Papers

Rubric-based tasks are increasingly addressed through reinforcement learning (RL), with rubric scores used as training rewards. However, these rewards typically supervise final answers without distinguishing the contributions of intermediate decisions. Many existing credit assignment methods rely on ground-truth answers to define process rewards, limiting their applicability to open-ended tasks without canonical solutions. To address this limitation, the proposed rubric-grounded credit uses task requirements as a shared reference for final answer evaluation and process supervision. The information returned by tools is assessed for the additional support it provides toward satisfying each rubric relative to that rubric's history of accepted support. By referencing these histories, credit distinguishes new support from evidence already present in the trajectory while recognizing partial support for each rubric. Dr.Credit uses rubric-grounded credit to supervise intermediate tool turns in an RL framework for deep research agents. The resulting process advantages are combined with GRPO outcome advantages to guide research decisions while retaining supervision of final-report quality. Evaluations on four in-domain and out-of-domain benchmarks show that Dr.Credit outperforms the evaluated open deep research baselines on every primary metric and submetric. Meanwhile, with an 8B-parameter backbone, the trained agent achieves average performance competitive with the evaluated frontier proprietary models. Further analyses suggest more efficient evidence acquisition and higher-quality reports under limited research-turn budgets, motivating the extension of rubric-grounded process supervision to a broader range of rubric-based tasks.

We give an affirmative answer to the planar local smoothing problem in Question~1.7 of D.~Ntalampekos and positive and negative answers to the basic approximation and level-set parts of his higher-dimensional Question~1.8. In every dimension $n\ge2$, each continuous Lebesgue monotone function in $W^{1,p}$ on a bounded open set admits uniform and strong $W^{1,p}$ approximation by monotone $C^{1,\alpha}_{\loc}$ functions, with unchanged Sobolev boundary values and no increase of the $p$-Dirichlet energy, for $1<p<\infty$. The energy can be made strictly smaller unless the original function is $p$-harmonic. In the plane we obtain smooth local replacement at every isolated $p$-harmonic critical point, with arbitrarily small $C^1$ and Sobolev error. A point of gradient index $-m$ can be resolved into exactly $m$ nondegenerate saddles. Together with Ntalampekos's planar theorem, this gives smooth monotone density with fixed boundary values; at a nonsmooth $p$-harmonic minimizer the energy increase is unavoidable but can tend to zero. In dimensions $n\ge3$, an explicit Lipschitz monotone function has a nonmanifold point on every level in an interval, although it admits smooth monotone approximation. A product extension of a planar homogeneous $7$-harmonic function also rules out a general discrete exceptional set under the exact boundary and energy constraints. The answer to Question~1.8 thus distinguishes the five basic approximation properties from the stronger topological and exceptional-set conclusions. Applications include constrained integral functionals, strict $BV$ convergence of superlevel sets, nonlinear flux convergence, and stability of persistence diagrams under tameness assumptions.

Unsupervised visible-infrared person re-identification (USL-VI-ReID) learns person representations that can be compared across modalities without identity annotations. In the unpaired setting, however, identity correspondences between modalities are often incomplete, leaving many identities without an observed counterpart in the other modality. Existing unpaired methods bridge this gap by generating or mapping features for the other modality, mainly by exploiting the statistics of visual features without explicitly separating content that is discriminative for identity from style that is specific to modality. Consequently, the generated features may distort identity cues or inherit bias from the source modality, undermining the reliability of supervision across modalities. We formulate unpaired learning across modalities as a semantic compensation problem and propose Semantic Modality Compensation (SMC), a framework based on prompt composition that decouples identity semantics from modality style within a shared visual semantic space. SMC first constructs a discriminative ReID space through augmented dual contrastive learning, yielding pseudo labels, cluster prototypes, and memory banks for each modality. It then learns visible and infrared modality prompts in the CLIP semantic space and maps clusters obtained from pseudo labels to identity semantic tokens. For each cluster lacking a reliable match in the other modality, SMC combines its identity token with the prompt for the target modality to synthesize a semantic counterpart in the missing modality. The synthesized counterpart is then projected back into the ReID space and injected into a compensation memory through confidence gating. Extensive experiments under both paired and unpaired settings demonstrate that SMC consistently outperforms state-of-the-art methods, with particularly large gains when identity mismatch is severe.

