Iterative

The fixed-charge network flow problem (FCNFP) couples continuous flow allocation with discrete arc-activation decisions, making it a canonical but computationally challenging model for a variety of network design and resource allocation problems. Exact mixed-integer linear programming formulations capture the fixed-charge structure faithfully, but often become difficult to solve on large networks. We propose a scalable continuous-optimization algorithm for large-scale single-commodity FCNFP based on an iteratively reweighted least-squares (IRLS) framework. The method replaces the discontinuous fixed-charge and linear arc cost objective with a smooth nonconvex Lasry--Lions surrogate and solves a sequence of weighted quadratic flow subproblems. Each subproblem is solved by a warm-started dual semismooth Newton method whose Newton systems have weighted graph-Laplacian structure, enabling the use of modern Laplacian solvers. To further improve the discovered arc supports of the challenging underlying combinatorial problem, we also develop an algorithmic variant that incorporates objective-driven perturbation restarts and an anchor-union restricted search that jointly leverages supports discovered by IRLS and by complementary FCNFP heuristics. Computational experiments on 410 benchmark, synthetic, and large-scale instances show that our method obtains the best objective quality among the evaluated scalable FCNFP algorithms, with a mean gap of $1.316\%$ to a time-limited MILP reference and a win-or-tie rate of $90.0\%$ among the non-MILP methods. The results indicate that combining smooth continuous optimization with support-level search is an effective strategy for producing high-quality feasible solutions to large-scale FCNFP.

Large language models (LLMs) have become ubiquitous in software development, with LLM-based automated program repair tools increasingly used during code review. In this report, we explore the iterative blind use of LLMs as bug-fixers. Across multiple models and repair environments, we find that LLMs consistently claim to detect bugs in entirely bug-free programs while the rate of repair of buggy programs is less than that of the damage to correct programs. We also explore the long-term dynamics of this iterative process, and find that this frequently reaches a pseudo-bug-fixing cycle where the same changes are added and removed again ad infinitum. Lastly, via mechanistic probing, we unveil the existence of a steering vector which controls the editing propensity, suggesting that LLMs have an internal representation of ``buggy code", and that this representation is what is falsely activated to induce pseudo-bug fixing. These results provide insight towards the dynamics of fully autonomous bug-fixing systems, as well as stopping conditions under ambiguous goals.

Learning solution operators across broad parameter ranges can require substantial coverage of both input functions and physical parameters, particularly for purely data-driven parametric models. In addition, the resulting models may fail silently outside the training distribution. We introduce equation recast, which reformulates parametric operator learning as the learning of a single canonical operator. Parameter-induced operator variations are derived analytically from the governing equation and absorbed into effective sources, enabling zero-shot prediction across new parameter regimes. Across multi-parameter, nonlinear, and singular PDE settings, equation recast supports extrapolation, integrates sparse heterogeneous datasets in a shared canonical representation, and uses loss of convergence as an internal warning signal for failure of the recast iteration. In high-fidelity tokamak simulations for nuclear fusion, the framework unifies electron-temperature data across four device geometries through canonical-domain mapping within one jointly trained operator. Equation recast provides a route toward reusable neural PDE solvers combining equation-guided transfer, data efficiency, and monitorable inference.

Text-guided image fusion has recently emerged as an effective paradigm for integrating multi-modal information while enabling flexible and task-oriented fusion control. However, existing text-guided fusion methods often rely on shallow semantic-visual interaction and limited attention mechanisms, which restrict their ability to robustly handle complex degradations and fully exploit textual guidance. In this paper, we propose an iterative text-guided image fusion framework that incorporates text-conditioned feature interaction across multiple fusion and refinement stages. The proposed method integrates deepest-level Cross-Attention, multi-scale Cross-Gate Fusion, and stage-specific text-conditioned modulation, allowing the global text embedding to condition hierarchical feature fusion and residual refinement. By repeatedly injecting the pooled text embedding across hierarchical decoder and refinement stages, the proposed framework provides degradation-aware global semantic conditioning while preserving complementary information from the visible and infrared modalities. Experiments on several benchmark datasets show that the proposed method improves several information-preservation and perceptual-quality metrics, while exhibiting metric-dependent trade-offs on some datasets.

Robust estimation of the relative pose between two cameras is a fundamental part of Structure and Motion methods. For calibrated cameras, the five point method together with a robust estimator such as RANSAC gives the best result in most cases. The current state-of-the-art method for solving the relative pose problem from five points is due to Nister [9], because it is faster than other methods and in the RANSAC scheme one can improve precision by increasing the number of iterations. In this paper, we propose a new iterative method, which is based on Powell's Dog Leg algorithm. The new method has the same precision and is approximately twice as fast as Nister's algorithm. The proposed method is easily extended to more than five points while retaining a efficient error metrics. This makes it also very suitable as an refinement step. The proposed algorithm is systematically evaluated on three types of datasets with known ground truth.

How many directions does a neural representation use to encode a concept? A common answer repeatedly erases probe directions and reports the stopping count or cumulative removed rank. We show that both quantities can change under an information-preserving invertible reparameterization, so neither is intrinsically a concept dimension. We distinguish model-defined population quantities (generating dimension, sufficient linear dimension, and minimum guarding rank) from procedure-defined quantities such as stopping count and cumulative edit rank. In a population Gaussian construction, an invertible shear preserves the prediction problem and all three quantities, yet changes the cumulative Euclidean erasure count from one to two. The separation holds for Moore--Penrose ordinary least squares and every finite nonnegative ridge weight. For a two-output full-QR procedure matching our motivating video analysis, cumulative edit rank similarly changes from two to the ambient dimension four. Conversely, the complete cumulative metric-QR trajectory is affine-equivariant when its positive-definite metric, probe, regularizer, and tie-breaking are transported consistently; exact covariance is one corollary, not a canonical semantic metric. In a known-rank finite-sample Adam/QR calibration, identity mixing stops after one accepted update in all 20 large-sample runs, whereas each tested shear $a\in\{.5,.75,1,1.25,2\}$ accepts at least two updates in all 20 runs. Controlled reparameterizations of frozen V-JEPA2 features preserve rank-zero predictions yet alter later Euclidean trajectories under practical optimization. These visual contact experiments are stress tests, not estimates of contact dimension. Iterative erasure therefore returns a procedure-relative estimand jointly determined by representation geometry and the full measurement procedure, not a semantic dimension by itself.

Offline reinforcement learning repeatedly trains policies from a fixed transition pool, making redundant data costly across seeds and hyperparameters, while naive subsampling can remove rare transitions needed for long-horizon credit assignment. We introduce CODS, a critic-guided selector that alternates between fitting an algorithm-matched critic and acquiring high-residual transitions before freezing a reusable subset. Unlike prioritized replay, CODS produces a static artifact; unlike one-shot residual selection, it refreshes scores as the critic changes. At a 10% budget, CODS retains 96.6% of eligible-pool performance across 20 valid D4RL task--algorithm cells. It exceeds ReDOR and OPER on 19/20 cells and every other subset baseline on 20/20; all six subset advantages remain significant under predeclared hierarchical inference with Holm correction. Holding total selector updates fixed, five acquisition rounds improve four representative cells by 11.23 points over one round and saturate thereafter. Equal-pass and equal-hour evaluations clarify that reuse, rather than a single-run speedup, creates the compute advantage. Mechanism and corruption interventions expose both useful sparse-reward enrichment and sensitivity to outliers. Finally, a whole-trace extension retains 95.4% of pooled ALFWorld success and 96.5% of pooled GSM8K exact match. CODS is therefore a reusable selection procedure, not a formal coreset guarantee.

