 backbone and combines them with geometric cues from a monocular depth foundation model. We fuse these complementary priors into a unified representation and apply a global matching formulation to estimate dense correspondences without recurrent updates or test-time optimization. Despite avoiding iterative refinement, our approach achieves strong cross-dataset generalization across challenging benchmarks. On Sintel Final, we obtain 2.81 EPE without refinement, significantly improving over state-of-the-art (SOTA) SEA-RAFT under comparable training conditions and outperforming RAFT, GMFlow (without refinement), and recent FlowSeek in the same setting. These results suggest that strong foundation priors can substitute for test-time scaling, offering a computationally efficient alternative to refinement-heavy pipelines.

We study scalar dyadic refinement operators on R^2 of the form (Vf)(x,y) = sum_{(j,k) in Z^2} c_{j,k} f(2x-j, 2y-k), where only finitely many mask coefficients c_{j,k} are nonzero. Under a fixed support-window hypothesis, we prove that for every compactly supported continuous piecewise linear seed g:R^2->R, the iterates V^n g admit exact ReLU realizations of fixed width and depth O(n). This gives a first genuinely two-dimensional extension of the exact realization theory for refinement cascades. Using the one-dimensional exact loop-controller framework, the proof transports the tensor-product residual dynamics exactly on the product of two polygonal loops and reduces the remaining seam ambiguity to a final readout and selector step. The matrix cascade is then handled by a fixed-depth recursive block, and general compactly supported continuous piecewise linear seeds are reduced to a finite decomposition together with exact clamped gluing on the support window. This identifies the tensor-product dyadic case as a natural first multivariate instance of the loop-controller method for refinement iterates.

We study homogeneous refinement operators $(Vγ)(t)=\sum_{j\in\mathbb Z}A_jγ(Mt-j)$, acting on compactly supported continuous piecewise linear curves $γ:\mathbb R\to\mathbb R^p$, where $M\ge2$ and only finitely many matrices $A_j\in\mathbb R^{p\times p}$ are nonzero. We prove that the iterates $V^nγ$ admit exact ReLU realizations of fixed width and depth $O(n)$. The main new ingredient is an exact loop controller for the residual dynamics. Instead of propagating scalar residual surrogates, the construction transports the residual orbit by a forward-exact state on a polygonal loop. Scalar factors and digit selectors are then recovered from this loop state by complementary CPwL readouts. The loop seam is not removed, but its remaining ambiguity is confined to the final readout/selector stage, where it is harmless because the scalar atom is supported away from the seam. This gives a homogeneous $M$-ary vector-valued extension of the scalar binary refinable-function construction with a more geometric controller architecture. We also record crude exponential bounds on the network weights and biases. Affine forcing terms are handled by expanding affine iterates into finite sums of homogeneous iterates, giving exact fixed-width realizations with depth $O(n^2)$, and anchored open curves reduce to compactly supported defects with affine anchor mismatch. We also describe homogeneous polygonal generators, including dragon-type examples and a self-intersecting Hilbert-type prototype in arbitrary dimension. The extended version includes stage-dependent forcing, finite-state stacking reductions, and further geometric constructions such as Koch-, Gosper-, Morton-, and connector-based Hilbert-type variants.

Web filtering systems rely on accurate web content classification to block cyber threats, prevent data exfiltration, and ensure compliance. However, classification is increasingly difficult due to the dynamic and rapidly evolving nature of the modern web. Embedding-based zero-shot approaches map content and category descriptions into a shared semantic space, enabling label assignment without labeled training data, but remain highly sensitive to definition quality. Poorly specified or ambiguous definitions create semantic overlap in the embedding space, leading to systematic misclassification. In this paper, we propose a training-free, adaptive iterative definition refinement framework that improves zero-shot web content classification by progressively optimizing category definitions rather than updating model parameters. Using LLMs as feedback-driven definition optimizers, we investigate three refinement strategies namely example-guided, confusion-aware, and history-aware, each refining class descriptions using structured signals from misclassified instances. Furthermore, we introduce a human-labeled benchmark of 10 URL categories with 1,000 samples per class and evaluate across 13 state-of-the-art embedding foundation models. Results demonstrate that iterative definition refinement consistently improves classification performance across diverse architectures, establishing definition quality as a critical and underexplored factor in embedding-based systems. The dataset is available at https://github.com/naeemrehmat/B2MWT-10C.