Ordered search is the problem of locating a target element in a sorted list of size $n$ using comparison queries. Classically, binary search requires $\lceil \log_2 n\rceil$ queries, which is optimal. Quantum algorithms offer a constant-factor speedup, but the precise constant has been a longstanding open question. We close this gap by exhibiting two new quantum algorithms for ordered search, each using the optimal $\frac{1}{\pi}\ln n+o(\log n)$ queries. The first, discovered by Claude Fable 5, is a simple zero-error algorithm derived from a continuum relaxation of the problem. The second, discovered by GPT-5.6-Sol (informed by Claude's zero-error algorithm), is an exact algorithm based on an analytic solution of the polynomial program of Farhi, Goldstone, Gutmann, and Sipser.

We report a three-month autonomous research-agent program testing five solid-state-physics-inspired compression mappings on pretrained language models, with predictions committed to git before any pilot data and a 3-sigma gate deciding PASS or SHELVE. The common anchor – area-law / Kohn-nearsighted decay of the one-particle density matrix – has a distance face (P001 Wannier, P002 tight-binding) and a rank face (P003 DMRG-truncated MLPs, P005 Wilson-RG, P011 tensor-train embeddings). P005 was pre-empted at Phase 1; three of four Phase-3 pilots were falsified. On the attention face, GPT-2-medium attention-versus-distance is best fit by a stretched exponential in 12 of 16 median-layer heads once probe padding is excluded, and a tight-binding cutoff costs +96% perplexity (P002); on Pythia-160M the Wannier sparsity 0.054 +/- 0.004 is indistinguishable from PCA, random-Haar and identity baselines (P001). On the rank face, per-token tensor-train bond dimension does not track surprisal (r = 0.016 vs a pre-registered 0.65) and the format inflates rather than compresses (P011). P003 is mixed: its scaling claim shelved (r = -0.434), its MPO premise died at stage-0, and its cross-paper check, r = 0.523 as first written, collapses to 0.047 under the same correction, leaving both cross-paper checks null. The results invert the pre-registered prediction that most attention heads behave like Kohn-nearsighted insulators, pointing instead to critical, glassy or heavy-tailed regimes; the inversion is specific to the <= 350M scale tested, while the rank-face no-gain result held to 7-8B. We contribute the pre-registration + 3-sigma + cluster-framing + append-only-catalogue discipline – including why our own enforcement gate was designed but not deployed – four pre-registered negative results with full data release, and the inversion. The catalogue holds eighteen concluded studies, seventeen negative.

We construct an embedded torus and an entire graph in $\mathbb{R}^4$ whose normal bundles are initially flat but lose this property instantaneously under mean curvature flow. We also give an example showing that the parallel principal normal condition is not preserved under mean curvature flow, even though the normal bundle remains flat along the flow.

We study convex optimization over compact convex sets for twice differentiable objective functions with positive definite Hessians, assuming access to the feasible set through a linear minimization oracle. Existing second-order Frank–Wolfe methods either provide only a local linear rate over general convex sets or achieve global linear and local quadratic convergence only over polytopes. We propose damped Newton Frank–Wolfe methods that approximately solve constrained damped Newton subproblems using Frank–Wolfe or away-step Frank–Wolfe inner iterations. We develop residual backtracking, using a root Newton stepsize as a safe reference, together with a switching rule that eventually takes full steps. Under Hölder smoothness assumptions for $p$th derivatives, we establish global linear convergence and local convergence with Q-order at least $1+\nu$ ($p=2$) and local quadratic convergence ($p=3$). Experiments on matrix sensing and ridge-regularized logistic regression show that the residual-backtracking variant is consistently robust and often achieves the best performance among the tested first- and second-order baselines.

