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We give a machine-checked proof, in Lean 4, of the universal property of multi- centered blowups: given a finite family Z of closed subschemes of a scheme X, presented on each chart by ideals, there is a scheme BlZ X over X, terminal among X-schemes on which every member of the family becomes an effective Cartier divisor. To the best of our knowledge this is the first formalisation of blowups, single- or multicentered, in any theorem prover. The proof is organised around the universal property of the multicentered dilatation of a ring. The comparison isomorphisms on overlaps, the cocycle identity, and the independence of the chosen presentation are obtained from the uniqueness part of this universal property. We give the exact theorem statement as formalized, the proof architecture, and the main new mathematical ingredients, together with the corresponding Lean code.

Existing continuous space-time video super-resolution methods often infer motion from only two endpoint frames and model the two motion directions independently, making them vulnerable to ambiguous correspondence and inconsistent trajectories. We introduce a continuous STVSR framework that combines long-context encoding, continuous HR feature lifting, and an endpoint-anchored PixelSpline. Long-range observations provide more reliable endpoint representations, while continuous upsampling constructs detailed appearance features directly on the requested HR grid. PixelSpline explicitly models each pixel's motion as a single continuous trajectory shared by both endpoints. Using this trajectory, our method warps endpoint colors into a coarse intermediate frame and aligns the HR features for residual reconstruction. Experiments across spatial and temporal upsampling settings demonstrate that the proposed framework offers a favorable quality--efficiency trade-off.

We study variants of the secretary problem, where $N$, the number of candidates, is a random variable with distribution $\mathbf p$. The decision maker, given prior distributional information about $\mathbf p$, wants to maximize the probability of success -- picking the largest number among the $N$ candidates -- using only the sequentially revealed relative ranks of the candidates. When $\mathbf p$ is fully known (full information setting), we show that single-threshold type of strategies can achieve $1/e$-approximation to the optimal probability of success among all possible strategies. In the sampling setting, we give an algorithm that finds a strategy with additive suboptimality at most $ε$ and provide its sample-complexity guarantee. We also give a sampling lower bound; for small $ε$, the upper and lower bounds match up to a logarithmic factor in $1/ε$.

Modern data systems often require aggregating information from multiple sources: some might be entirely untrustworthy, while the remaining presumably reliable sources may still suffer from a small amount of corruption. We study robust mean estimation under this practical scenario, which is formulated through the double corruption model: samples are divided among $N$ users, each with $n$ samples. $\varepsilon$ fraction of the users could be arbitrarily corrupted, while each of the remaining ``good'' users still have $α$-fraction ($α>0$) of corrupted samples. The goal is to estimate the unknown mean $μ$ with small $\ell_2$ error. This is a challenging scenario because we must handle two types of adversarial corruption: user-level corruption and sample-level corruption. When the unknown distribution has covariance matrix bounded by the identity matrix, we design a sum-of-squares (SoS) algorithm that achieves an $\ell_2$ error of $\sqrtα$ with probability at least $2/3$ as long as the total number of samples $nN=\widetildeΩ(d/α)$. The estimation error and sample complexity are min-max optimal under the mild condition. For comparison, treating all $nN$ samples as $(\varepsilon+α)$-corrupted and applying standard robust mean estimation only achieves an error of $\sqrt{\varepsilon+α}$. Thus, our new algorithm removes the adverse effect of untrustworthy users and achieves the optimal error as if only sample-level corruption is present. Also, our SoS algorithm extends to the heterogeneous setting where each user's local mean could be additionally shifted by $\sqrtβ$ in $\ell_2$ distance. We show that an error of $O(\sqrt{α+β})$ can be achieved with probability at least $2/3$ when $nN=\widetildeΩ(d/(α+β))$.

In this work, we evaluate a simple inference-time scaling approach based on \textit{turn-level best-of-N sampling} (\method) for large language model (LLM) agents on complex, long-horizon tasks. We instantiate this using a \textit{generator-selector} framework with two LLMs; at each turn, a \emph{generator} model generates $N$ candidate actions and a \emph{selector} model selects one of them, which is then executed in the environment. This paper is closely related to the work of \cite{zainullina2025guided} who used critic models for guided search at inference time. Different from their work, we evaluate if off-the-shelf, open-weight LLMs can be effective at comparing different candidate actions directly. Experiments on long-horizon terminal tasks show that \method can lead to significant performance improvements, both in terms of accuracy (5--10\%) and consistency across repeated attempts. Analysis of agent trajectories reveal a shift in agent behaviour towards desirable patterns such as reduction in number of attempts to solve the task, improved task instruction following, debugging and testing.

