Papers

We extract rank and regularized exponents from cyclic generic factors of the quantum connection and show that these data persist under the birational comparisons considered here. Applications include showing non-rationality of cubic threefolds, ordinary Gushel–Mukai threefolds, very general quartic fourfolds, and products of the threefolds with $\PP^1$.

Language models draft engineering calculations, but answer accuracy does not show whether they reject an impossible problem. We tested 14 models on 30 pairs of mechanics problems, each with a valid version and one made impossible by changing a given value or assumption. Two independent solvers verified every answer key and showed that each flawed problem was physically impossible. We scored solving of valid problems separately from rejection of their flawed counterparts. Each reply required a "solved" or "cannot solve" status; rejection meant "cannot solve" or withholding an answer. The initial prompts did not warn that problems could be flawed. Across three recent models, 12 of 90 replies failed to reject a flawed problem. In 11 of these replies, the model stated the flaw, answered a corrected problem and still reported the original as "solved", according to artificial intelligence raters and numerical checks. We later retested four models from one provider, offering "flawed" instead of "cannot solve" and asking them to name and explain the defect. Three models showed statistically significant increases in rejection, but valid-problem solving fell in three. Evaluations therefore need to score both versions and distinguish flaw recognition from the reported status.

Provable guarantees for preparing quantum Gibbs states, such as rapid mixing or gapped coherent preparation paths, are known only for restricted Hamiltonian families and usually must be re-derived for each new family. Building on homomorphic polynomial transduction, a generalization of decoded quantum interferometry (DQI) and Hamiltonian DQI (HDQI), we show how relative decoding transfers such a guarantee from a source Hamiltonian $H_A$ to a target $H_B$. Writing each Hamiltonian as a sum of $m$ Pauli terms, the subsets of terms whose product is proportional to the identity, its relations, form a binary linear code, $K_A$ for the source and $K_B$ for the target, with the Pauli-label matrix as parity-check matrix as in DQI. Starting from the canonical thermofield double (TFD) of $H_A$, a Bell transform, a reversible label map, and a coherent decoder for the quotient code $K_B/K_A$ prepare an approximate TFD of $H_B$, and hence its Gibbs state. Because this decoder only resolves target relations absent from the source, the reachable inverse temperature is set by the relative distance $d_{\rm rel}$, the fewest terms in any such relation. It can far exceed the ordinary distance $d_{\rm ord}$, the fewest terms in any target relation, which bounds the uniform exact decoding radius of DQI and HDQI. We show that linear $d_{\rm rel}$ with efficient decoding at linear radius certifies a constant inverse temperature. As an example, starting from a nearest-neighbor spin chain whose TFD is known to be preparable at every finite temperature, a sparse classical parity-check matrix yields bounded-degree, geometrically nonlocal, noncommuting targets with $d_{\rm ord}=3$ and $d_{\rm rel}=\Theta(m)$. To our knowledge, this gives a new class of efficiently preparable TFDs.

Latent reasoning lets a large language model (LLM) think in a continuous space and verbalize only the answer. We argue that an effective latent thought must meet five requirements: it should be useful, helping produce the correct answer rather than merely changing it, diverse, so that resampling yields different reasoning trajectories, explainable, so that a decoded chain of thought (CoT) reflects reasoning the answer actually follows, refinable with more inference compute, and efficient, costing less than an explicit CoT at comparable accuracy. Current methods rarely meet these requirements: they learn shortcuts from the question, distill the explicit CoT into their weights, or imitate it one token at a time. We focus on flow matching in a learned latent space, the family we argue is best placed to meet them, and identify the training choices that make it work. The result is Flow-based Latent Reasoning (FLaRe), a simple recipe covering what the latent space encodes and how to shape it, where to train the flow, how to read out the answer, and a final stage of training on the model's own verified thoughts. A probe for each requirement shows that FLaRe improves on prior latent methods in all five. It also compares favorably with them on arithmetic benchmarks, while reaching 97% of the accuracy of explicit CoT at a quarter of its latency.