Recent work on large language models (LLMs) has emphasized the importance of scaling inference compute. From this perspective, the state-of-the-art method Scattered Forest Search (SFS) has been proposed, employing Monte Carlo Tree Search with carefully crafted initial seeds and textual optimization for multi-turn program correction. However, its complexity makes it unclear what factors contribute to improvements in inference performance. To address this problem, we analyze SFS and propose a simpler method, \textsc{Iterative Refinement of Repair Instructions} (IRRI), which fixes initial programs and iteratively refines repair instructions. Because of the simplicity of IRRI, we theoretically establish the non-elimination of IRRI using Oracle-Guided Inductive Synthesis (OGIS). Experiments on several program generation benchmarks suggest that IRRI achieves inference performance comparable to state-of-the-art methods. These results indicate that, even without complex search structures, refining initial programs with high-quality repair instructions alone can effectively improve inference performance.

Text-to-SQL systems often struggle with deep contextual understanding, particularly for complex queries with subtle requirements. We present PV-SQL, an agentic framework that addresses these failures through two complementary components: Probe and Verify. The Probe component iteratively generates probing queries to retrieve concrete records from the database, resolving ambiguities in value formats, column semantics, and inter-table relationships to build richer contextual understanding. The Verify component employs a rule-based method to extract verifiable conditions and construct an executable checklist, enabling iterative SQL refinement that effectively reduces missing constraints. Experiments on the BIRD benchmarks show that PV-SQL outperforms the best text-to-SQL baseline by 5% in execution accuracy and 20.8% in valid efficiency score while consuming fewer tokens.

Accurate autoregressive prediction of 3D turbulent flows remains challenging for neural PDE solvers, as small errors in fine-scale structures can accumulate rapidly over rollout. In this paper, we propose FlowRefiner, a flow matching-based iterative refinement framework for 3D turbulent flow simulation. The method replaces stochastic denoising refinement with deterministic ODE-based correction, uses a unified velocity-field regression objective across all refinement stages, and introduces a decoupled sigma schedule that fixes the noise range independently of refinement depth. These design choices yield stable and effective refinement in the small-noise regime. Experiments on large-scale 3D turbulence with rich multi-scale structures show that FlowRefiner achieves state-of-the-art autoregressive prediction accuracy and strong physical consistency. Although developed for turbulent flow simulation, the proposed framework is broadly applicable to iterative refinement problems in scientific modeling.

Large Language Models (LLMs) can propose rules in natural language, sidestepping the need for a predefined predicate space in traditional rule learning. Yet many LLM-based approaches ignore interactions among rules, and the opportunity to couple LLMs with probabilistic rule learning for robust inference remains underexplored. We present RLIE, a unified framework that integrates LLMs with probabilistic modeling to learn a set of weighted rules. RLIE has four stages: (1) Rule generation, where an LLM proposes and filters candidates; (2) Logistic regression, which learns probabilistic weights for global selection and calibration; (3) Iterative refinement, which updates the rule set using prediction errors; and (4) Evaluation, which compares the weighted rule set as a direct classifier with methods that inject rules into an LLM. We evaluate multiple inference strategies on real-world datasets. Applying rules directly with their learned weights yields superior performance, whereas prompting LLMs with the rules, weights, and logistic-model outputs surprisingly degrades accuracy. This supports the view that LLMs excel at semantic generation and interpretation but are less reliable for precise probabilistic integration. RLIE clarifies the potential and limitations of LLMs for inductive reasoning and couples them with classic probabilistic rule combination methods to enable more reliable neuro-symbolic reasoning.

While guided decoding, especially value-guided methods, has emerged as a cost-effective alternative for controlling language model outputs without re-training models, its effectiveness is limited by the accuracy of the value function. We identify that this inaccuracy stems from a core distributional gap: existing methods train static value functions on trajectories sampled exclusively from the base policy, which inherently confines their training to a narrow and suboptimal view of the potential output space. We propose Iterative Value Refinement, a evolutionary framework designed to narrow this gap. It employs Value Exploration to provide a more comprehensive and robust training signal, complemented by Iterative Self-Refinement, which uses the improved value function from one iteration to guide the generation of higher-quality data for the next. Extensive experiments on text summarization, multi-turn dialogue, and instruction following demonstrate the effectiveness of our framework in aligning language models. Our approach not only achieves alignment but also significantly reduces computational costs by leveraging principled value function optimization for efficient and effective control.