We present HyScale, a long-context training system for learned sparse attention. Learned sparse attention is a promising architecture for million-token contexts, widely adopted in production since DeepSeek-V3.2. Selection, however, grows into the training bottleneck. For each query, it scores every previous token whereas sparse attention reads only $k$; worse, current systems materialize a full score table and repeat selection during recomputation. Our key insight is that the output of selection is not an activation, but rather a set of indices. Building on it, HyScale introduces FlashTopK and selection replay. FlashTopK finds each query's exact top-$k$ on the fly without a score table, while selection replay reuses forward-pass selection in recomputation. Together with holistic system optimizations tackling end-to-end challenges, HyScale speeds up GLM-5.1 training on 1M-token sequences by $2.07\times$ over Megatron-LM on 512 H20 GPUs. It also speeds up the CSA layers of DeepSeek-V4-Flash and the QSA layers of Qwen3.8-Flash-Next by $2.01\times$ and $1.57\times$ at 1M tokens on 32 H800 GPUs.

AI research agents automate the cycle of proposing, implementing, and evaluating experiments, opening a path toward recursive self-improvement. Yet their ability to propose experiments outpaces their capacity to execute them in real environments, making outcome prediction a key capability for sustained self-improvement under limited experimental budgets. We investigate language models as Research World Models (RWMs), which predict the outcomes of candidate interventions across research environments. Our evaluation draws on over 2,600 experimental records from nine research environments spanning pretraining, post-training, and inference, representing more than 171,000 H100 GPU-hours of experimentation. Research knowledge acquired from real experimental experience improves RWM predictions of unseen interventions within the same environment (Spearman +0.27), and can be reused across environments. For example, using only pretraining experience from OLMo3, Marin, and Nanochat, an RWM reduces selection regret in the Qwen3 environment by 78% compared with zero-experience setting. These benefits extend to multi-round Autoresearch under a fixed selection budget: RWMs with in-env and cross-env research knowledge increase the best gain achieved by 15.8% and 11.6%, respectively. Ablations across 13 language models used as RWMs show that adding research knowledge can improve intervention ranking more than changing models or increasing reasoning effort alone. These findings support language models as RWMs and motivate accumulating experimental data for future RWM training.

Graph neural networks (GNNs) deployed as cloud services can be *stolen* through *model-extraction attacks*, which train a surrogate from query responses to reproduce the target's behaviour, and a growing line of ownership defenses tries to prevent or trace such theft. The title of this paper asks two questions: *how hard is it to steal a GNN?*, and *can we stop it?* Prior work cannot answer either, because experiments use inconsistent datasets, threat models, and metrics. We introduce *GraphIP-Bench*, a unified benchmark which evaluates both sides under a single black-box protocol. It integrates twelve extraction attacks, twelve defenses spanning watermarking, output-perturbation, and query-pattern-detection families, ten public graphs covering homophilic, heterophilic, and large-scale regimes, three GNN backbones, and three graph-learning tasks, and it reports fidelity, task utility, ownership verification, and computational cost on shared splits, queries, and budgets. We further add a joint attack-and-defense track which runs every attack on every defended target and measures watermark verification on the resulting surrogate, which exposes the protection that a defense retains after extraction. The empirical picture is short: stealing a GNN is easy at medium query budgets and most defenses do not change this; several watermarks verify reliably on the protected model but lose most of their verification signal on the extracted surrogate, which exposes a gap that single-model evaluations miss; and heterophilic graphs are systematically harder to steal, while a cross-architecture mismatch between target and surrogate reduces but does not prevent extraction. We release *GraphIP-Bench* with reproducible scripts and configurations, and integrate the attacks and defenses into the PyGIP library.