Generative models are often evaluated through singular artifacts, whereas human creativity typically emerges through iterative generation, appraisal, and refinement. This pilot study examines whether iterative search improves LLM creativity by adapting FunSearch to recipe generation for the 2024 Pillsbury Bake-Off and evaluating outputs against human benchmarks using TTCT-based LLM evaluation. Across two experiments, we test iteration count, generator temperature, and in-loop selection-scorer model size. Results show that iterative generation-selection can produce recipes with creativity scores comparable to human benchmarks, but additional iterations alone do not improve creativity. The in-loop evaluator matters most: a smaller selection scorer yields significantly higher scores across most TTCT dimensions, while temperature has limited effects except for originality. These findings suggest that evaluator design is a first-order design variable in subjective creative search.

Synthetic 3D scene generation is increasingly used as a data source for computer vision and embodied AI, but existing generators often optimize perceptual realism without reliably satisfying task-critical functional constraints. This mismatch limits the usefulness of synthetic data for downstream training, where accessibility, traversability, and spatial rule compliance are often essential. We present iARCS, an iterative agentic reinforcement learning framework that adapts a pretrained scene generator to natural-language task requirements. iARCS uses a two-stage strategy: universal-reward pretraining to improve physical plausibility and layout quality, followed by task-specific fine-tuning with LLM-generated reward programs that are iteratively refined from training feedback. Experiments show improved constraint fidelity on walkability, reachability, and clearance-focused tasks, effective task-specific constraint optimization, and competitive scene diversity. We further show that data generated by iARCS improves a base generator, supporting its value as a practical synthetic data generation tool rather than only a controllable scene editing method.

Unmanned aerial vehicle (UAV) photogrammetry requires camera networks that provide sufficient surface coverage, image overlap, parallax, and resolution, yet conventional flight patterns are often poorly adapted to scene geometry resulting in local reconstruction errors. This paper proposes an iterative hybrid discrete-continuous viewpoint planning method for targeted UAV photogrammetry from a proxy reconstruction. The method scores sampled surface points using photogrammetric heuristics based on frontality, imaging distance, parallax, and multi-view observation count, while also evaluating the full viewpoint set in terms of visibility, pairwise overlap, and graph connectivity. Candidate viewpoints are generated around weakly observed regions, refined using clustered Covariance matrix adaptation evolution strategy (CMA-ES) optimisation, and removed when redundant. The final flight path combines close-range detail viewpoints with wider model-coverage viewpoints, balancing local reconstruction quality with global image-network robustness. Evaluation on three synthetic scenes shows that the proposed method improves both reconstruction accuracy and completeness compared with prior UAV path-planning methods.

This work studies model-free reinforcement learning for co-safe linear temporal logic (sc-LTL) objectives in finite Markov decision processes, which can be reduced to maximal reachability objectives via the standard product construction. For this problem, direct sample-based bootstrap methods (e.g., TD or Q-learning) may fail to converge to optimal policies due to the noncontractive nature and nonuniqueness of solutions to the Bellman equation. We develop a new two-step model-free reinforcement learning method that first uses a discounted surrogate to identify a clamp set that resolves this nonuniqueness, and then applies undiscounted policy evaluation and greedy policy improvement with guarantees of finding an optimal solution. We prove almost-sure convergence of the policy evaluation step and finite termination of the policy iteration algorithm at an optimal policy. These theoretical results are validated through numerical experiments on a stochastic grid world.

Hasse clustering is an algorithm that extracts common patterns in sequential data and represents them in graphical forms. As the number of expected clusters grows, however, the algorithm can become infeasible to run due to combinatorial complexity. In this article, we describe a theory of gluing wiring diagrams, allowing iterative applications of Hasse clustering to achieve the same result as a single application. We test our theory in the context of classifying videos of figure skating jumps.

Zermelo's algorithm is a classical method for computing the maximum likelihood estimator in the Bradley--Terry (BT) model, but its convergence can be slow in practice. To accelerate computation, Newman introduced a family of Zermelo-type fixed-point iterations parameterized by $α$, with Zermelo's algorithm recovered at $α=1$. Empirical evidence suggests that the choice $α=0$ often converges substantially faster, making it a promising alternative, yet the mechanism underlying this acceleration remains elusive. This paper provides theoretical insight into this phenomenon through a systematic local convergence analysis. We derive closed-form expressions for local convergence factors under synchronous and asynchronous updates and analyze their dependence on $α$ via spectral analysis of the associated Jacobian matrices. For synchronous updates, we show that the algorithm may fail to converge when $α<1$, and its local convergence factor is quasi-convex in $α$ under the population BT model. In contrast, asynchronous updates are always locally convergent, and their local convergence factor is provably monotonically increasing in $α$ under the population BT model of consistently ordered bipartite comparison graphs, establishing the optimality of $α=0$ in this setting. We further establish asymptotic approximation results for the population convergence factors under the BT model, justifying their practical relevance. Numerical experiments on synthetic and real-world datasets confirm the theory. Our analysis complements existing convergence results and shows that the acceleration of $α=0$ arises not only from the parameter choice but, more importantly, from the use of asynchronous updates.

The mammalian kidney concentrates urine using a mechanism with no analogue in current neural architectures: the countercurrent multiplier. Two anti-parallel flows joined at a hairpin recirculate a weak magnitude-bounded local pump into a large axial gradient achieving a four-fold concentration increase from a single-effect gradient that never exceeds 200 mOsm at any point. We formalize this mechanism as a differentiable sequence operator the Countercurrent Multiplier (CCM) layer and study it as an alternative to residual iterative refinement.

Span-level rationales are often assumed to improve controllability in text detoxification, but it remains unclear when such guidance helps and when it introduces trade-offs. We present Awareness-Enhanced Guidance for Iterative Safeguard (AEGIS) as an exploratory framework for studying span-guided multilingual detoxification across English, Mandarin Chinese, and Korean. AEGIS combines span-level detector outputs with frozen generator backbones, allowing harmful spans, intensity labels, and target attributes to be provided as structured guidance during rewriting. Rather than claiming state-of-the-art detoxification performance, we analyze how span guidance affects the balance between toxicity reduction and meaning preservation across generator families, model scales, and languages. Our results suggest that span-guided detoxification is conditionally useful: explicit rationales change the trade-off between toxicity reduction and meaning preservation, but their effects depend strongly on the generator backbone and the linguistic context. These findings highlight both the promise and the limitations of span-level control signals for multilingual detoxification.

Given a binary-labeled linearly separable dataset, and the objective is to compute the maximum-margin separating hyperplane, also known as the hard-margin Support Vector Machine (SVM) classifier. This paper investigates whether, if given an initial separating hyperplane, can it be exploited to reach this unique optimum more efficiently. We present a geometric approach that gradually improves the alignment of the hyperplane, starting from an initial separating hyperplane, while preserving separation and continuously increasing its margin until convergence to the global optimum. At each iteration, the method considers only local information, namely the current active set, and aims to re-align the hyperplane according to the optimal separating hyperplane of this reduced subset. Consequently, the original convex quadratic optimization problem is addressed through a sequence of smaller subproblems. The paper presents the algorithm in detail, together with a preliminary experimental evaluation and several theoretical findings. The results suggest that, when an initial separating hyperplane is available, the proposed method can be competitive on larger datasets and, in some cases, can outperform state-of-the-art approaches that solve the optimization problem directly.