Canonical ideal quotients of extriangulated categories admit natural one-sided triangulated or pretriangulated structures. A fundamental question is whether these quotient structures still retain enough information to recover higher orthogonality properties of the subcategory being factored out. We show that, for a strongly functorially finite $n$-rigid subcategory, such information is encoded by the nilpotency of the canonical suspension and, equivalently, of the canonical loop. More precisely, this nilpotency characterizes two-sided maximal $n$-orthogonality. We further establish an objectwise recognition criterion that combines one-sided higher orthogonality with the vanishing of the $n$th suspension or loop. In the triangulated setting, our results give a converse to the known truncation construction and show that the quotient is $n$-truncated if and only if the subcategory is $(n+1)$-cluster tilting. Moreover, in the nonsplit case, the nilpotency index is exactly $n$. These results turn truncation from a consequence of higher orthogonality into a sharp criterion for recognizing it.

Nonlinear preconditioning makes it possible to adapt gradient updates to the growth of the objective's curvature, but combining its design with suitable stepsize selection is challenging. We propose adaptive dual preconditioned gradient descent (adaptive DPGD), which combines curvature-based preconditioner design with a linesearch-free stepsize rule based on local information. For convex objectives, we establish linear convergence under local strong convexity of the objective. By adapting the stepsize rule, we extend the method to weakly convex objectives and establish asymptotic stationarity without global Lipschitz smoothness. Moreover, our local assumptions give greater freedom in preconditioner design. We exploit this freedom to develop a semiautomatic recipe guided by the objective's curvature, yielding a family of preconditioners that includes those underlying normalized and hyperbolic gradient descent. Experiments on convex and weakly convex problems with real data demonstrate the effectiveness of the preconditioner design and adaptive stepsize selection.

LLM pretraining corpora are normally cleaned by a stack of hand-written heuristics. A heuristic scraper extracts the main content from HTML, and dozens of rule-based filters then clean it, so corpus quality is capped by the coarseness and accuracy of the rules. In this work, we propose ReScraper, a unified language model of only 0.6B parameters that replaces this entire stack. To train ReScraper, we carefully curate supervised data from the outputs of three teacher models, so it learns to first extract the main content from raw data and then choose among four operations: keeping the page as extracted, editing out noisy lines and spans, deleting it entirely, or rewriting it when it is poorly written but informative. Based on the same crawled data pool, pretraining 400M, 1.4B, and 2.8B models on our curated data improves the DCLM Core score by a relative 3.8–4.7% over the strongest baseline at each scale, including the costly multi-agent curation. Our analyses show that each operation plays a distinct and complementary role, and that extracting and cleaning in one model outperforms a cascade of separate models. ReScraper also concentrates its operations on the pages that need them, raising the quality of poor pages the most while keeping the corpus diverse. These results demonstrate the feasibility and effectiveness of AI4AI for pretraining data curation, where a small learned model takes over an entire stage of the pipeline from hand-written heuristics. We open-source our code at https://github.com/cxcscmu/ReScraper

World models for manipulation are typically trained from video, yet the events that determine how manipulation unfolds, such as making and releasing contact, are difficult to observe visually and are often easier to sense through touch. We present the Dexterous Tactile World Model (DTWM), a video world model for future-frame prediction of egocentric manipulation from both observed video and tactile signals from a glove worn on each hand. We condition a pretrained video diffusion transformer on each hand's tactile signal through a zero-initialized residual at the corresponding hand location in the video tokens, while a causal mask prevents predicted frames from accessing future information. Compared with a vision-only model matched in architecture, parameters, and training, DTWM reduces the underestimation of hand motion from 23% to 9%, while reducing the perceptual error in the hand region by 7.4% across three training runs per model. The benefit also increases over the prediction horizon, with the improvement in the later predicted chunks being about 4.1x larger than in the first. DTWM also outperforms other visual-tactile world models under the same setting, and training with touch improves future-frame prediction even when no touch is available at inference. Ablations show that the model benefits from both the magnitude and spatial location of force: replacing the tactile signal with binary contact states, either per hand or per location, increases prediction error. The observed course of the force indicates whether the interaction will persist or change.