Agentic workflows enable AI agents to perform recurring repository tasks on schedules or in response to repository events. Existing studies examine workflow definitions and outputs, but provide limited evidence of what happens during execution. We present GH-AWTrace, a dataset linking 25,014 verified GitHub Agentic Workflows across 5,051 repositories to 4,112,526 run records and 562,877 nonempty execution log archives. The dataset preserves execution evidence subject to GitHub's log-retention limits and links it to repository metadata and generated workflow configurations. Illustrative cases show how the logs expose tool denials, provider failures, changes in an agent's approach, and delegation among agents. These observations enable research on execution failures, tool use, and the relationship between reported run outcomes and visible task progress. Coverage varies across workflows, and the logs provide partial observations rather than complete agent trajectories. Video: https://youtu.be/KIlfmZhHxtA

As LLMs improve, data agents are emerging as a new interface for analytics, while semantic query processing engines use LLMs to operate over structured and unstructured data. Existing benchmarks largely evaluate agents and semantic query engines in isolation, leaving it unclear whether agents can decide when and how to use semantic operators in end-to-end analysis. We introduce AvalancheBench, a multimodal enterprise analytics benchmark that generates observed data from latent world specifications and evaluates data agents on their ability to recover that world. The benchmark's 3 validated tasks contain 58 questions spanning text, images, and documents. Questions are provided together as a multi-part analytical brief and may share intermediate results, exposing the avalanche effect: errors can propagate through legitimate dependencies, and inappropriate reuse can cause otherwise unrelated questions to fail. AvalancheBench measures analytical fidelity, monetary cost, and capability-adjusted token cost (CATC), a new metric that weights token use by model capability to separate technical efficiency from provider pricing. We evaluate 5 model-harness configurations across 3 agent harnesses using Snowflake Cortex AISQL as the engine, with the best configuration reaching macro analytical fidelity of 0.82. Agents fail primarily in constructing the analysis: failing to recover facts that require semantic computation costs 45.1% of lost points, yet incorrect operator outputs account for only 2.5%, versus 36.3% from agents misusing or avoiding semantic operators. Misinterpreting requirements costs the most, at 51.5%. Errors also spread between questions: 29% of lost points come from reusing another question's results. Finally, monetary cost and CATC produce different Pareto frontiers, distinguishing economically attractive configurations from those that are technically resource efficient.

The dilation of a geometric graph measures how much longer the path between pairs of points becomes when restricted to graph edges, rather than following the direct path through the ambient space. The minimum dilation tree of a point set is the spanning tree with minimum dilation, where edge lengths in the tree are given by distances in the ambient space. In the Euclidean plane, computing the minimum dilation tree is NP-hard, but no hardness of approximation result is known. On the other hand, the minimum spanning tree is an $(n-1)$-approximation to the minimum dilation tree, but no asymptotically-better approximation algorithm is known for general point sets in the Euclidean plane. We give the first sublinear approximation algorithm for the minimum dilation tree in the Euclidean plane. Our approximation ratio is $\tilde{O}(n^{14/15})$ and our algorithm runs in polynomial time. This resolves an open problem proposed by Eppstein in 1996.

Automated identification of individual animals is moving from small curated studies toward shared benchmarks and reusable foundation models. This progress is useful, but current evaluation leaves the evidence behind a match unresolved, i.e., high retrieval accuracy does not show whether a model used animal features or identity-correlated shortcuts. We address this with Counterfactual Foreground Retrieval (CFR), an evidence-aware evaluation protocol. CFR evaluates the same query-gallery task under different views: full image, foreground-only, and shortcut-only. The full-image measures standard retrieval performance; the foreground-only measures foreground-supported retrieval; and shortcut-only view measure how much identity signal is recoverable from background, or silhouette. This turns a retrieval score into an evidence profile: how well the model performs on the original images, how much of that performance remains when only the animal is visible, and how much identity signal remains recoverable when the animal is removed. We release around 0.5M masks for 34 datasets and code for mask generation and CFR evaluation.