Disentangled representation learning is a powerful paradigm for robust attribute prediction. While recent methods address attribute correlations, hidden correlations remain underexplored, where data under the value of a certain attribute exhibit underlying modes correlated with other attributes. To preserve mode information and achieve disentanglement, we jointly discover modes and enforce mode-based conditional independence. Yet, the interdependency between these two modules may lead to error amplification under naive iterations. We propose Coordinated Disentanglement with Iterative mode Discovery (CoDID), an end-to-end framework featuring a dynamic architecture that adapts to evolving number of modes, and a coordination mechanism that mitigates error amplification via meta-optimization. Empirical results demonstrate the state-of-the-art performance on diverse tasks.

Validating autonomous driving systems requires diverse, regulation-compliant test scenarios. In simulation-based testing, scenarios are defined as executable scripts. Yet automatically generating such scripts from regulatory descriptions remains an open challenge, and existing approaches face fundamental trade-offs. Retrieval-assemble methods achieve reasonable compilation rates but lack scalability, whereas retrieval-based full-script generation suffers from low compilation success rates. We present Chat2Scenic, the first iterative retrieval-augmented framework to generate scenario scripts in Domain Specific Language (DSL). Specifically, Chat2Scenic provides a chatbot interface that supports interactive scenario refinement and integrates Retrieval-augmented Generation (RAG) to ground scenario generation in regulatory knowledge and DSL syntax. Furthermore, we propose an open benchmark for scenario generation comprising 123 scenarios from various regulations, including NHTSA and United Nations Vehicle Regulations, as well as other sources. Extensive evaluation with State-of-the-Art (SOTA) Large Language Models (LLMs) demonstrates that Chat2Scenic achieves 76.42% Compilation Success Rate (CSR) and 58.17% Framework Accuracy (FA), outperforming existing methods (Retrieval Assemble with 30.08% CSR, 11.03% FA and Retrieval full script generation with 16.26% CSR, 10.86% FA). To facilitate future research, we release our code as open source at https://github.com/TUM-AVS/chat2scenic.

Bilevel optimization underpins many machine learning applications, including hyperparameter optimization, meta-learning, neural architecture search, and reinforcement learning. While hypergradient-based methods have advanced significantly, a gap persists between theoretical guarantees and practical single-loop implementations required for efficiency. We bridge this gap by establishing sharper convergence results for single-loop approximate implicit differentiation (AID) and iterative differentiation (ITD) methods, leveraging our proposed analytical framework, decoupled norm analysis (DNA). For AID, we improve the convergence rate from $\mathcal{O}(κ^6/K)$ to $\mathcal{O}(κ^5/K)$, where $κ$ is the condition number of the inner-level problem. For ITD, we prove that the asymptotic error is $\mathcal{O}(κ^2)$, exactly matching the known lower bound and improving upon the previous $\mathcal{O}(κ^3)$ guarantee. Numerical experiments on synthetic and real tasks corroborate our theoretical findings.

We propose OptiAgent, a multi-agent framework that, given a natural language description of an Operations Research problem, is able to output a solver-ready mathematical formulation as well as executable code. Our architecture prioritizes the mathematical modeling step, where dedicated agents extract structures, such as decision variables and constraints, enabling iterative self-correction. We introduce a novel multi-loop validation architecture with four specialized feedback mechanisms, each targeting a distinct failure mode such as misinterpretation, structural defects, mathematical inconsistencies, validation failures, and code errors. Alongside accuracy, our modular design improves the process of solving optimization problems by improving transparency, as each agent exposes its reasoning and feedback, making the full modeling process auditable. Our framework achieves state-of-the-art performance on 3 out of 4 benchmarks across LP, MILP, and Nonlinear Programming tasks, while remaining highly competitive on the remaining dataset.

Code-switching (CS), alternating languages within the same utterance, poses significant challenges for automatic speech recognition (ASR) due to limited CS training data. This paper applies an iterative pseudo-labeling training approach to CS-ASR for the first time, demonstrating its effectiveness in leveraging unlabeled data to improve CS-ASR performance. The approach comprises three phases: pseudo-label generation, two-stage bilingual model training, and iterative improvements. It begins by generating pseudo-labels from a large unlabeled corpus, creating a semi-supervised dataset. This dataset supports a two-stage training framework where the model is pre-trained and then fine-tuned on supervised CS data. Iterative refinements further enhance the model's accuracy in handling complex CS scenarios. Our approach significantly advances CS-ASR systems, achieving notable Mix Error Rate (MER) reductions on SEAME's devman (6.35%) and devsge (8.29%) subsets.

Adversarial attacks guide and provide additional training and test data for both adversarial training and adversarial robustness validation, and expose the 'piecewise linearity' of deep learning based models. Since adversarial attacks and adversarial robustness are mathematically defined problems that can be optimised directly with end-to-end differentiable search, adversarial robustness is more widely applicable than other robustness metrics such as corruption and perturbation robustness, and new kinds of adversarial attacks are beneficial for robustness testing. Attacks are targeted or non-targeted depending on whether the image is modified to misclassify to a particular class or to any incorrect class; we focus on the non-targeted setting. Finding the optimal input data points and hyper-parameters for generating non-targeted adversarial attacks remains a challenge for current methods like the Fast Gradient Method, Basic Iterative Method and Virtual Adversarial Method. We propose a new method, the "Binary Iterative Method" (BinIM), which uses a divide-and-conquer paradigm to optimise parameters and hyper-parameters for the generation of non-targeted attacks. We compare our method to other gradient-based adversarial attacks evaluated over pre-trained networks (InceptionV3, InceptionV2, ResNet V2 152) on classification tasks. On 1000 randomly-sampled images from the standard ImageNet dataset, the Binary Iterative Method outperforms all other gradient-based methods, qualitatively making the classifier misclassify with confidence up to 0.995 while reducing the probability of the true label to 2.21e-09 (approximately 0).

As AI coding agents become more autonomous, they increasingly ship code iteratively, with the codebase persisting across sessions. This persistence creates a new attack surface: a misaligned or prompt-injected agent can distribute attacks across pull requests (PRs) and time its payload for the PR with the best natural cover. To study the resulting dynamics, we introduce Iterative VibeCoding, a setting for AI control, the study of safely deploying capable but potentially untrusted AI. In Iterative VibeCoding, a coding agent builds software over a sequence of PRs in a persistent codebase while pursuing a covert side task. Our benchmark includes two task families: CLI tools and Flask web services, across 20 total task variations. We use Claude Sonnet 4.5 as the attack agent and GPT-4o as the monitor. We compare gradual attacks, which distribute the side task across PRs, against non-gradual attacks concentrated in a single PR. No single monitor is robust to both: which strategy evades best (success while evading the monitor) depends on the monitor type, so a defender cannot close off both gradual and non-gradual attacks with any one monitor. High evasion (>= 65%) generalizes across model attack agent backends (Sonnet 4.5, Gemini 3.1 Pro, Kimi K2.5), confirming this is a property of the persistent-state attack surface rather than a single model's capability. Evasion also remains high across state-of-the-art monitor models and the gap between gradual and non-gradual evasion widens for more capable models. We introduce a stateful link-tracker monitor that tracks suspicious buildup across PRs. On both task families, it detects gradual attacks substantially better than diff monitors that merely see more accumulated history. Combining this stronger monitor with trajectory monitors in a four-monitor ensemble reduces gradual-attack evasion from 93% under the weakest standard diff monitor to 47%.