Imprecise annotations may support several plausible labelling distributions, yet learning methods often resolve this ambiguity into a single predictive distribution. This can obscure what the annotation evidence leaves unresolved. We introduce epistemic learning from credal supervision, a framework that uses convex sets of plausible labelling distributions, called credal sets, as supervision and learns sets of predictive distributions. We instantiate the framework with the pessimistic–optimistic credal classifier (POCC), which combines a shared backbone with two classification heads trained to minimise worst-case and best-case losses over the supervision sets. Their outputs define a predictive credal set whose spread provides an uncertainty score. We also show how credal labels can be obtained through a simple relaxation of existing probabilistic labels, reducing commitment to their precise probability assignments. This construction admits closed-form inner optimisation under cross-entropy loss, enabling efficient training. Assuming the supervision sets contain the true conditional label distributions, and other regularity assumptions, we establish a finite-sample generalisation bound for the averaged predictor with an explicit penalty for supervision imprecision. We evaluate POCC using human annotator disagreement and teacher predictions, alongside label smoothing as a controlled proxy for annotation imprecision. Across these settings, POCC achieves a favourable balance of predictive accuracy, calibration, and uncertainty-based selective classification versus competitive baselines.

Personalized LLMs must decide, for each stored preference, whether the current context calls for applying or suppressing it, which we call its applicability. They frequently over-personalize, applying preferences the context rules out, yet existing benchmarks score only the final response and cannot tell where this failure arises. We decompose preference handling into three stages and measure each separately: (1) knowing whether a preference applies, (2) deciding on an explicit Apply/Suppress label, and (3) generating a response consistent with that label. Using linear probes, we first show that this applicability signal remains decodable from hidden states during generation. By making the decision explicit, we then find that in most settings wrong decisions faithfully followed outnumber correct decisions lost in generation. We thus locate the failure in the decision, which breaks once the model is also asked to answer. To determine whether this reflects lost sensitivity or a response bias, we propose ABIDE (Apply-Bias Investigation via Decision-score), which adapts signal detection theory to Apply-vs-Suppress decision scores read directly from logits. ABIDE reveals a generation-induced Apply bias: merely stating an answer-generation objective shifts the decision score toward Apply while sensitivity is largely preserved, and the shift persists under controls for prompt structure, cascades across preference slots, and prompt wording. Finally, we show that subtracting a single bias scalar, estimated on a held-out split, from the decision score at decoding time reduces leakage while largely preserving fulfillment.

For every $n\geq 4$ and every $H$ in a neighborhood of $n-1$ (depending on $n$), we prove the existence of a properly embedded strongly stable CMC hypersurface in $\mathbb H^n$ with mean curvature $H$ and infinitely many ends, invariant under the action of a Schottky group. In particular, stable Bernstein-type rigidity fails in this range.

This paper examines idempotents in algebras and categories that arise from factorizations of the identity morphism. In the diagrammatic and combinatorial contexts considered here, these factorizations correspond to generalizations of meanders, where a meander is understood to be a curve in the plane that wanders transversely back and forth across a given straight line. By formulating the algebra of the Temperley-Lieb Monoid in terms of planar curve combinatorics, one can understand idempotents in the Temperley-Lieb Monoid in terms of meanders. Corresponding results are shown for the Brauer Monoid and for the Tangle Monoid and Tangle Category.

High-dimensional Bayesian optimization (HDBO) seeks sample-efficient optimization when the number of variables is large relative to the evaluation budget. Recent LLM-based and agentic BO methods incorporate task knowledge and adapt search decisions during a run, but have primarily been evaluated on low- and moderate-dimensional problems. We ask whether this paradigm can transfer to the higher-dimensional regime. Our experiments show that these methods do not remain reliable in the high-dimensional regime, where the challenge is not only where to evaluate, but also which modeling assumption and search geometry to use when the objective's useful structure is unknown. We therefore introduce HERA, a Hypothesis- and Evidence-guided Research Agent that uses task context, optimization feedback, and structural diagnostics to revise search hypotheses, select and configure HDBO strategies, and determine their execution length. PRISM, its numerical optimization engine, generates and evaluates candidates sequentially within each search block, updating numerical models after each observation. HERA remains competitive with strong numerical HDBO baselines and outperforms the evaluated LLM-based and agentic methods on four metadata-free synthetic functions. Across eight real-world tasks, HERA achieves the best mean final objective among all evaluated systems on most benchmarks. Further analyses show that structural diagnostics change strategy use, metadata effects vary across tasks, and adaptive search blocks reduce inference cost.