We give a fast algorithm for solving min-cost $k$-commodity flow. The basic idea is to construct an auxiliary linear program that has low rank and whose minimum value is at most $1/k$ times the minimum value of the original problem (thus, solving this auxiliary linear program will make at least $1/k$ fraction of progress in the original problem). Low-rank linear programs can be solved quickly using black-box techniques. Thus, our algorithm runs in time $\tilde{O}(\operatorname{poly}(k)(n^{2.5}+m\sqrt{n}))$ on a directed graph with $n$ vertices and $m$ edges. We do not rely on any fast matrix multiplication.

We study Borel subgroups of the automorphism group of an affine variety X and their associated Lie algebras. We prove a bijective correspondence between the set of Borel subgroups of Aut(X) and the set of maximal nested unipotent subgroups of Aut(X). We show that if X is factorial of dimension at most 3, then the Lie algebra of every maximal nested unipotent subgroup has the special property of being what we call "integral"; we also show that this fails for X = affine space of dimension > 3. As an application of our results, we show that Nagata's automorphism is contained in a unique Borel subgroup.

A significant problem in endoscopic image analysis is that the machine learning (ML) models used for this purpose usually underperform when applied on images acquired from endoscopes that are different from those used to acquire the images of their training set. The main difference of the images originating from different endoscopes is their color distributions, which depend both on the image sensors and the light sources used. Although previous studies have highlighted this challenge, to the best of our knowledge it has not been previously explicitly tackled. This study focuses on this problem and proposes very simple but impactful method. It implements a reference-based image harmonization that reduces global appearance differences between endoscopic datasets. Specifically, it extracts global color statistics from a chosen reference dataset in the CIE-Lab color space and applies a statistical channel-wise transformation to map each target image toward the appearance of the images of the reference dataset. The method is evaluated in the context of polyp detection in both flexible colonoscopy and capsule endoscopy datasets using a dataset-level cross validation protocol. The results indicate that the proposed harmonization consistently improves cross-dataset performance up to 30.7%, outperforming relevant baseline and state-of-the-art methods. The results indicate that a substantial part of the generalization gap is driven by low-level appearance variation that can be mitigated without retraining.

Molecular hydrogen (H$_2$) is the key ingredient for star formation in galaxies. However, how H$_2$ is distributed in and around galaxies is an open question in astronomy. We report the detection of H$_2$ (covering excitation levels $J = 0$ to 3) in a unique environment at a distance of 139 kpc from a starbursting luminous infrared galaxy. This is the furthest from a galaxy that H$_2$ has been directly detected to date. This H$_2$ system is unlike any seen before, with a high molecular-to-atomic hydrogen ratio (2%) and an accompanying low neutral hydrogen column density (log$_{10}[N($H I$)/\mathrm{cm}^{-2}] = 18.52^{+0.13}_{-3.58}$). Our measurements reveal that the H$_2$ bearing cloud is traveling at $\sim$100 km s$^{-1}$ relative to the host galaxy, has a super-solar metallicity, and excites at a single, cold temperature ($245^{+25}_{-21}$ K) indicating a lack of the ”typical” core-envelope structure seen in other H$_2$ clouds. Furthermore, our analysis points to the H$_2$ likely being formed through interactions between galactic winds and the gaseous halo surrounding the galaxy. The properties of this cloud suggest that the H$_2$ is short-lived, yet it presents crucial information on the microphysics of the wind-CGM interactions.

Time reversal $\Theta$ squares to $-1$ on a half-integer spin, so every state is orthogonal to its time reverse. This sign has been read only from quantum objects. The equilibrium state loses it, but the classical record keeps it. For a detector that resolves handedness, the probabilities that one stretch of record is followed by the time reverse of another measure the cohomology class of time reversal, $\Theta^2=\pm1$. Their matrix carries this sign in its signature, a topological integer that survives equal emission and absorption losses. A programmed emitter on quantum processors reads it in about $10^3$ shots.