Pervasive data contamination -- stemming from measurement errors, outliers, or adversarial corruption -- has motivated the development of robust statistical methods. In this context, we propose a two-stage Adversarial Contamination-resistant Iterative Hard Thresholding (AC-IHT) algorithm for high-dimensional regression with contamination. Our nonconvex algorithm achieves minimax near-optimal (up to logarithmic terms) estimation by iteratively updating the coefficient vector and the contamination vector with different thresholding scales. We further demonstrate that our AC-IHT estimator is signal-adaptive: under proper signal conditions, it adaptively attains a sharper estimation rate and more accurate support recovery. Moreover, it enjoys the strong oracle property, laying a theoretical foundation for asymptotic inference. Numerical experiments confirm its superior finite-sample performance. Finally, we discuss theoretical extensions of the proposed procedure to generalized linear models and to heavy-tailed noise settings.

Web-agent benchmarks overwhelmingly measure depth -- pinning one obscure answer behind a chain of constraints -- while breadth, exhaustively enumerating a closed set and filling each item's attributes, is barely evaluated, especially outside English. Breadth is also hard to build: certifying that a gold set is complete and every cell correct is far costlier than checking a single answer. I introduce \textsc{Ko-WideSearch}, a Korean breadth-search benchmark built by an automated synthesize-and-verify pipeline. Each task names a set-parent entity -- a TV season, a dynasty, a league, an administrative region, an election -- and asks for its full membership plus a per-item attribute table, graded by Item-, Column-, and Row-F1. It spans 228 tables over 190 entities and sixteen categories across three difficulty tiers, set by two structural knobs I dial independently -- table width and a 2-D composite key -- so cross-product membership climbs from 0% to 100% across the tiers. A single normalization-aware comparator is shared between gold construction and grading, so stable date and count columns are not over-dropped on formatting alone. Across twenty web agents, the failure is consistent: agents recover the set but not the rows (e.g.\ Item-F1 92.8 against Row-F1 53.7), accuracy falls steadily as the knobs harden, and neither more search nor more spend closes the gap. Broken down by cell, the hard part is finding the right value, not formatting it: open-ended free-text cells fail most, while cells with a standard answer such as a date or a name usually come out right.

Unlike diffusion-based models that operate in continuous latent spaces, autoregressive unified multimodal models produce images by sequentially predicting discretized visual tokens. These tokens are derived from a codebook that maps embeddings to quantized visual patterns. The language-like architecture enables unified multimodal models to effectively capture text conditional information for generation, making them promising for text-to-image tasks. This also raises an interesting question: how safe are the images generated in such an autoregressive way? In this work, we propose iterative self-improving codebooks for safe autoregressive generation. We leverage the understanding and judgment capabilities of the unified multimodal model itself to identify unsafe generated images without human annotation. Subsequently, the inherent representations in the codebook are fixed to eliminate harmful mappings. Our method comprises two steps: first, we use the unified model to identify unsafe generations and construct corresponding harmful and safe image-text pairs. These pairs are used to construct the Harmful Space and guide updates to the codebook, thereby eliminating harmful outputs. Second, we perform adaptive fine-tuning on the codebook within the harmless space using safe image-text pairs to ensure the quality of generated images. These two steps are repeated until no further improvement is observed, producing a safety-enhanced model codebook. Without additional external feedback, the safety of models is improved iteratively.

Differentially private (DP) training of neural networks is often hindered by the large amount of noise required by gradient-based methods such as DP-SGD, which repeatedly inject high-dimensional noise in parameter space throughout training. In this paper, we propose a new framework for DP learning that avoids iterative optimization in parameter space. Instead of updating the target model using privatized gradients, we employ a hypernetwork trained on public datasets to map a private dataset to the parameters of the target model. Specifically, each example is embedded into a low-dimensional representation, the embeddings are aggregated and perturbed to obtain a DP dataset embedding, and the hypernetwork generates the target model parameters from this noisy embedding. Because privacy noise is injected only once into a low-dimensional dataset representation, our approach can significantly reduce the adverse effect of noise. We theoretically show in a synthetic setting that, under a fixed privacy budget, models produced by our approach achieve higher utility than those trained with DP-SGD. Moreover, we apply our approach to LoRA fine-tuning of diffusion models and show that it achieves lower FID than LoRA models trained with DP-SGD and other public-data-guided methods.

We present an iterative algorithm to compute an arc-length parameterized spline interpolating a set of points. This differs from other methods where the computed spline either does not interpolate the original points or the parameterization is not the arc-length of the returned curves. Our method is applicable in any dimension $D \ge 2$, and we illustrate it with numerical results for plane curves.

Operator learning is an emerging field at the intersection of machine learning and scientific computing. By learning mappings between function spaces, neural operators provide data-driven surrogate models for families of partial differential equations (PDEs). Once trained, these models can evaluate solution operators efficiently, making them suitable for many-query applications such as real-time prediction and parameter sweeps. However, maintaining high approximation accuracy and stable long-term predictions remains challenging for complex forward and inverse problems. To address these challenges, we propose the Starter-Iterator Neural Operator (SINO), which incorporates the initialization and residual-correction structures of classical iterative solvers into neural operator learning. The frequency-domain Starter captures dominant global spectral features and provides an informed initial approximation, while the latent-space Iterator applies successive residual-based corrections to refine local and multiscale solution structures. Experiments on representative time-dependent PDEs, including the Navier-Stokes and acoustic wave equations, together with applications to image super-resolution and weather forecasting, show that SINO achieves competitive accuracy and stable performance across the benchmarks considered in this work.

AI-driven engineering workflows face particular challenges in crash safety design: unlike aerodynamics, crash events involve highly nonlinear contact dynamics, material nonlinearity, and discrete state transitions that are difficult to capture with data-driven surrogate models. To the best of our knowledge, we present the first foundation model--orchestrated workflow for crash safety design that enables surrogate-assisted exploration for pedestrian protection, reducing evaluation time from hours per CAE simulation to seconds. The workflow integrates four components: (1) a surrogate trained on CAE crash simulations to predict pedestrian leg injury metrics from design parameters, achieving an average $R^2=0.87$ and providing distribution-free conformal prediction intervals; (2) multiobjective evolutionary search (NSGA-II) to discover diverse feasible parameter sets under user-specified constraints; (3) a morphing-based geometry generator that maps parameters to topology-preserving 3D shapes; and (4) a natural-language interface in which an LLM orchestrates the workflow and a vision--language model supports semantic comparison of generated designs. In an automotive front-bumper case study, the workflow produces 35 distinct safety-compliant alternatives from a single exploration, a process that would require weeks with conventional CAE iteration. These results suggest that foundation models can serve as integration layers between ML surrogates and physics-based simulation, helping bring AI capabilities to safety-critical engineering domains.

This paper focuses on automatically generating informative ad descriptions in sponsored search. Unlike ad titles which are usually optimized to attract user click feedbacks, ad descriptions have a longer text span and possess the potential of incorporating world knowledge to address user search intents while presenting the fine-grained selling points of the ads. We propose Interactor, a multi-turn iterative creation framework optimized with agentic RL for ad description generation. The generation model acts as a policy that interacts with a customized environment consisting of multiple generative reward models. Given initial generations by the policy, the customized GenRMs evaluate multi-dimensional qualities including knowledge capacity and landing page consistency, providing both binary signals and reasoning feedbacks. The policy then iteratively refines the descriptions based on such feedbacks to ensure continuous improvement. Experiments on industrial datasets show that the Interactor framework significantly outperforms state-of-the-art approaches in generating knowledge-rich and faithful ad descriptions. Since May 2026, it has been deployed online in a leading search ads system, contributing to both ad revenue and user experience.