Predicting molecular profiles from histopathology remains challenging because whole-slide images contain spatially organized, heterogeneous tissue patterns, while gene expression comprises thousands of correlated targets. We introduce MoSPR (Morpho-Spatial Program Regression), a linear framework that couples an adjacency-informed histology representation with a low-rank molecular basis. MoSPR clusters frozen patch embeddings into morphology microstates, aggregates their spatial adjacencies across the training cohort, and groups microstates with similar adjacency patterns into shared macrostates. Each slide is then represented by global morphology and macrostate-specific deviations, which are linearly mapped to coefficients of a training-derived low-rank gene-expression basis. Across three cancer cohorts from The Cancer Genome Atlas, MoSPR achieves the highest mean gene-expression prediction scores among all evaluated methods. Without pathway-level supervision, pathway scores derived from its predicted expression profiles rank first in eight of nine comparisons across three pathway collections. Ablation studies on the breast cancer cohort show complementary gains from adjacency-derived macrostate representation and low-rank molecular prediction. Moreover, with half of the training data on this cohort, MoSPR exceeds the full-data gene-prediction score of the strongest competing baseline. Finally, its linear formulation enables exact decomposition of each predicted expression profile into global and macrostate-specific molecular contributions, providing an interpretable link between spatially coherent macrostate regions and their associated molecular programs. Our code is available at https://github.com/Radisen-Panthera/MoSPR.

Self-evolving language models improve by generating tasks and learning from their own feedback, but adapting the task generator often requires a separate challenger-training loop. Can we generate tasks adapted to the current solver without explicitly training a challenger? We introduce Direct Self-Evolving Optimization (DEO), which replaces challenger parameter updates with solver-guided task sampling. The KL-regularized challenger objective defines an exponential tilt of a fixed base task distribution. DEO uses this distribution as a sampling target: a frozen LLM generates and mutates tasks, the solver scores them, and an approximate Metropolis selection rule refines the training pool. Only the solver is trained. Theoretically, for an idealized variant that samples exactly from the tilted distribution, and under regularity, local gradient-dominance, and initialization conditions, we show that DEO learns distributionally robust reasoning ability. In experiments, DEO achieves reasoning performance competitive with R-Zero while using over $50\%$ less wall-clock training time, and improves reasoning accuracy over a no-walk ablation. Replacing the task generator with a frozen API-only LLM further improves the local solver, illustrating a capability enabled by removing challenger training.

We establish strong and explicit forms of a one-sided Nullstellensatz for polynomial rings D[x1, . . . , xn] over arbitrary division rings D with central indeterminates. To this end, we employ the theory of integral dependence over left ideals and the notion of G-left ideals, which plays a role analogous to that of G-ideals in the classical theory. We prove that the Jacobson radical of any left ideal of D[x1, . . . , xn] coincides with the intersection of all G-left ideals containing it. As a consequence, we obtain an explicit description of Jacobson radicals of left ideals of polynomial rings over division rings in terms of integral dependence.

Pathological assessment relies on recognizing fine-grained visual details in histological images. Vision-language models (VLMs) increasingly support pathology interpretation, yet their ability to perceive these details remains inadequate. This weakness leads to inaccurate cellular observations that can persist even when final answers are correct. In this paper, we propose ASPECT to improve visually grounded reasoning through explicit supervision of cellular appearance and abundance. ASPECT trains intermediate visual tokens through pathology feature reconstruction, cell feature alignment, and count supervision. Three-stage supervised fine-tuning teaches the model to perceive, generate visual tokens, and reason, followed by reinforcement learning that rewards answer correctness and consistency with reported measurements. We also introduce PathoVernier, a benchmark of 759 expert-reviewed questions from five pathology datasets covering four cellular composition tasks. It evaluates both final answers and intermediate measurements to expose errors hidden by answer accuracy. On PathoVernier, ASPECT achieves relative accuracy gains of approximately 19.2% over the strongest baseline, Gemini-3.1-Pro, and 99.3% over its Qwen3-VL-8B backbone, while reducing RAWR, which measures counting errors within correct responses, by 28.1% and 42.7%, respectively. ASPECT also improves over its backbone on three external pathology benchmarks covering classification and question answering beyond cellular composition tasks.