In galaxy clusters, it is common to conceptually distinguish the central, brightest cluster galaxy (BCG) from the more diffuse intracluster light (ICL). So far, however, this distinction has lacked a clear physical basis, confusing both theoretical and observational studies. We address this by presenting a dynamically motivated definition of the two stellar components, evaluated using cluster zoom simulations from the Three Hundred project. We start with a motivational hindcasting approach, robustly tracing stars from the centres of 107 present-day clusters back through the merger hierarchy. We find that the majority of the final BCG stellar mass is typically contributed by the central galaxies of only 3 to 5 progenitor haloes. Most accreted galaxies contribute no stars to the BCG, instead surviving as satellites or depositing stellar material throughout the cluster. This naturally leads to a definition of the BCG stellar population as originating from the central galaxies of the most massive infalling systems. These are delivered to the cluster centre via efficient dynamical friction and subsequently undergo violent relaxation. The ICL arises from the complementary population of stars tidally stripped from the outskirts of all infalling systems. We therefore develop a forecasting method, identifying stars in the BCG and ICL via the dynamical fates of their originating stellar systems. Applying this to 261 clusters, we find the resulting components remain spatially interleaved, but occupy distinct regions of phase space. Our physically defined BCG matches conventional aperture-based selections with high completeness, while providing a direct interpretation in terms of hierarchical assembly.

We establish an $L^1$-theory for a class of elliptic operators with unbounded coefficients, extending our earlier semigroup generation results and those of Canale–Rhandi–Tacelli to the endpoint $p=1$. The $L^1$-realization generates a positive analytic $C_0$-semigroup that is compact for every positive time. We characterize the generator domain through weighted estimates and prove consistency with the corresponding $L^p$-semigroups for $1<p<\infty$.

In daily life, each person exhibits unique speaking habits, leading to subtle yet consistent lip-shape variations even when pronouncing the same word. Although recent talking head generation methods have achieved impressive visual fidelity and lip synchronization, they largely overlook user-specific customization, especially the motion patterns that characterize individual speaking habits. These habits are difficult to model and capture, as their motion patterns are highly fine-grained and often similar across individuals. As a result, many approaches produce overly uniform facial motions and fail to capture diverse, person-specific articulation patterns. To address this, we propose TalkLikeYou, an efficient framework that imitates how a target person speaks in talking head generation. Our method models habit in motion-space and achieves real-time performance through Flow Matching with only one sampling step during inference. We further adopt a two-stage imitation learning strategy to capture subtle distinctions between habits, allowing users to specify a target habit through either a preset style from the dataset or a reference video. In addition, we introduce a new metric PLAD that projects mouth motions onto representative articulation axes to evaluate imitation accuracy and generation diversity. Extensive experiments demonstrate that TalkLikeYou generates high-quality talking heads in real-time and significantly improves speaking habit imitation compared with prior methods. The code is available at: https://github.com/BQ-Wang0511/TalkLikeYou

Workplace sensing studies combine long-running behaviour traces with self-reports, yet the tools that collect those data often sit apart from the interface that returns results. We present TrustmeWatcher, the application built for the TRUST-ME project to connect this work. TrustmeWatcher reuses ActivityWatch's OS-level watchers for computer-activity collection and adds its own application layer. It turns the collected traces into an interactive screen-time dashboard, synchronizes responses from short questionnaires completed on the StreamDeck, and presents questionnaires alongside video highlights. Activity records and self-reports are aligned into labelled records for model development. The scope of this paper is limited to ActivityWatch data as model input. Artificial intelligence (AI) uses these activity records to predict six normalized state scores and an overall well-being score. The trained model runs locally, and the dashboard presents its predictions in semantic bands. Explainable artificial intelligence (XAI) helps users understand how recorded activity contributed to a prediction. Privacy Control lets users pause or resume the camera and eye tracker used by the study. We describe the workflow, its user-device and sensing-setup boundaries, and its use with records from 17 participants. The result is a deployed application and study workflow that integrates activity review, study data collection, privacy control, local prediction, and a participant-facing interface for XAI evaluation.

