Papers

Structure leads to function: Knowing all possible ways to stack and slide identical monolayers enables the design of functionalities such as nonlinear optical responses and ferroelectricity in layered materials. Besides, mounting experimental evidence points to differing stacking configurations in few-monolayer and bulk samples. To exemplify the core concepts for stacking arbitrary monolayers, ground-state and metastable non-moiré SnSe stacks were first identified using density functional theory and employed to validate a “divide and conquer” combinatoral approach for determining the most probable stacking configurations in materials with an arbitrary number of identical monolayers. A small number of point groups accounts for all possible stacks, which explains experimental second-harmonic optical responses. Finite-temperature effects are also studied despite the granularity of available data. This comprehensive framework readily generalizes to provide a predictive description of arbitrary metastable few-homomonolayer stacks.

Open-system dynamics govern decoherence, transport, and engineered dissipation in quantum many-body systems. We propose a quantum algorithm for simulating time-independent, finite-range Lindblad dynamics with bounded local strength on a constant-dimensional lattice of $n$ sites, allowing noncommuting jump operators. For time $T\ge1$ and diamond-norm error at most $\epsilon$, it has depth $O(T\operatorname{polylog}(nT/\epsilon))$ and gate count $O(nT\operatorname{polylog}(nT/\epsilon))$. These results extend the HHKL spatial decomposition to open systems. The main obstacle is that the reversible overlap corrections used for unitary dynamics have no direct analogue for dissipative channels. We overcome this by retaining the environment in a shared unitary dilation, keeping information lost from the system coherently available and making the spatial corrections reversible. We prove exponential occupation bounds for the environmental states generated by the decomposition, allowing compact representation and coherent simulation of local factors on the inputs that arise. The construction reduces each short-time evolution to a constant number of parallel layers on regions of logarithmic diameter, using nearest-neighbour gates and polylogarithmic auxiliary density. We also prove unconditional worst-case lower bounds using time-independent, purely dissipative processes that transport quantum information. For circuits with local quantum and classical communication, the lower bounds are $\Omega(nT)$ for the expected gate count and $\Omega(T)$ for depth on time scales up to the lattice diameter. They match the upper bounds' leading time and volume dependence up to polylogarithmic factors. At fixed time and sufficiently small fixed error, we further prove a depth lower bound of $\Omega(\log n/\log\log n)$, showing that global accuracy can require increasing depth as the lattice grows.

We investigate the cosmological dynamics and thermodynamic properties of a viscous variable generalized Chaplygin gas (VVGCG) model in a spatially flat Friedmann–Lema^{\i}tre–Robertson–Walker universe, described by $P=-B/\rho^\alpha$, where $B=B_0V^{n/3}$. The model includes a bulk-viscous pressure $\Pi=-3\xi H$, with $\xi=\xi_0\rho^{1/2}$. We find that the physically viable branch corresponds to $\xi_0<0$, for which the positive viscous pressure dominates at early times, producing decelerated expansion. As the volume increases, the effective pressure changes sign at a finite volume $V_c$, while the transition to acceleration occurs at a larger volume $V_f$. At large volume, the equation-of-state parameter approaches a phantom-like regime for $n<0$. A detailed thermodynamic analysis of the thermal and caloric equations of state, entropy, heat capacity, and isothermal and adiabatic stability shows that the stability conditions and $c_V>0$ are simultaneously satisfied for $n<0$ and $\xi_0<0$. The entropy vanishes as $T\rightarrow0$, consistent with the third law, while the model admits a finite minimum volume and corresponding maximum temperature. Thermodynamic consistency is further verified through the fundamental thermodynamic identity. The framework also contains several existing Chaplygin-gas models as special cases. Constraints from the Hubble-57 data yield $\alpha=0.0024$, $n=-0.0182$, and $\xi_0=-0.0015$, consistent with the thermodynamically stable parameter region. Thus, the VVGCG model provides a consistent description of cosmic evolution from an early decelerating phase to late-time phantom-like acceleration while remaining thermodynamically stable throughout the evolution.

By making use of partial information decomposition, we analyse information transmission through a local processor which receives two streams of integrated inputs. We revise previously stated conditions for contextual modulation that are based on the components of partial information decomposition, and introduce a condition for the presence of signal integration. Exact results are obtained for information-theoretic measures and the components of partial information decomposition using the Ibroja method. A general class of activation functions is considered along with a particular divisive normalisation transfer function. These results are applied with several activation functions, of additive, multiplicative, subtractive and divisive forms, with graphical illustration, and the conditions for modulation and integration are tested in each case. The revised information-theoretic conditions are also applied to noisy data obtained from a realistic simulation of a model layer 5b pyramidal cell in three distinct regimes defined by experimental design and characterised by the values of the input basal and apical amplitudes. Evidence for driving basal input with modulating apical input, driving apical input with modulating basal input, and of apical-basal signal integration is presented.