We present a modular two-agent simulation framework for evaluating conversational shopping assistant architectures. An independent buyer agent, configured with personas, missions, and patience levels, is paired with an interchangeable responder that integrates with a real e-commerce search API. Holding the buyer constant across experiments enables controlled comparison of responder designs on identical scenarios. Using 2011 conversations across 14 persona buckets, we establish four empirical findings. First, rolling-window memory outperforms intent-extraction memory on all quality metrics while being 35% faster per query. Second, illustrating rapid evidence-driven iteration, a systematic failure analysis of a responder version enables targeted fixes that reduce failure and near-failure rates by 62% across the full dataset. Third, swapping the responder LLM backbone from Gemini2.5 to Llama3.3~70B costs 0.16--0.45 points despite identical architecture. Finally, we document systematic philosophical disagreement between frontier LLM judges: Gemini rewards process correctness while Claude demands concrete outcomes, despite using the same evaluation prompt.

Missing data is a common challenge in spatiotemporal systems, arising in applications such as air quality monitoring and urban traffic management. Traditional machine learning approaches, like recurrent and graph neural networks, rely on iterative propagation, which tends to accumulate errors over time and space. Recent diffusion-based methods mitigate error propagation but require iterative sampling and often depend on problem-agnostic Gaussian priors, limiting both efficiency and effectiveness. To address these limitations, we propose GiFlow, a Graph-Informed Flow Matching framework for spatiotemporal imputation. GiFlow replaces the typical Gaussian prior with a graph-informed prior constructed via spatiotemporal filtering of observable signals, which better aligns the source distribution to the target and thereby simplifies the generation trajectory. The flow field is parameterized by a hybrid vector field model that integrates spatial attention, temporal attention, and spatiotemporal propagation, enabling joint modeling of spatial and temporal dependencies. Extensive experiments on both synthetic and real-world datasets demonstrate that the proposed GiFlow outperforms the state-of-the-art approaches in spatiotemporal imputation. The code is available at https://github.com/zepengzhang/GiFlow.

Security misconfigurations remain a leading cause of OS-level compromise, and manually keeping systems compliant with standards like Defense Information Systems Agency (DISA) Security Technical Implementation Guides (STIGs) is a tedious and expensive process. Existing compliance automation tools can reduce some of this burden, but they depend on static, pre-written corrective actions. In this paper, we introduce SHIELDS, a multi-agent system that uses large language models (LLMs) to approach OS hardening as an iterative, feedback-driven process. Instead of applying fixed remediations, SHIELDS continuously proposes fixes and refines them based on feedback from target system execution and validation scans. We evaluate the system across multiple virtual machine configurations using six contemporary LLMs ranging from 20B to 400B parameters, and find that SHIELDS successfully remediates up to 73% of scan findings. Our results also suggest that success in this setting depends less on model size (parameter count) than on effective tool use and information gathering, paving a practical path toward reducing the burden of security compliance in environments where compute is limited or security and privacy needs drive local model use.

E-commerce platforms in emerging markets often operate with underdeveloped product catalogs that contain only category taxonomies but lack structured attribute schemas. This absence of fine-grained product attributes limits search capabilities -- preventing faceted filtering, degrading query understanding, and weakening semantic representations used by search systems. We present BEATS, a human-in-the-loop LLM framework for bootstrapping product attribute taxonomies entirely from scratch. Our approach extends a multi-stage LLM generation pipeline with two critical production stages: (1) proactive quality checking by model developers to filter erroneous outputs, and (2) human annotation by domain-expert local staff to validate generated attributes. The framework operates iteratively -- prompts at each generation stage are refined based on quality check observations and annotator feedback across successive rounds, progressively improving attribute quality. Once the attribute taxonomy is established, we employ LLMs to perform structured attribute tagging on individual product items, enriching their contextual representations. The enriched catalog directly benefits multiple components of the search system: enabling granular attribute-based filtering, providing structured features for ranking models, and improving semantic representations for dense retrieval. We validate the generated taxonomy by training dense retrieval models on attribute-enriched product data, demonstrating consistent improvements over baselines using original catalog information. Our system has been deployed at Rakuten Taiwan, enriching 9 major categories spanning 2,694 sub-categories with 67,277 generated attributes, and over 5.4 million products have been tagged with the generated attributes, with plans to enrich the entire product catalog.

Mixture-of-Experts (MoE) and looped architectures scale models along two orthogonal axes, namely parameter capacity and effective depth. However, mainstream looped architectures rely on dense backbones that couple parameter count with per-token FLOPs, which makes it impossible to isolate the effect of iterative computation under matched budgets. To this end, we present LoopMoE, a looped MoE language model that integrates sparse routing with iterative weight-shared computation through two designs. The first is IterAdaLN, which resolves weight-sharing symmetry via a modulation signal jointly conditioned on the iteration index and the per-token hidden state. The second is a capacity-balancing strategy that recovers the attention-to-FFN active parameter ratio of well-tuned non-looped references. Together, these designs enable the first strictly controlled, head-to-head evaluation of a looped MoE against a Vanilla MoE under identical total parameters, per-token FLOPs, and active sublayer ratios. At the 3B scale, LoopMoE outperforms the Vanilla MoE on 8 of 9 downstream benchmarks with an average improvement exceeding 1 point. At the 9B scale, LoopMoE continues to outperform the matched Vanilla MoE, indicating that the architectural gain persists at larger scale. Our work establishes a controlled synthesis of sparsity and recurrence, and suggests a promising direction for looped language models.

We study simultaneous alternating power iteration for fixed-order asymmetric rank-one spiked tensor models. Our main contribution is a finite-iteration local theory that is independent of any particular initialization. Once the iterates enter a sufficiently small neighborhood of the planted rank-one direction, their error decomposes into a geometrically decaying transient and an intrinsic noise floor caused by fixed orthogonal noise contractions at the planted point. The deterministic finite-sample conditions are stated explicitly, but under a coarse fixed-order multilinear noise event they reduce to a conservative high-signal regime for fixed or slowly expanding local radii. We then separate the warm-start mechanism from any specific spectral construction. A generic one-sweep principle shows that, if a sign-compatible initializer has correlation $γ_N$, first-sweep noise level $a_N$, and $a_N/(γ_N^{d-1}ω_{N,d})\to0$, then one can choose an expanding radius $r_N=o(ω_{N,d})$ for which the first sweep enters the local basin. After entry, the local affine contraction yields convergence to the unique informative local fixed point in that basin. For centered-Gram initialization, we verify the required correlation and same-sample first-sweep noise bound under i.i.d. finite-fourth-moment noise by a signal-preserving noise-only leave-one comparison and an averaged leave-one slice-contraction estimate, which we call a pressed-back estimate. The leave-one comparison keeps the spike fixed and averages over the deleted coordinate, so planted coordinates enter through $\ell_2$-weighted sums rather than worst-case incoherence bounds.

Recent advances in large language models and agentic AI systems have enabled significant progress in mathematical discovery, from solving competition problems to tackling research-level conjectures. However, open problems in computational mathematics have received comparatively less attention: research in this area often requires not only proofs but also numerical experimentation, adversarial constructions, and algorithm design. In this paper, we introduce an agentic research system, Iteris, designed for open problems in computational mathematics. We apply Iteris to two open problems from a recent Simons Workshop collection (arXiv:2602.05394). In these case studies, Iteris generated numerical evidence, constructions, and proof drafts that led, after expert review and correction, to verified results. The first result is a phase diagram for the asymptotic comparison between conjugate gradient and randomized coordinate descent on power-law spectra; the second is a counterexample showing that QR factorization with column pivoting can fail to select well-conditioned submatrices even under low coherence. These case studies suggest that agentic AI systems can participate meaningfully in research workflows for open problems in computational mathematics, while human validation remains essential.