Causal discovery seeks to determine directional relationships among variables in complex systems, yet observational data alone generally do not identify causal direction. Complete identification therefore requires assumptions beyond linearity and acyclicity. A key approach is the Linear Non-Gaussian Acyclic Model (LiNGAM), which formulates linear structural equation model estimation as a blind source separation (BSS) problem. LiNGAM treats disturbances as mutually independent random variables under independent sampling, relying on higher-order statistics (HOS) and non-Gaussianity for identifiability. This restricts identifiability when multiple disturbances are Gaussian and ignores potentially informative temporal dependence. To broaden causal identifiability, we formulate linear acyclic causal discovery with mutually independent disturbance processes and transfer established BSS identification conditions to causal structure recovery. Under this formulation, replacing the mutual information cost with mutual information rate enables identification under a broader class of disturbances, including Gaussian processes with nonproportional covariance functions. Synthetic experiments reveal the limitations of methods relying solely on HOS or sample dependence, while their joint exploitation provides near-perfect causal recovery across the tested disturbance settings. Experiments on real functional magnetic resonance imaging (fMRI) data further demonstrate that jointly exploiting HOS and sample dependence improves the bootstrap stability of estimated ancestral directionality.

We report the growth and physical properties of HoCo$_2$ thin films on Si substrate by pulsed laser deposition. Well-defined Kiessig fringes in the x-ray reflectivity data yield a film thickness of $35 \pm 1$~nm and demonstrate smooth film surface and interface profiles. Atomic force microscopy confirms the high morphological quality of the films, revealing subnanometer surface roughness of $\sim$170~pm. Two independently prepared films exhibit a reproducible ferrimagnetic transition at $T_{\mathrm{C}}=77\pm3$~K, demonstrating retention of the characteristic magnetic ordering of bulk HoCo$_2$. However, the absence of resolvable thermal hysteresis indicates a predominantly continuous, second-order like transition in the films, in contrast to the first-order transition of bulk HoCo$_2$. At 5~K, the films exhibit clear magnetic hysteresis with a coercive field of $\sim$600~Oe, substantially larger than the negligible coercivity of bulk HoCo$_2$. X-ray photoelectron spectroscopy reveals comparable Ho $4d$ and Co $2p$ core-level line shapes and broadly similar valence-band spectra for the bulk and film, indicating preservation of the essential local electronic environment and occupied electronic structure.

Target tracking is the problem of estimating the state of a target system using measurements collected (oftentimes) by mobile sensors. Trajectory optimization for mobile sensors must account not only for dynamical and operational constraints, but also for uncertainty in estimating the target system's state. We propose an estimation-aware optimal control method for target tracking that accounts for the nonlinear dynamics of both the mobile sensor and target system, the nonlinear covariance dynamics in extended Kalman filtering, and nonlinear measurement models. Furthermore, it ensures constraints on the mobile sensor are satisfied in continuous time (within numerical precision). In numerical simulations, the proposed method achieves estimation-aware target tracking while satisfying the mobile-sensor constraints in continuous time, even under sparse time discretization.

Hyper-connections widen the residual stream of a Transformer to $n$ parallel streams. Their manifold-constrained version (mHC) mixes the streams at each layer with a doubly stochastic matrix, which it computes by Sinkhorn normalization of exponentiated logits. We give a geometric theory of this design on the Birkhoff polytope. First, a doubly stochastic mixer splits the stream into a mean channel, on which mHC is exactly a residual network, and a difference channel, which each layer contracts by its second singular value $\sigma_2 \le 1 - n \min_{ij} H_{ij}$. Thus the extra width is a fading memory with a horizon of $1/(1-\sigma_2)$ layers, and among nonnegative mixers only the permutations do not collapse. Second, the Sinkhorn-logit map is a global chart, and its logit gradient is exactly the Fisher-Rao gradient. Thus logit gradient flow follows a squared Fisher-Rao metric, and the straight-through update is exactly entropic mirror descent. Third, under logit gradient flow the logarithm of each entry moves at a rate of at most $4n^3\|\nabla f\|_\infty \varepsilon$, where $\varepsilon$ is the distance to the nearest permutation. Thus gradient flow approaches and leaves the vertices only at rate $1/t$, but mirror descent moves at an exponential rate. Fourth, the local convergence factor of Sinkhorn is $\sigma_2^2$, so a fixed iteration budget limits the horizon. Experiments confirm the predicted rates.