Frontier models can now perform well on individual embodied navigation tasks through multi-round multimodal reasoning with simple tools. Across successive tasks, however, an agent must also rely on an evolving map and earlier search records, both of which may be incomplete or conflict with new observations. We present NavHarness, a training-free embodied harness towards lifelong navigation that makes memory processing part of the navigation loop. During navigation, its multi-round agentic session draws on maps, task records, and house knowledge, checking them against observations and recording corrections to guide its actions. NavHarness preserves this experience across fresh conversations for new tasks or recovery attempts, while outcome verification and run-end summaries support its later reuse. On GOAT-Bench, NavHarness improves s-SR over context-only independent sessions by 18.6 points with Astra and 22.6 with Opus 5. Using SLAM-estimated poses, NavHarness with GPT-6 Astra achieves state-of-the-art task success of 83.7 s-SR with 36.9 e-SR on GOAT-Bench and 85.9 s-SR on IR2R-CE. To understand these gains, we examine how experience is carried between sessions and find that structured recovery handovers outperform length-matched summaries. In extended deployments across houses, consolidation improves navigation beyond retaining maps and task records, with case studies showing how agents use earlier experience to interpret new goals, investigate unresolved questions, and resume failed searches. We suggest that progress towards lifelong navigation depends on how successive reasoning sessions build on prior experience, alongside improvements in single-task capability.

In a predictor-corrector arc-search method, a point on the predictor arc is first selected and a corrector is then computed at that point. Since the Karush-Kuhn-Tucker (KKT) matrix changes with the selected point, this correction may require a second factorization in each iteration. We propose a one-factorization arc-search method (OFAS) for semidefinite programming (SDP) that avoids this second factorization, retains the corrector after the arc step, and uses only one KKT factorization per iteration. The key is a three-term decomposition of the complementarity mismatch at the selected point on the arc, which allows the correction to be assembled from linear-system solutions using the factorization at the current iterate. We also propose a curvature-amplified variant (CA-OFAS) that amplifies the second-order arc term. The proposed methods are formulated with a homogeneous self-dual embedding. For a wide long-step neighborhood, we prove that both methods reduce the homogeneous complementarity and residuals below $\varepsilon$ in $O(n \log(1/\varepsilon))$ iterations for an $n$-by-$n$ SDP matrix variable. Numerical experiments show that the one-factorization structure and the correction after the arc step are associated with reductions in computation time. Compared with the Mehrotra-type method, CA-OFAS reduces the geometric-mean computation time by 17% on SDPLIB and 13% on neural network verification SDP problems.

Artificial-intelligence (AI) agents hold promise for automating bioimage analysis, yet no benchmark evaluates whether they can carry out real-world analyses end to end. Such analyses are hard for agents because 2D images, 3D volumes and time-lapse sequences are often too large to read as context, so an agent must choose and run an analysis through code, specialized software and rendered views. Published studies make this capability testable, because each pairs raw images with a peer-reviewed result. We introduce BIABench, a benchmark of 16 tasks reconstructed from published biological studies that retain their scientific questions, imaging data and ground truth. The tasks span eleven analysis subtasks and modalities from H&E histology to single-molecule localization microscopy. Each submission receives an outcome score, which compares the output files with the ground truth using field-standard metrics, and a process score, in which a vision-language model judges method choice and quality control against an expert-written rubric. We evaluated general-purpose and biology-specific agents across several language models, with repeated runs of every task. Routine two-dimensional tasks were solved well, but on some tasks that added a third dimension or a time axis no agent scored above 0.19. Neither biological specialization, stronger models nor detailed expert instructions closed this gap. The agents were also unreliable, with scores varying more between repeated runs of one agent than between different agents, and without ground truth a correct run could not be told from a wrong one by its process score or by the time spent. Released openly with its data and code, BIABench provides a verifiable framework for evaluating, and eventually training, agents for reliable long-horizon bioimage analysis.