The burgeoning field of LLM-based Multi-Agent Systems (MAS) promises to tackle complex tasks through collaborative intelligence, yet fundamental questions regarding their scaling behavior and intrinsic collective dynamics remain underexplored. This paper systematically investigates how the performance of a homogeneous MAS evolves as the number of agents increases, isolating the variable of collaboration from model or knowledge heterogeneity. We propose the Sequential Iterative Multi-Agent System (SIMAS) framework, a minimalist architecture centered on sequential inter-agent communication, to clearly observe scaling effects. Through extensive experiments across diverse tasks and model scales, we establish that MAS performance does not scale monotonically with agent count but follows a pattern of diminishing returns, governed by a trade-off between collaborative synergy and coordination overhead. Our findings reveal that effective MAS requires a sufficiently capable base LLM, that task type critically modulates the optimal agent count, and that collective intelligence is an emergent property contingent on strategic interaction design rather than a guaranteed outcome of agent plurality. The performance degradation stems coordination overhead rather than merely long-context failure, and the scaling tendency generalizes across interaction architectures like structured debate topologies. This work provides a foundational understanding of MAS scaling laws, offering practical guidance for designing efficient collaborative systems and challenging the prevailing assumption that more agents invariably lead to better performance.

This study presents an iterative AI-guided workflow that accelerates graphite-based anode development by improving both formulation feasibility and process robustness. Sequential learning via AI/ML-guided multiobjective inverse design for anode optimization was implemented using the Citrine Platform. Starting from a noisy, incomplete dataset, the Citrine Platform was used to generate early surrogate models, which despite low predictive certainty highlighted missing process constraints. By iteratively adding feasibility labels and boundary condition failures, the workflow rapidly converged toward manufacturable, higher-performing formulations. Fabrication reliability improved from frequent process failures to 100% successful cell production, while the fraction of cells delivering $\geq$ 350 mAh g$^{-1}$ increased from 28.4% to 84.8%, with capacity retention rising from 42.1% to 97.3%. These results demonstrate that structured, feedback-driven AI workflows can transform imperfect industrial data into actionable guidance, enabling faster, more reproducible optimization of battery electrode manufacturing.

Embodied Large Language Models (LLMs) are increasingly used as reasoning modules in robotic control pipelines to improve human-robot interaction, but their memory and generation latency make real-time deployment difficult. Pruning can reduce these costs, but for controllers that undergo multiple pre- and post-training phases, the crucial question is not only how much to prune, but when pruning should occur. In this work, we propose Before Parc Fermé (BPF), a pruning strategy performed during RL that compresses embodied LLM controllers while they are still being optimized for closed-loop behavior. This allows pruning decisions to account for the task-specific supervision and closed-loop feedback that shape the final controller. We propose two variants: BPF-RL, which performs iterative pruning during RL by removing part of the model at predefined training intervals, and BPF-SFT/RL, which first prunes part of the model structure during SFT and then further compresses it during RL using the same iterative strategy as BPF-RL until the target pruning ratio is reached. We evaluate BPF on RobotxR1, an LLM-based autonomous-driving control pipeline, using an established LLM pruning framework (LLM-Pruner), and compare it against post-training pruning, post-training pruning with RL recovery, SFT-stage pruning, and smaller dense models from the same family. Our results show that BPF provides the best task-performance vs. memory and throughput trade-off among the considered pruning strategies. When compressing the larger RobotxR1 models, BPF-SFT/RL achieves a $1.69\times$ better size-end-to-end performance trade-off than directly selecting a smaller dense model from the same family, measured as removed parameters per lost percentage point of control adaptability. On the Jetson AGX Orin mounted on the target robotic platform, the compact models improve decode throughput by up to $27\%$.

Infant biometrics presents unique challenges due to the physiological differences between infants and adults, compounded by the scarcity of available data for research that limits the development of robust matching systems. This paper proposes a novel data augmentation method that uses iterative techniques to generate diverse variants of segmented fingerprints by inducing errors in a convolutional neural network trained to extract fingerprint ridges and valleys. Experiments on real infant fingerprints demonstrate the method's effectiveness in expanding fingerprint variability, with augmentations exhibiting significant fluctuations in minutiae counts while still retaining visual similarity to the originals. The study also highlights the method's customizable nature for applying varying levels of changes to fingerprint segmentations. Future research includes training segmentation and matching neural networks using datasets augmented by the proposed framework.

Large language models (LLMs) are increasingly used as generators in iterative neural architecture search (NAS), yet no formal convergence theory exists for this class of algorithms. We model iterative LLM-NAS as a parametric Cross-Entropy (CE) method over executable programs and prove six results: (1) iterative LLM fine-tuning on elite architectures is equivalent to the CE update restricted to the LLM parametric family; (2) expected architecture quality is monotonically non-decreasing across cycles; (3) elite-set probability converges to a fixed point at a geometric rate C_t >= 1-(1-rho_0)^t; (4) delta-based generation achieves a strictly higher valid-generation rate than full-code generation under a first-order Markov token-error model; (5) the MinHash-Jaccard novelty filter prevents mode collapse; (6) proxy reliability admits the closed-form rho_S = (6/pi) arcsin(rho_P(SNR)/2), yielding the practical diagnostic sigma^2_arch >> sigma^2_noise as a necessary condition for trustworthy proxy-based rankings. Testing against a 22-cycle, three-LLM, six-dataset experiment with 3,300 generated architectures confirms two predictions quantitatively, two at direction-of-effect level, and explains the proxy-reliability ceiling effect previously reported empirically but left unexplained.

The topic of Co-creation, i.e., AI agents interacting with humans to generate outputs (e.g., art), has gained significant attention recently. However, most studies focus on adult-human interactions in a digital setting. This paper explores a novel ludic co-creation scenario involving children and Large Language Models (LLMs) interacting through a physical board game to create written stories. Our goal is to develop a multi-agent framework capable of producing high-quality narratives suitable for young players. At the core of our approach is an iterative Writer-Editor process in which one LLM generates stories while another evaluates them and provides feedback for refinement. Through a simulation study involving multiple LLMs, we show that this iterative interaction consistently improves the perceived quality of generated stories across successive loops. The results indicate that a small number of refinement steps may be sufficient to achieve high-quality outputs in interactive storytelling systems.

Unsupervised learning methods -- topic modeling, partition-based and density-based clustering -- produce data groupings without human guidance, yet choosing and evaluating those groupings should not itself be unsupervised. We present \emph{SmartIterator}(SI), a visual analytics approach that treats the full sequence of grouping results across a parameter sweep as a first-class analytical object. For each method family, SI provides a structured six-phase workflow that guides the analyst through systematic exploration of grouping results -- from quality-metric overview through transition-stability assessment, membership-confidence evaluation, content and context inspection, and recurrent-archetype verification to an informed decision -- building cumulative understanding of data structure along the way. The workflows are operationalized through \emph{IteraScope}(IS), a coordinated visual display combining quality-metric charts with semantic color encoding, a 1D group embedding with Sankey-style transition flows and violin plots of membership confidence, a 2D group embedding with HDBSCAN-detected recurrent archetypes that highlights iterations capturing all persistent patterns, and domain-specific linked views for contextualized interpretation. We demonstrate the three workflows on: (1)~simulated social-media messages from the VAST Challenge 2011 (density-based clustering, validated against ground truth), (2)~EU population statistics across ${\sim}1\,500$ NUTS-3 regions (partition-based clustering), and (3)~30 years of IEEE VIS papers (NMF topic modeling). The workflows constitute the main contribution: they provide actionable, method-specific guidance for navigating parameter spaces, studying how data structure evolves across configurations, and grounding analytical understanding in domain context -- yielding knowledge about the data that no single ``best'' result can provide.