Model Predictive Control (MPC) provides a structured and constraint-aware mechanism for decision-making, but its reliance on optimization-friendly analytical dynamics models limits its use in tasks with contacts and other hard-to-model state dependencies. Model-free reinforcement learning avoids explicit modeling assumptions but typically requires large amounts of interaction data. We present a learning-based MPC framework that combines the data efficiency and structure of local model-based planning with learned components that compensate for incomplete dynamics and finite-horizon myopia. The method augments a nominal analytical model with a residual dynamics network that learns missing state-dependent effects from data and combines the resulting planner with a learned action-value critic that injects long-horizon MDP structure into the local iLQR optimization. To make this practical at reinforcement-learning scale, we develop a GPU-accelerated batched iLQR solver that evaluates learned dynamics and critic networks inside the optimal-control loop and solves thousands of trajectory-optimization problems in parallel. The complete system is integrated into a robotics simulator, enabling scalable model-based reinforcement learning under incomplete dynamics. Experiments on biased and incompletely modeled control tasks show that the approach improves closed-loop control performance while preserving the model-based structure needed for efficient constrained trajectory optimization.

Motivated by Kepler's long battle with the orbit of Mars, we present a family of orbits that satisfy his second law, conserving angular momentum around a central mass, and also fulfill Ptolemy's belief in an equant — a point around which the angular speed is constant. For specific values of the angular momentum, these orbits can be written in terms of Legendre polynomials and functions of the second kind. They are analytic except at perihelion where they are twice differentiable. They resemble the "ovoid" (egg-shaped) or "metopoid" (face-shaped) orbits that Kepler considered on his way to the ellipse.

Generative AI (GenAI) allows for improved user experience within conversational agents for diabetes management by supporting dynamic, context-aware conversations. In this study, we elicited patient preferences for the communication style of a GenAI-based conversational agent (uMatter) developed to support diabetes management. We conducted an online survey with 125 individuals with type 2 diabetes. The survey included a discrete choice experiment to evaluate participant preferences for different types of messaging attributes. The survey also elicited participant perceptions and feedback on the messages from uMatter. We found significant preference heterogeneity for the inclusion of emojis within the messages. Additionally, qualitative findings indicated that participants had different desired personas and communication styles for the conversational agent. We propose strategies from recent human-computer interaction and natural language processing research that can be used to design GenAI-based conversational agents that align with the communication preferences of patients.

We study a log-Hardy-Littlewood-Sobolev (log-HLS) inequality under constraints and a naturally induced Wasserstein flow. The constrained log-HLS inequality is dual, in a variational sense, to the constrained Trudinger-Moser-Onofri-Aubin inequality. The corresponding gradient-flow formulation leads to a parabolic-elliptic Patlak-Keller-Segel (PKS) system whose global dynamics exhibit a dichotomy between global existence and finite-time blow-up depending on the initial mass. Remarkably, the constraint raises the critical mass threshold of the flow by a factor of two compared with the unconstrained setting. This provides a distinct mechanism for suppressing blow-up from those arising in related formulations of the PKS-system, where blow-up is mitigated through additional effects such as a forcing term, coupling with a fluid equation, or the ambient flow generated by harmonic perturbations of the Newtonian potential.

Inline citations are central to scholarly communication, yet verifying their use is becoming increasingly challenging because of growing review pressures. We conducted a mixed-methods exploratory study to investigate how reviewers verify inline citations, the factors shaping their verification practices, and how they envision GenAI supporting this process. Across interviews (n=12) and a survey (n=203) of reviewers from HCI and AI venues, we found that reviewers' perceptions of citation importance, verification practices, and desired AI autonomy varied across citation types, reviewer characteristics, and research backgrounds. These findings highlight the need for adaptive support tailored to different citation types and reviewer practices, while revealing diverse preferences regarding the use of GenAI for this process. Moreover, effective citation verification should involve collaboration among reviewers, authors, and the broader research community, rather than relying solely on individual reviewers.

We develop an algebraic-dynamical correspondence for type-I oscillatory blow-up solutions of autonomous ODEs with asymptotically quasi-homogeneous vector fields. Periodic solutions of the balance law arising from asymptotic expansions of blow-ups are related to periodic orbits on the horizon for the desingularized vector field. Unlike the stationary case, the correspondence involves a positive periodic scaling function and a nontrivial time reparametrization. We further establish the correspondence of linearized structures: distinguished phase and scaling directions generate invariant subbundles, while the remaining characteristic multipliers are identified through associated quotient bundles. These results yield a criterion for the existence of type-I periodic blow-up solutions based on periodic solutions of the balance law and their characteristic multipliers, without explicitly constructing compactifications or periodic orbits at infinity. The theory also clarifies the difference between stability information in the balance law and in dynamics at infinity. Two examples illustrate the correspondence.