The projection of queries and keys are central to the attention mechanism in Transformer architectures. While they are mathematically symmetric, they play different roles in attention mechanisms. The question of whether there is an effect from their functional distinction on their geometric development in training remains unanswered. We investigate the problem through the training of small GPT-like Transformers on character-level WikiText-103 for three different depths (4, 6, and 8 layers), three types of initialization for queries and keys, and four random seeds, resulting in 36 runs and 54 trajectories of average layers across seeds. We track the effective dimensionality of those layers using participation ratios and discover that effective dimension of queries expand while keys shrink, and that $PR_Q - PR_K$ is positive in all trajectories studied. In connection to attention, the shrinking of keys leads to a narrower spectrum of $QK^\top$ and more peaked attention weights. In order to determine if this connection is causal or coincidental, we directly control the spectrum of keys during training across five seeds: restricting it to make it shrink sharpens the attention with high directional confidence, while keeping it constant to the level of initial dispersion makes attention softer. Additional token-level checkpoint analyses show that the monotonic paired-contrast trend is not universal across pretrained families, but survives as an early-training regime that later decays over a full pretraining run, and the link between interaction-rank geometry and attention entropy remains visible in several models.

BF16 is now standard in large-scale pretraining, including in fused attention kernels such as FlashAttention, and these kernels are widely trusted. When we used FlashAttention-3 to pretrain a 450M-parameter transformer on 50B tokens, however, we ran into a problem: training was healthy for 25B tokens, then the gradient norm grew a thousandfold and the loss ended 0.2 nats above FP32 attention, without a single NaN. Recomputing the attention backward of just two layers in FP32 removes almost all of the excess gradient. Part of the cause is known: a fused multiply-add in the forward softmax, so far treated as an extreme-input NaN case and never fixed in FlashAttention-3. Repairing it stops the blow-up, but the query gradient is still wrong by more than its own size, and training still drives attention logits to thousands of times their size under accurate gradients. The remaining error comes from a broken conservation law. The softmax score gradient sums to zero along every row, which makes the query gradient blind to where the keys sit as a group; rounding it to BF16 leaves a small nonzero sum that leaks the mean key into the gradient, and the leak grows exactly as late training makes keys large and attention sharp. We introduce GProj (gauge projection), which restores the zero sum after the cast with two rank-one corrections per row. It cuts the remaining median query/key gradient errors from 219%/13% to 0.34%/0.37%, on par with FP32 attention, for 4.7% more time per training step. In matched from-scratch runs it trains to the same loss as FP32 attention, while FlashAttention-3 and key smoothing both destabilize.

Although recent 3D generative models produce increasingly realistic assets, controllable 3D asset editing remains challenging. Existing methods are limited by scarce training data, insufficient source-aware modeling, and a lack of practical evaluation protocols. To address these limitations, we present Alchemy3D, a unified framework for training and evaluating versatile 3D asset editors that covers data construction, model architecture, and benchmark evaluation. Specifically, we curate Alchemy3D-1M, a large-scale 3D editing dataset containing 1.25M assets and 1.38M editing pairs across seven editing types. On this data, we train a family of generative flow models for general-purpose 3D asset editing. The model family supports image- and text-conditioned editing, few-step inference, and transfer to multi-view 3D part segmentation. We further introduce GEdit3D-Bench, a large-scale, open-world benchmark with a multi-dimensional evaluation protocol. Across existing and newly introduced benchmarks, our method outperforms prior methods on most metrics of editing fidelity, source preservation, and visual quality.