In this work, we propose BAIT (Boundary-Aware Iterative Trap), a three-step jailbreak framework that elicits malicious information through internal disclosure by target large language models (LLMs), instead of external feedback from judge LLMs. BAIT first asks the model to identify the protection boundary, then requires it to refine that boundary, and finally requests a detailed example. By expanding each step upon the model's previous responses, BAIT turns the model's own reasoning and consistency tendency into a disclosure pathway. Experiments on AdvBench, JailbreakBench, AIR-Bench, and SORRY-Bench demonstrate that BAIT consistently achieves strong attack success rates across top-tier large language models, significantly advancing conventional jailbreak baselines. Further analysis reveals that: 1) prevention-oriented framing significantly outperforms direct knowledge requests; 2) the refinement step plays a critical role in disclosure escalation; and 3) the first two steps have a certain chance of eliciting harmful content while triggering little filtering. These findings underscore the necessity of safeguarding against internally driven reasoning trajectories that progressively cross safety boundaries.

Formal verification of large C programs is impeded by state-space explosion: Bounded Model Checking (BMC) tools must encode the entire state space up to the predetermined bound by unrolling all nested constructs. We present ConVer, a top-down compositional verification tool. Given a C program with a top-level assertion, ConVer decomposes verification top-down: it uses a large language model (LLM) to synthesise function contracts from the system property, then alternates system-level and function-level checks in a CEGAR-CEGIS loop, refining contracts whenever a check fails via SMART ICE learning. We evaluate ConVer on four benchmark suites of increasing difficulty and against other state-of-the-art (SOTA) tools. On the Frama-C benchmark of 45 simple C programs, ConVer achieves 82-96% verification success across three LLM backends, with 93-95% of converged programs requiring only a single CEGAR-CEGIS iteration. On the X.509 parser benchmark (6~programs) and LF2C-Simple suite (17 programs), ConVer achieves 33-50% and 82-88% success respectively. On the VerifyThis suite of 11 recursive and loop-intensive programs, the Pre-Abstraction strategy achieves 55-64% success. In addition, we present ESBMC-LF a preprocessor tool that converts LF models to C while preserving the properties of the LF files, enabling ConVer to verify them. We transpile the LF Verifier Benchmarks using ESBMC-LF to C; we denote those LF-Hard. We show that ConVer successfully verifies 67% of LF-Hard benchmarks overall.

Efficiently solving Poisson equations on complex, irregular domains remains a fundamental challenge in scientific computing, as classical iterative solvers often suffer from prohibitive runtime due to ill-conditioned systems. While neural operators offer a fast alternative, they typically rely on large-scale labeled datasets or struggle with unstable training dynamics when using physics-informed residual losses. We propose \textsc{NPSolver}, a neural Poisson solver trained without solution labels via iterative physics supervision. Instead of relying on fully converged numerical solutions or raw PDE residuals, \textsc{NPSolver} utilizes a small number of preconditioned conjugate gradient (PCG) steps to refine its own predictions, providing a more stable and well-scaled training signal. Theoretical analysis confirms that this iterative supervision serves as a well-conditioned error proxy and that a stop-gradient design is essential for optimization stability. To better capture boundary-driven features under mixed boundary conditions, we further introduce the Boundary-Aware Transolver (\textsc{BA-Transolver}) architecture that explicitly separates interior and boundary tokenization. Extensive evaluations on 2D and 3D irregular geometries demonstrate that \textsc{NPSolver} outperforms both physics-informed and data-driven baselines. Furthermore, a downstream thermal control task highlights the model's capability for conducting efficient and reliable gradient-based boundary control. We will release our codes and data at https://github.com/intell-sci-comput/NPSolver.

Agentic retrieval-augmented generation (RAG) systems in complex B2B (business-to-business) settings may often receive free-form response feedback. Rather than generic feedback signals such as style, preference, or overall response quality, we focus on actionable factual corrections. We identify these instances and convert them into compact knowledge-base entries, which we call factual nuggets. We introduce Iterative Nugget Optimization (INO), an index-time optimization method that uses the production agentic RAG as a test harness: it creates an initial nugget, probes it with the triggering query and paraphrases, reflects over failed retrieval and answer traces, and revises the nugget until it is discoverable. We evaluate INO with two production B2B knowledge-assistance agents across multiple companies that use our system: a product support agent that answers questions over company-specific knowledge bases, and a support ticket agent that assists support engineers. INO consistently improves results over baselines in terms of discoverability and usage of factual corrections, in automated and human evaluations.

Coding agents are increasingly used as iterative development partners, but most benchmarks still evaluate one specification followed by one final assessment. This leaves out a basic question: can an agent keep its own codebase working as requirements change? We introduce EvoCode-Bench, a benchmark of 26 stateful coding tasks and 227 evaluated rounds. Each task preserves the agent's workspace for 5-15 rounds, states requirements through observable behavior, and uses cumulative executable tests to check new requirements and still-active prior ones. We evaluate 13 coding agents with two metrics: MT@4, a four-attempt fail-stop multi-round score, and SR, a single-round score from a reference-completed prior state. For most agents, SR exceeds MT@4 by 22-40 points. The gap also changes rankings: the highest-SR agent (78.9) ranks only third in persistent execution (44.0 MT@4). Even the strongest agents achieve only about 50% success on multi-turn metrics, and aggregate pass rate drops below half of round-1 performance by round 5. Failure analysis shows tier-dependent behavior: weaker agents fail early, while stronger agents survive long enough to expose specification-tracking and regression failures. We release the benchmark data and Harbor multi-turn infrastructure.

Recent LLM-guided evolutionary search methods have shown that iterative program mutation can discover strong algorithms, but they typically optimize each task independently, even when related tasks share reusable structure. We introduce Evolutionary Multi-Task Optimization (EMO) for LLM-guided program discovery, and propose EMO-STA (Shared-Then-Adapt), a two-stage framework that first evolves a shared archive of executable programs across a task family and then adapts selected shared candidates to each target task. Within EMO-STA, we explore multiple adaptation strategies, including warm-starting from the shared archive, adapting the best average shared program, and adapting the shared program that performs best on each target task. Across eight task families spanning continuous optimization, geometric construction, modeling, and algorithmic optimization, EMO-STA improves over matched-compute single-task evolution in most settings, with STA Best-Local providing the strongest in-distribution adaptation and STA Best-Shared yielding robust transfer to unseen tasks. Compute-allocation experiments show that allocating a substantial fraction of the family-level budget to shared evolution is consistently beneficial, with roughly balanced shared and adaptation budgets often being optimal. Beyond compute efficiency, we show that shared evolution can mitigate overfitting in low-evidence settings (e.g. few training data), including ARC tasks and time-series feature engineering, by favoring programs that generalize across all tasks rather than exploiting task-specific brittle artifacts.