Code-as-policy agents often use execution feedback to retry failed programs. Additional sampling and task guidance can also improve success, leaving the contribution of failure-specific feedback unclear. We study this question in simulated robot manipulation. A fixed lookup selects feedback templates using failure labels and the API variant. A frozen code model generates a fresh program after each scene reset. On the same 252 initial failures, Qwen2.5-Coder-7B recovers 85.3% within five retries, compared with 68.3% for resampling with the same retry cap. The advantage persists under fixed total-token budgets. Feedback from other episodes and fixed task guidance yield similar recovery point estimates, with no detected benefit from matching the coarse failure label. In a separate study, a fixed guided prompt used from the first attempt achieves an observed overall success rate similar to that of template-based feedback. Template-based feedback also lowers recovery on a nut-insertion task requiring a rim grasp, consistent with an incompatible center-grasp instruction. Evaluations of robot self-repair should include resampling, mismatched feedback, and concise, task-compatible static guidance as baselines.

We investigate whether a multiscale tensor-network architecture provides a useful inductive bias for reconstruction-based anomaly detection in collider jets. Jets are produced by a branching cascade, so their internal structure is naturally organised across angular and momentum scales. This motivates an autoencoder that compresses information hierarchically and can reorganise short-range correlations before coarse-graining. Guided by this picture, we formulate a Multiscale Entanglement Renormalization Ansatz (MERA)-inspired autoencoder acting on ordered jet constituents. To our knowledge, a MERA-inspired autoencoder has not previously been proposed, and this architecture has not been explored in collider anomaly detection. We compare this architecture to a dense autoencoder, the corresponding tree-tensor-network limit, and classical baselines within a background-only reconstruction framework. The paper is organised around two main questions: whether locality-aware hierarchical compression is genuinely supported by the data, and whether the disentangling layers of MERA contribute beyond a simpler tree hierarchy. To address these questions, we combine benchmark comparisons with a training-free local-compressibility diagnostic and a direct identity-disentangler ablation. In the nominal benchmark, the MERA-inspired model attains a higher mean AUC than the dense autoencoder at all three latent dimensions while using roughly one-third of its trainable parameters. The locality-preserving multiscale structure is well matched to jet data, and, at the strongest compression bottleneck, the trained disentanglers move substantially away from the identity and are accompanied by a positive mean performance shift. Overall, the study supports locality-aware hierarchical compression as a useful and parameter-efficient inductive bias for reconstruction-based jet anomaly detection in this benchmark setting.

Safe reinforcement learning (RL) aims to learn policies that optimize rewards while satisfying constraints. Predominant approaches rely on soft-constrained policy optimization, which has achieved empirical success but does not provide formal safety guarantees for the learned policy. In contrast, methods with strict guarantees typically rely on explicit certificate functions, whose construction requires the direct synthesis and verification of control-invariant sets, a process that scales poorly with state dimension and often yields overly conservative behavior. In this paper, we present the Provably Safe, yet Scalable RL (PS2-RL) framework, a novel two-phase architecture for learning provably safe policies in a scalable manner, designed to overcome the key bottlenecks of prior methods. Rather than explicitly computing invariant sets, PS2-RL leverages a learned backup policy to forward-integrate the system dynamics, generating an implicit control-invariant set online. In the first phase, the backup policy is trained with the safe-arrival value function to achieve rapid, safe recovery to the certified base set for invariant-set construction. In the second phase, an RL policy is trained end-to-end through a differentiable projection layer that strictly enforces the safety guarantees induced by the learned backup policy. By maximizing the volume of the implicit control-invariant set in the first phase, the resulting PS2 policy from the second phase is performant and scalable, while maintaining provable safety. Crucially, PS2-RL imposes no restrictions on the underlying RL algorithm and can be plugged into any existing training pipeline. We establish theoretical guarantees for the proposed framework and evaluate it on robotic control tasks with state dimensions up to 10, a regime in which prior provably safe RL methods struggle or become impractical.