Interactive robot planning requires robots to infer and execute human intentions from natural language instructions that are often ambiguous, incomplete, or underspecified. Although large language models (LLMs) provide a powerful interface for clarification, relying on the generative model to drive an multi-turn conversation can introduce systematic failures. We propose a Bayesian framework that treats clarification as an active learning problem over grounded Signal Temporal Logic (STL) task specifications. Our method uses LLMs to initialize candidate formal specifications and translate informative contrasts into natural-language clarification questions, while Bayesian optimization maintains uncertainty estimation over user intent and selects queries that maximize information gain. After convergence, the inferred STL specification is passed to a formal planner to synthesize a verifiable robot trajectory. Across four simulated and real-world task domains, our approach generally achieves higher task satisfaction and requires fewer clarification rounds than LLM baselines, while helping smaller models close the performance gap against larger reasoning models.

Given $n$ points in a metric space, partitioned into groups, $X_1,\dots,X_m$, and integer quotas, $k_1,\dots,k_m$, summing to $k$, the Fair Max-Min Diversification problem asks for a set of $k$ points, exactly $k_i$ from each group $X_i$, maximizing the minimum pairwise distance. Addanki et al. (ICDT 2022) described a ball LP for this problem and rounding algorithms that yield a factor 2 approximation whose fairness holds only in expectation and a factor 6 approximation with relaxed fairness guarantees, as well as an $(m+1)$-approximation with exact fairness. We introduce two new algorithms. The first method refines the rounding of Addanki et al., yielding a 2-approximate solution that is $\varepsilon$-fair with high probability, meaning that from every group $X_i$, at least $(1-\varepsilon) k_i$ points are chosen. The second method in polynomial time returns a 4-approximation to the optimal value of the exact fairness version. In time $n^{O(1)} 2^{O(k)}$, which is fixed-parameter tractable in $k$, we achieve an exactly fair 4-approximation. Our method adapts the augmenting procedure behind Haxell's theorem (Graphs Combin., 1995). This approximation factor does not depend on $m$. Moreover, we show that no rounding of the ball LP achieves a smaller factor with exact fairness.

Large language models (LLMs) are now the default cognitive core of embodied household agents, yet the plans they emit are rarely checked against a grounded model of the environment before execution, and the task-success they report is often measured on benchmarks so saturated that no method can be separated from another. We present SAGE (Symbolic Action-Gating and Editing), a single-LLM planner built from two lightweight mechanisms: a domain-agnostic symbolic gate (~250 lines of Python, zero tokens, $O(|\pi|)$) that blocks precondition-violating actions with typed reasons as a runtime safety monitor, and a local edit that regenerates only the failed sub-goal's suffix, keeping completed and untouched work intact; a hybrid seed+live memory store supports cold-start coverage. We evaluate under a leak-free protocol (leave-one-out retrieval) over five open-weight models and a 75-task AI2-THOR benchmark. On the standard benchmark goal-completeness saturates (52% of instances trivially solved) and SAGE ties strong hierarchical baselines. On a harder, method-agnostic multi-goal composition, SAGE's completeness lead re-emerges large (+0.06 to +0.23 across four models). Under injected mid-execution failures, SAGE recovers as reliably as whole-plan replanners at 2.4-3.3x fewer LLM calls. As a verify-before-execute gate, the symbolic monitor blocks unsafe actions before actuation and raises simulator-reported step-success for every planner tested (up to +0.11), a signal the verifier never sees (non-circular). Because the gate calls no model (0.008 ms/plan), it is a safety layer that runs essentially free on the edge: SAGE planning reproduces its quality on a Jetson AGX Orin, where small-model verification helps most. We release the benchmark, the leak-free protocol, the recovery and safety-gate harnesses, and a verifier-portability study (auto-induced on ALFWorld, 0.89 held-out).

We study the weighted Karcher mean on the Lie group $\operatorname{UT}_n$ of upper triangular matrices with positive diagonal entries. Using a divided-difference description of analytic functions on upper triangular matrices and the Parlett recurrence, we prove the existence, uniqueness, and analyticity of the weighted Karcher mean and derive recursive formulas for its computation. The theory yields explicit expressions in low dimensions and formulas for weighted geometric means on $\operatorname{UT}_n$. More generally, the results reveal a close relationship between divided differences, analytic matrix functions, and nonlinear matrix means on triangular Lie groups.