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

Recent work due to Goel et al. gave the first efficient algorithms for learning with distribution shift in the challenging PQ framework. In this setting, a learner receives labeled training examples, unlabeled test examples, and must make correct predictions on the test set but is allowed to abstain from predicting on out-of-distribution points. Their results rely on ${\cal L}_2$ sandwiching approximations, a strong requirement that leads to poor bounds for several basic function classes such as DNF formulas. Here, we show that the weaker notion of ${\cal L}_1$ sandwiching suffices for efficient PQ learning. As a consequence, we obtain the first quasipolynomial-time PQ learning algorithm for DNFs under the uniform distribution and essentially match the guarantees known for ordinary PAC learning. More broadly, our bounds provide exponential improvements for several classes including constant depth circuits and constant degree polynomial threshold functions. Our main technical ingredient is Iterative Chow Filtering, a new procedure that uses low-degree Chow parameters to identify and remove test points incompatible with the training distribution.

Deploying large language model (LLM)-driven conversational agents in enterprise settings requires prompts that are simultaneously correct at launch and resilient to the non-deterministic behavioral drift that characterizes production LLM deployments. Existing prompt optimization frameworks address prompt quality as a one-time compile-time problem, leaving open the equally critical question of how to detect and repair prompt regressions caused by silent LLM behavior changes over time. We present PRISM (Prompt Reliability via Iterative Simulation and Monitoring), a closed-loop framework that treats prompt engineering as a continuous reliability engineering problem rather than a one-time authorship task. PRISM takes as input plain-language agent requirements, a set of configured tools and memory variables, and an initial draft prompt. It automatically generates test cases from requirements, simulates full multi-turn conversations against a platform-faithful LLM environment, evaluates pass/fail using an LLM-as-judge, diagnoses root causes of failures, and surgically repairs the prompt -- iterating until all tests pass. Critically, PRISM is designed to run on a scheduled basis (daily), treating LLM behavioral drift as a first-class reliability concern. We evaluate PRISM across 35 enterprise conversational agents over a three-week deployment period on the Yellow.ai V3 platform. PRISM reduces median prompt authoring time from 2 days to under 30 minutes, achieves 99% production reliability across all evaluated agents, and successfully identifies and repairs production regressions caused by LLM behavioral drift within a 24-hour detection window. Our results suggest that continuous, simulation-driven prompt optimization is both tractable and necessary for reliable enterprise conversational AI at scale.

In physical systems, whenever a continuous symmetry is spontaneously broken, the system possesses excitations called Goldstone modes, which allow coherent information propagation over long distances and times. In this work, we study deep neural networks whose internal layers are equivariant under a continuous symmetry and may therefore support analogous Goldstone-like degrees of freedom. We demonstrate, both analytically and empirically, that these degrees of freedom enable coherent signal propagation across depth and recurrent iterations, providing a mechanism for stable information flow without relying on architectural stabilizers such as residual connections or normalization. In feedforward networks, this results in improved trainability and representational diversity across layers. In recurrent settings, we demonstrate the same mechanism is valuable for long-term memory by propagating information over recurrent iterations, thereby improving performance of RNNs and GRUs on long-sequence modeling tasks.

Iterative self-refinement is a simple inference-time strategy for machine translation: an LLM revises its own translation over multiple inference-time passes. Yet document-scale refinement remains poorly understood: 1) which pipelines work best, 2) what quality dimensions improve, and 3) how refiners behave. In this paper, we present a systematic study of document-level literary translation, covering nine LLMs and seven language pairs. Across nine translation-refinement granularity combinations and five refinement strategies, we find a robust recipe: document-level MT followed by segment-level refinement yields strong and stable improvements. In contrast, document-level refinement often makes fewer edits and leads to smaller or less reliable gains. Beyond granularity, A simple general refinement prompt consistently outperforms error-specific prompting and evaluate-then-refine schemes. Our large-scale human evaluation shows that refinement gains come primarily from fluency, style, and terminology, with limited and less consistent improvements in adequacy. Experiments varying model strength reveal refinement projects outputs toward the refiner's distribution rather than performing targeted error repair. These findings clarify the mechanisms and limitations of current refinement approaches.

Evaluating and predicting the performance of large language models (LLMs) in multi-turn conversational settings is critical yet computationally expensive; key events -- e.g., jailbreaks or successful task completion by an agent -- often emerge only after repeated interactions. These events might be rare, and under any feasible computational budget, remain unobserved. Recent conformal survival frameworks construct reliable lower predictive bounds (LPBs) on the number of iterations to trigger the event of interest, but rely on static budget allocation that is inefficient in multi-turn setups. To address this, we introduce \emph{Dynamic Allocation via PRojected Optimization} (DAPRO), the first theoretically valid dynamic budget allocation framework for bounding the time-to-event in multi-turn LLM interactions. We prove that DAPRO satisfies the budget constraint and provides distribution-free, finite-sample coverage guarantees without requiring the conditional independence between censoring and event times assumed by prior conformal survival approaches. A key theoretical contribution is a novel coverage bound that scales with the square root of the mean censoring weight rather than the worst-case weight, yielding provably tighter guarantees than prior work. Furthermore, DAPRO can be employed to obtain unbiased, low-variance estimates of population-level evaluation metrics, such as the jailbreak rate, under limited computing resources. Comprehensive experiments across agentic task success, adversarial jailbreaks, toxic content generation, and RAG hallucinations using LLMs such as Llama 3.1 and Qwen 2.5 demonstrate that DAPRO consistently achieves coverage closer to the nominal level with lower variance than static baselines, while satisfying the budget constraint.

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.

Iterative Retrieval-Augmented Generation (iRAG) has emerged as a powerful paradigm for answering complex multi-hop questions by progressively retrieving and reasoning over external documents. However, current systems predominantly operate on parsed text, which creates two critical bottlenecks: (1) \textit{Coarse-grained attribution}, where users are burdened with manually locating evidence within lengthy documents based on vague text-level citations; and (2) \textit{Visual semantic loss}, where the conversion of visually rich documents (e.g., slides, PDFs with charts) into text discards spatial logic and layout cues essential for reasoning. To bridge this gap, we present \textbf{Chain of Evidence (CoE)}, a retriever-agnostic visual attribution framework that leverages Vision-Language Models to reason directly over screenshots of retrieved document candidates. CoE eliminates format-specific parsing and outputs precise bounding boxes, visualizing the complete reasoning chain within the retrieved candidate set. We evaluate CoE on two distinct benchmarks: \textbf{Wiki-CoE}, a large-scale dataset of structured web pages derived from 2WikiMultiHopQA, and \textbf{SlideVQA}, a challenging dataset of presentation slides featuring complex diagrams and free-form layouts. Experiments demonstrate that fine-tuned Qwen3-VL-8B-Instruct achieves robust performance, significantly outperforming text-based baselines in scenarios requiring visual layout understanding, while establishing a retriever-agnostic solution for pixel-level interpretable iRAG. Our code is available at https://github.com/PeiYangLiu/CoE.git.

Iterative ptychographic reconstruction algorithms are widely used for coherent diffractive imaging but can exhibit slow convergence under realistic experimental conditions. We propose a machine learning-augmented approach that accelerates iterative ptychographic reconstruction by introducing a learned fast-forward operator applied during reconstruction. Following an initial warm-up using standard iterations, the fast-forward operator advances the reconstruction toward a more converged state, after which conventional iterative updates are resumed. This strategy preserves the physical consistency and flexibility of established ptychographic solvers while reducing the number of iterations required for convergence. The model is trained on diverse ptychographic datasets and evaluated on experimental data acquired in a different year, demonstrating robustness and temporal generalization. Compared with conventional iterative solvers, the machine learning-augmented method achieves comparable reconstruction quality while converging faster in terms of Poisson negative log-likelihood, yielding over a two-fold reduction in wall-clock time. The approach has been integrated into an existing reconstruction pipeline and deployed in production at a synchrotron beamline, demonstrating practicality for real-time experimental operation.