Hierarchical text embedding models offer variable-length representations, while quantization reduces numerical precision; both aim to improve computational efficiency. This work is an empirical benchmark study of how these two orthogonal, already-established techniques interact. We evaluate 38 tasks from the Massive Text Embedding Benchmark (MTEB) using four transformer-based embedding models, covering 1D and 2D hierarchical representations combined with 32-bit, 8-bit, and binary quantization, for 168 configurations per task. We report each efficiency dimension separately: theoretical per-vector storage and end-to-end evaluation time. Under a Friedman test with Nemenyi post-hoc analysis, int8 quantization is statistically indistinguishable from float32 for pair classification and re-ranking and costs at most 1.5 percentage points overall, whereas binary quantization is significantly worse across every task category. Halving the embedding dimension once is not statistically detectable above $m=16$; two successive halvings always are. Combining an 8x dimensionality reduction with int8 yields a 32x reduction in per-vector storage at 94.4% of baseline effectiveness. Because evaluation times were measured once, we treat them as indicative: we find no evidence that quantization speeds up evaluation, whereas sampling from intermediate layers shortens it substantially. Retrieval degrades far faster than every other category, so we report findings per task category.

Recursive self-improvement requires AI systems to improve the models and infrastructure used by subsequent systems. LLM compression offers a concrete efficiency objective: retain a pretrained model's behavior within a smaller model storage budget. We study whether coding agents can carry out this step autonomously. We formulate compression as a terminal task in which an agent receives a source checkpoint, storage limit, inference environment, and time budget, then constructs compressed weights and executable inference code. The agent controls its algorithm and experiments; perplexity feedback guides search, and independent verification checks the final model. Across six agents and six model--size settings, 29 of 36 submissions pass verification. Selecting the lowest-perplexity agent design per task yields an average 3.4% perplexity increase over BF16 and 77.33% downstream accuracy, compared with 79.56% for BF16. Recorded experiments reveal how agents achieve these outcomes and where improvement breaks down. Agents lower PPL in 21 of 24 revisions at nearly fixed storage; complete-model feedback reverses 17 of 79 prior local rankings; and generation and inference tests expose failures that likelihood alone misses. The results identify representation design, experimental judgment, and capability validation as central to agent-driven model compression, a measurable component of efficiency-oriented self-improvement.

A fault-tolerant (FT) connectivity oracle for an $n$-vertex graph $G=(V,E)$ determines whether $G- F$ is connected for any query set $F\subseteq E$. When the number of failures is unrestricted, prior constructions exhibited a sharp contrast between randomization and determinism: randomized oracles use only $\widetilde{O}(n)$ space [Duan and Pettie, SICOMP 2020], whereas no deterministic construction was known to improve upon storing $G$ explicitly, requiring $Θ(n^2)$ bits in the worst case. The promise that $F\subseteq E$ is essential for subquadratic space: allowing arbitrary queries $F\subseteq V\times V$ forces quadratic space. For queries containing at most $f$ failures, Khanna, Konrad, and Putterman [SODA 2027] recently constructed deterministic oracles using $\widetilde{O}(\sqrt{f}n)$ space that also report approximate distances with polylogarithmic stretch. Their result improves upon the classical $O(fn)$ space bound for deterministic connectivity oracles [Pătraşcu and Thorup, FOCS 2007], but offers no space savings over storing $G$ when $f=Θ(n^2)$. We present the first deterministic connectivity oracles with subquadratic space for failure sets of unrestricted size, using $\widetilde{O}(n^{7/4})$ space. We also establish the first polynomial separation between deterministic and randomized connectivity oracles, proving that every deterministic oracle requires $\widetildeΩ(n^{3/2})$ bits in the worst case. For queries containing at most $f$ failures, we obtain deterministic connectivity oracles using $\widetilde{O}(f^{2/5}n)$ space, improving the dependence on $f$ in the bound of Khanna et al., and prove a lower bound of $\widetildeΩ(f^{1/4}n)$ bits.

We introduce LongBanana, to our knowledge the first expert-designed and expert-verified benchmark for long-context multi-reference image synthesis in the age of agent-driven image generation. The task requires retrieving dispersed visual evidence, rejecting distractors, binding entities and relations, and composing one coherent final image from multiple references. LongBanana contains 90 carefully designed tasks organized by a 3-by-3 taxonomy; each task includes about 32 reference images, 20 constraints, and 50 evaluation items, yielding 4,670 expert-specified atomic evaluation items in total. Its graph-grounded evaluation design instantiates each task with reference images and an entity-relation graph, then converts node, edge, and whole-graph obligations into checklist items for Content Fidelity, Relational Binding, and Global Constraint Satisfaction. Reviewed expert labels include a 15% double-labeled subset with 89.4% exact agreement and 0.83 quadratic weighted kappa. We further introduce LongBanana-Gen, an agent-harness framework for long-horizon image generation; experiments show that minimal agent harnesses improve over direct generation, while a ReAct-Plan-Exec-Reflect (RPR) workflow yields harness-dependent gains by strengthening evidence grounding and repair. Together, LongBanana provides an auditable testbed for measuring dense visual evidence use and a shared target for developing stronger agent-driven image-generation systems. Code and data are available at the project page: https://long-banana.com/.