Suppose a committee, expert panel, or other group is making judgments on some issues, where these may be not just yes/no-questions, such as whether a defendant is guilty, but also variables with many possible values, such as macroeconomic or meteorological variables or travel directions. Furthermore, there may be interconnections between different issues, as in the case of economic or climate variables. How can the group arrive at "intelligent" collective judgments, based on the group members' individual judgments? We investigate three challenges raised by this judgment-aggregation problem. First, reasonable methods of aggregation (such as defining the collective judgment for each issue as the average or median judgment) can produce inconsistent collective judgments. Secondly, many methods of aggregation are manipulable by strategic voting. Finally, not all methods of aggregation are conducive to tracking the truth on the issues in question. We prove new impossibility or possibility theorems on all three challenges, identifying what it takes to produce collective judgments in a consistent, non-manipulable, and truth-tracking manner and thereby to achieve collective intelligence through aggregation. Overall, the median method, though imperfect, performs reasonably well. We also note the relevance of our analysis for non-human group decisions.

Methods for generalization in model-based reinforcement learning typically assume that an agent cannot recover the latent context governing the environment dynamics from its own experience, and therefore supplies it externally. We formalize and test this assumption with predictive sufficiency, which quantifies what access to the context adds to next-step prediction under the visitation distribution an agent induces, and separates that quantity into a history-recoverable part, a residual requiring the true context, and the deficit added by a finite model. We classify context-aware algorithms by the predictive risk their conditioning set can target and demonstrate across environments of increasing identification difficulty that the headroom does not follow the MDP class. The same task under different priors leaves predictive headroom in one setting and nothing distinguishable from zero in another, where the agent's behavior implicitly identifies the context and any benefit of such a mechanism cannot be attributed to missing information. Where headroom persists, the learned state exposes it only partially, and adding the true context still lowers the risk. Our contribution is a practical criterion for matching contextual mechanisms to the information available to them, estimated from the ordinary trained agent without a reference policy.

Wikidata is one of the largest open knowledge bases, yet answering a complex question over it still requires a SPARQL query that names the right entities and properties and chains their relations. Language models offer a natural-language alternative but answer largely from memory, which is least reliable for less prominent entities. We study agents that instead answer by exploring the graph, and argue that two obstacles limit them: the lack of training data recording how a solver explores, and interfaces that add large graph results directly to the model's context. We test three hypotheses: that the difficulty of graph search can be controlled through the structure of a question rather than only through obscure entities or wording; that much of the failure on long-horizon search comes from how retrieved evidence is managed rather than from the model itself; and that, in a suitable environment, open-weight models can match commercial closed ones. We construct multi-hop questions on a frozen Wikidata snapshot by replacing named entities with nested conditions, checking after each expansion that the target remains unique and that every new condition is necessary. We release 10,235 solving traces over single-entity and multi-hop questions, together with the recursive language model (RLM) harness that produced them, in which models batch graph calls, keep results in persistent Python state and interpret selected evidence through sub-calls. On 100 questions, the harness improves both models we ran under both interfaces compared with direct tool calling over the same functions: gpt-6-luna rises from 49 to 61 correct answers, doubling its multi-hop accuracy, and Qwen3.8-27B, an open-weight model served on a single GPU, from 60 to 74.

Starting from the robust foundation of the peculiar velocity based upwind (PVU) Boltzmann scheme, which fails to recognize contact discontinuities, this paper introduces new variants for the numerical solutions of equations of gas dynamics. A modified partial differential equation (MPDE) analysis of the original scheme reveals that the numerical diffusion coefficient corresponding to the peculiar velocity part does not vanish as the Mach number goes to zero. The numerical discretization of the peculiar velocity term is redesigned so that the numerical diffusion depends only on the bulk fluid velocity across the stationary contact discontinuities, enabling its exact capture in 1D and exact capture of slip surfaces in 2D. The resulting variants achieve low numerical diffusion while preserving the robustness of the original scheme, as demonstrated through several 1D and 2D benchmark compressible flow test cases.

We introduce a post-training method for diffusion language models (DLMs) that minimizes Maximum Mean Discrepancy (MMD) between generated and reference distributions in the feature space of a frozen pretrained DLM. To estimate MMD, we retain contextual features at individual token positions, obtaining multiple observations per sequence from a single extractor pass. We optimize this objective using policy gradients for discrete models and direct differentiation through generated latents for continuous models. In both cases, computing the loss directly from these features enables efficient post-training without full sampling trajectories or jointly trained auxiliary models. Experiments show lower generative perplexity at comparable entropy on OpenWebText and better accuracy-computation trade-offs on GSM8K. On 16B DMax-LLaDA2.0 models with hybrid masked-uniform diffusion, we increase decoding parallelism with similar or higher accuracy on math and code benchmarks.