Computer-use agents (CUAs) have recently achieved superhuman performance on several long-horizon benchmarks. However, their computational cost limits their use in long-horizon tasks and real-time domains such as video games. A key bottleneck is representing each screenshot as thousands of visual tokens, which accumulate into long contexts as agents reason over extended interaction histories. We observe that most of these visual tokens are either semantically irrelevant to the agent's next action or temporally redundant across screenshots. Building on this observation, we introduce Visual Token Routing (VTR), a joint training framework for learning sparse visual representations that preserve the information needed for action prediction. In VTR, we train the vision-language model together with a lightweight spatio-temporal router that examines each image region in the current and previous screenshots and decides whether its visual token enters the language model. We optimize the router using an adaptive loss to keep the number of visual tokens as small as possible while minimizing performance degradation. With just 2,000 training steps, VTR matches the performance of the full-resolution model on OSWorld, CUA-World, and video game action prediction, while using 2.5-5.8x fewer visual tokens. These savings reduce inference cost by up to 3.3x and speed up prefill by up to 2.9x. VTR also outperforms lowering the image resolution and other baselines for dropping tokens, by up to 12.8 points on OSWorld. Overall, VTR enables computer-use agents to process only the visual tokens they need, allowing them to be used in long-horizon tasks and real-time domains at a fraction of the computational cost. Code and models are available at https://pranjal2041.github.io/vtr

Video generation models synthesize realistic motion, but can they respond correctly to changes in initial geometry? We introduce GeoFlip, a video generation benchmark centered on physical outcome flips induced by geometry. With shared physical settings and textual prompts held fixed, GeoFlip applies controlled interventions to support extent, object placement, and mechanism configuration, constructing paired scenes with contrasting reference events, such as remaining stable versus falling or tipping. These pairs test whether models translate geometric differences in the first frame into correct physical evolution. The benchmark comprises 482 scene pairs and 964 reference videos across six physical categories, with reference outcomes established through procedural scene construction, physics simulation, and numerical validation and verification of physical events. We evaluate 16 models for image to video generation along three dimensions: event correctness, structural integrity, and similarity to reference videos. We examine evaluation consistency with independent vision language judges. On the 442 conditions shared by all models, the highest event correctness averaged across tasks is 27.98%, revealing substantial limitations in physical generation conditioned on geometry. Model strengths vary across physical mechanisms, and the three evaluation dimensions capture distinct capabilities. Typical failures include ignoring geometric changes, generating incorrect object motion, bending rigid objects, and introducing additional components. Rank correlations between judges reach 0.906 for event correctness and 0.929 for structural integrity. By combining controlled geometric interventions, verifiable physical references, and multidimensional evaluation, GeoFlip assesses progress from visual realism toward physical consistency conditioned on geometry.

Common methods for monitoring features in large language models (LLMs) such as linear probes and sparse autoencoders (SAEs) assume that features maintain a consistent representation across contexts. LLMs, however, can flexibly adopt different perspectives or "personas" that suggest different underlying systems of conceptual relations. In this paper, we examine whether prompting an LLM to adopt a persona alters the representational geometry of the model's latent space. We extract representations of over 9,000 common words and 33 semantic axes from models adopting liberal and conservative political personas and compare these against two neutral baselines. We find that persona conditioning systematically alters both the projections of words onto semantic axes and the alignments among the axes themselves in directions consistent with the specified ideology. We then test the implications of this reorganization for two safety-relevant features: truthfulness and morality. Linear probes, SAE-based classifiers, and classifiers built from manually selected word representations, all trained without a persona, produce divergent results when applied to models conditioned on political personas, producing politically slanted ratings of truth and morality on controversial statements. These findings suggest that internal representations, as they are conventionally extracted, can exhibit different geometric relations when the model adopts personas, potentially undermining monitoring efforts.

Faithfulness requires that algorithmic explanations accurately reflect the model's behavior. Yet existing operationalizations of faithfulness can disagree about whether the same explanation is faithful, leaving developers and auditors to choose among conflicting evaluations. In this paper, we investigate disagreement among evaluation criteria and offer a practical path forward for evaluating explanation faithfulness. We first identify how operationalizations of faithfulness differ. We introduce a faithfulness functional that locates their disagreements in what an explanation claims about the model, which comparisons bear on that claim, and how agreement across those comparisons should be aggregated, and we reconstruct existing evaluation criteria within it. We argue these reconstructions support understanding faithfulness as a common though incompletely specified relation between the model and explanation, so the differences reflect choices left open by the general requirement. Justifying an operationalization then comes down to justifying these choices, which, on our view, draws on explanatory, institutional, and normative considerations. We support this argument with a case study of adverse action notices, reconstructing the evaluation implicit in an industry-proposed procedure and identifying which of its choices the setting justifies and which remain open. Our work gives auditors and practitioners a way to navigate disagreeing evaluations of faithfulness. It also explains why the literature should expect multiple operationalizations, while showing how concrete settings can narrow the choice among them. More broadly, our analysis shows how a shared requirement of faithfulness can support contextually justified evaluations despite disagreement among existing metrics.

A central yet under-explored question in Multimodal Large Language Models (MLLMs) is where to connect---how visual information from a hierarchical vision encoder should be wired into the layer-wise semantics of a large language model. Mainstream MLLMs inject a fixed single-layer visual representation into the LLM and treat all LLM layers as a single consumer, ignoring that different layers demand different visual granularities. Recent multi-layer fusion methods either compress hierarchical features on the encoder side or rely on predefined sparse or hierarchical layer-to-layer connections, and therefore stop short of modeling adaptive cross-layer interactions between the ViT and LLM hierarchies. We address this gap with DGP (Dynamic Gated Pathways), a routing mechanism that establishes all-to-all connections between every ViT layer and every LLM layer, with each LLM layer dynamically gating its preference over visual layers conditioned on its own semantic state. Built on top of LLaVA-1.5-7B and 13B, DGP delivers consistent gains over the LLaVA-1.5-7B baseline (e.g., +4.2 on SQA$^{I}$, +3.3 on MM-Vet, +3.1 on VizWiz and LLaVA$^{W}$) and surpasses prior multi-layer visual fusion methods on most benchmarks. Layer-wise routing analyses further show that different LLM layers do select different visual granularities on demand, supporting both the effectiveness and interpretability of the proposed dynamic gated pathways. The code is available: https://github.com/YingyingYan1/DGP.

Grain growth during heat treatment strongly affects the microstructure of polycrystalline materials and, consequently, their mechanical properties. Although numerical methods such as front-tracking or front-capturing simulations can accurately describe grain growth, their high computational cost limits their use for long or non-isothermal thermal cycles. In previous work, grain growth was successfully predicted under isothermal conditions by treating grain size distributions as time series and forecasting their evolution using recurrent neural networks, allowing complete grain growth trajectories to be generated in seconds rather than through costly PDE-based simulations. In the present work, this forecasting framework is reformulated to handle non-isothermal conditions by explicitly incorporating thermal information into the model architecture. Grain size distributions are encoded using a convolutional neural network, thermal descriptors are embedded through a dedicated multilayer perceptron, and temporal evolution is predicted using a recurrent network. Instantaneous temperature and thermal rate are provided at each time step, allowing the model to adapt its predictions to changing thermal conditions. The framework is trained and evaluated on datasets generated from validated front-tracking simulations across a wide range of non-isothermal thermal paths. The results show that the thermally conditioned model accurately reproduces grain growth dynamics under complex thermal histories, achieving, in k-fold cross-validation over all simulations, mean relative errors of 2.99% (one-hour cycles) and 4.51% (four-hour cycles) with coefficients of determination exceeding 0.99, and mean relative errors between 1.91% and 14.66% on ten simulations following four unseen thermal histories of increasing complexity.