Reinforcement learning has greatly advanced the capabilities of large language models, but its memory demands remain a barrier to broader adoption. We introduce LoGRA, an approach to RL post-training that reduces memory by retaining useful learning signals in low-rank gradient sketches. These compact representations support both model updates and efficient policy synchronization. To prevent overly large updates from disrupting learning, we complement gradient compression with predicted-KL step control, which estimates policy changes before applying each update and adjusts its magnitude accordingly. With all techniques combined, LoGRA reduces average training memory usage by up to 45.7% across reasoning tasks without compromising performance. It also enables stable training of a 27B-parameter model for over 1,100 steps on a single eight-GPU node, where dense Adam runs out of memory, making previously memory-infeasible RL training practical. Code is available in the \href{https://github.com/skzhang1/labs-molt/tree/logra/examples/scripts/logra}{Molt library}.

The extensive use of GPUs in cloud computing, accelerated by the spread of large language model (LLM) services, and the growing need for multitenancy have driven the development of innovative solutions for efficient GPU resource management. Multi-Instance GPU (MIG) technology from NVIDIA enables shared GPU usage in cloud data centers by providing isolated instances, which are offered as MIG-backed virtual GPUs (vGPUs). However, MIG placement rules often lead to fragmentation and suboptimal resource allocation. In this work, we formally model the MIG-aware virtual machine (VM) placement as a binary integer linear programming (BILP) problem aimed at maximizing request acceptance, consolidating resources, and reducing migration overhead. Building upon this formulation, we propose OrigaMIG, a MIG-aware placement optimizer. OrigaMIG places each arriving request at once with a lightweight greedy rule and calls the solver only when a request cannot be placed or the GPUs of a class become fragmented. Each call solves the BILP on a small neighborhood of physical machines (PMs), keeps the rest of the data center fixed, and executes the solution as live migrations. We compare OrigaMIG with the default placement and with two state-of-the-art MIG-aware policies in simulation, across six loads, eleven variants of the workload and the hardware, and data centers of up to 4096 PMs. On 256 A100 and A30 GPUs in 128 PMs, OrigaMIG keeps fewer PMs active than the stronger policy in 29 of 30 paired runs while migrating 29% to 49% fewer VMs, and it uses the least energy per admitted GPU-hour at every load. Against the default placement, it keeps up to 12.5% fewer PMs active and admits up to 7.8 percentage points more of the requested GPU memory. On small data centers, it stays within 4.1% of the optimal number of active PMs.

This paper introduces a new extrapolation framework within the Calculus of Variations. We develop a robust quantitative theory of the $\Gamma$-convergence approach of De Giorgi by combining it with Gagliardo's work on relative completions in interpolation theory. A central new tool is the extrapolation of \emph{variational $K$-functionals}, which associates to an arbitrary family of functionals a dynamic penalty method that simultaneously characterizes their $\Gamma$-limits and yields explicit rates of convergence for minimizers. As a technical foundation we prove compactness extrapolation theorems also involving Gagliardo completions. To illustrate the mechanism, we apply the technique to variational models arising in image processing, notably the Rudin–Osher–Fatemi (ROF) and Chan–Esedoglu models. Our main result in this setting is a contribution to the inverse regularity problem associated to discrete approximations of the ROF model: we show that the required regularity of the observed image that guarantees a prescribed optimal rate of convergence is measured in terms of the decay of variational $K$-functionals. Surprisingly, our characterization is explicitly captured by using the recently introduced spaces of Brezis, Van Schaftingen, and Yung. Moreover, our methods unify, and considerably extend, classical pointwise convergence and $\Gamma$-versions of the Bourgain–Brezis–Mironescu and Maz'ya–Shaposhnikova formulae, as well as related results in a variety of settings that involve BMO-type functionals, heat kernels, Sobolev spaces on metric measure spaces, ... By bridging De Giorgi's variational convergence with Gagliardo's completion through variational $K$-functionals and extrapolation of compactness, this work establishes a quantitative approach to the Calculus of Variations.

We prove counting formulae for the number of directed Hamiltonian paths and directed Hamiltonian cycles in any complete multipartite graph. The method is based on a collapsing technique relating general path graphs with coloured vertices to legally coloured path graphs.

Robot learning in simulation depends on the objects the simulator offers. Many tasks need objects with separate parts, joints that allow the required motion, and physical properties that remain valid under contact. Existing methods recover this structure anew for every image: generative models predict parts and joints that mostly fail to settle or move in simulation, and general-purpose agents need a long session of model calls for each photograph. AffordCraft builds such an asset from a single RGB image and a task instruction by retrieval instead of generation: it locates the object and the part to operate, selects a matching entry from a library of articulated assets, and fits it to the image while keeping its parts and joints intact. Without any box or mask marking the object, AffordCraft produces a physically valid asset for 1,703 of 2,000 photographs from 31 categories. Five generative methods pass on at most 45% of the same photographs and, at the median, need 10 to 78 times our GPU time per valid asset. On 50 cluttered images, 162 of 237 annotated objects pass the same physical test after automatic detection. Growing the library from 141 to 11,372 entries needs no change to the method and raises category coverage from 46% to 100% and the share of selections with the requested label from 18% to 51%. We also build manipulation tasks from the constructed assets, both with single objects and in composed scenes; policies trained on scripted demonstrations complete both kinds of tasks from initial states unseen in training.

A quantum channel is called incompatibility-breaking if it always destroys the incompatibility of quantum measurements. On the other extreme are incompatibility-preserving channels, which never destroy incompatibility. This work studies both types of channels through the mathematical framework of zonotopes and zonoids, an approach that provides a complete characterization of compatibility for dichotomic measurements and is particularly powerful in the qubit setting. Using the language of zonoids, we present necessary and sufficient conditions for when a qubit unital channel is incompatibility-breaking, which are also sufficient for nonunital channels. As one of our main results, we demonstrate the superactivation phenomenon of two incompatibility-breaking qubit channels that are no longer incompatibility-breaking when used in parallel. Translating this result into the task of quantum steering, it says that two copies of a two-qubit Werner state can be steered at noise threshold $1/2$, even though this is impossible using just one copy. For the problem of incompatibility preservation, we prove that a quantum channel with matching input and output dimensions will preserve general incompatibility if and only if it is a unitary transformation. When the output dimension is larger, this result no longer holds, and we offer a conjectured form of a general incompatibility-preserving channel.

Human–robot co-transportation of deformable objects requires predicting object deformation during motion, since obstacle clearance depends on both the grasp points and the unactuated interior. We present a hierarchical planning framework that combines a learned cloth model with a reduced-order whole-body model of a dual-arm mobile manipulator. A physics-residual conditional recurrent variational autoencoder (p-cRVAE) predicts the full cloth configuration from grasp-point observations by learning a residual correction to a computationally efficient linearized physics model, limiting error accumulation over 40-step planning horizon. The predicted cloth dynamics are embedded in a model predictive path integral (MPPI) planner using a reduced-order representation of a dual-arm mobile manipulator that preserves the non-holonomic base constraint and arm workspace limits. An MPC layer subsequently refines the sampled motion into smooth, executable references for whole-body control. The reduced-order formulation achieves tracking performance comparable to the full 17-DoF model while reducing computation time by approximately 80%. Across four co-transportation scenarios and two carrying speeds, the proposed framework maintains cloth-obstacle clearance where a corner-following baseline results in collisions, while whole-body refinement reduces final cloth deformation from 0.93\,m to 0.28\,m.

Machine learning (ML) studies using clinical data often rely on preprocessing and filtering pipelines before model development. The filtering decisions made in these pipelines can alter the dataset's statistical structure and may artificially reduce or increase the complexity of the prediction task. We argue that filtering choices should be treated as part of the scientific method rather than as a routine preprocessing step. We further discuss the need for explainable and transparent preprocessing pipelines that allow researchers to understand why specific filtering choices are made and how these choices affect the resulting data distribution and model performance. All of the source code for this work is available on GitHub.