Fluorescence microscopy reveals where proteins localize, but only a limited number of proteins can be imaged in the same cell; generating these images from amino-acid sequence and the cell's morphological context enables in silico localization of unimaged proteins. The two conditions, however, play asymmetric roles: morphological context is spatially aligned with the target, whereas sequence is non-spatial and must specify protein-dependent localization within it, with recurring coarse patterns shared across proteins and finer protein-specific variation. Existing generators condition on both jointly, without separating what each explains. We introduce FACET (Factorized Asymmetric Conditioning for Efficient Transport), a probabilistic generative framework that encodes this structure as an explicit inductive bias: sequence semantics are learned from what context leaves unexplained, coarse localization regularities are shared across proteins through a semantic memory, and protein-specific variation is a bounded residual around them. A variance-preserving state projection further lets FACET perform continuous stochastic transport through a pretrained diffusion predictor with minimal parameter overhead. On held-out proteins, FACET improves spatial overlap by 34.3% on the Human Protein Atlas and 14.0% on OpenCell over a backbone-matched baseline, and reduces FID by 27.2% and 46.5%, respectively, with 75% fewer network evaluations. It also substantially improves protein-association structure recovery and yields better-calibrated predictions, while detailed ablations show complementary contributions from its design choices. These results identify factorized asymmetric conditioning, rather than generator capacity alone, as a key lever for high-fidelity, efficient, and biologically meaningful cellular image synthesis.

Tabular foundation models (TFMs) outperform established machine learning models on tabular benchmarks through in-context learning. Building on this success, interest is growing in applying them to data streams, where data arrive continuously and evolve over time. On a stream, a TFM adapts by updating its context rather than its parameters, so its accuracy and cost depend on which examples it keeps and how often it rebuilds its context. We therefore present a systematic study of TFMs on data streams, covering memory management, computational cost, and stream-specific challenges such as concept drift and delayed labels. We find that TFMs achieve the highest predictive performance and that simply retaining the most recent examples is as effective as existing memory management techniques. They also recover faster than streaming learners after drift and keep the highest accuracy under label delay. This accuracy, however, comes at a high serving cost, since a nearly unchanged context is re-encoded at every prediction. These results point to architectural efficiency as the way forward for in-context stream learning.

The Toothbrush Cluster (1RXS J0603.3+4214) is known for its northern radio relic, radio halo, and highly disturbed X-ray morphology. It shows features of both shock-driven and turbulent reacceleration, the latter of which is invoked to explain its radio halo. However, how kinetic energy from the merger is distributed into gas motions across spatial scales remains unclear. We probe the intracluster medium (ICM) dynamics in the southern, X-ray-brightest region of the cluster using a 167 ks XRISM/Resolve observation. We conduct both full-array and quadrant sub-array analyses by fitting the spectra with single and multi-component thermal models in the 3-8 keV band. The full-array spectrum favours two ICM components with a transonic line-of-sight (LOS) velocity difference of $\Delta v_{\mathrm{bulk}}=1635^{+165}_{-110}$ km s$^{-1}$, while the velocity dispersions are much lower, at $\sigma_{v,1\mathrm{D}}\sim$245-310 km s$^{-1}$. The sub-array analysis likewise reveals multiple components in at least three quadrants, with LOS bulk velocities ranging from $-2520^{+295}_{-230}$ to $+930^{+70}_{-110}$ km s$^{-1}$. The velocity dispersions remain modest at $\sim$215 km s$^{-1}$, corresponding to a turbulent pressure support of about 3-6% on scales dominating the observed line broadening. Cooler gas is detected in the NE and SW, with $kT_{\mathrm{NE}}=3.13^{+0.33}_{-0.30}$ keV and $kT_{\mathrm{SW}}=2.32^{+0.43}_{-0.37}$ keV, likely associated with a third, northern subcluster identified in weak-lensing and optical studies. Our results indicate a complex ICM kinematic structure, with evidence for at least three subclusters exhibiting supersonic bulk velocity offsets and much smaller velocity dispersions. This shows that the merger geometry has a significant line-of-sight component and may indicate that the cluster collision is relatively young, with the turbulent cascade not yet fully established.

Behavioral Foundation Models (BFMs) aim to solve a wide range of downstream tasks without test-time policy learning by inferring a task vector from the reward function. While efficient, the retrieved policies are often suboptimal because of how this task vector is inferred, typically with ordinary least squares (OLS). OLS minimizes reward reconstruction error but leaves the ordering of rewards unconstrained, which can bias the successor measure of the retrieved zero-shot policy away from that of the optimal policy. In this work, we propose BLS, an efficient test-time inference method that balances minimizing reward reconstruction error with reducing successor-measure mismatch. Theoretically, we provide a suboptimality gap upper bound characterized by both successor-measure and reward-function residuals. Empirically, we evaluate BLS on top of state-of-the-art BFMs across benchmarks for locomotion, manipulation, and humanoid control. BLS outperforms existing task inference baselines with negligible computational overhead. Project page: https://embodiedai-ntu.github.io/BLS

We introduce CNP-Flow, a flow matching framework for temporal generation that learns conditional source distributions through flow reversal. Whereas standard conditional flow matching (FM) incorporates conditioning through the vector field and draws source samples from a standard Gaussian, CNP-Flow uses a conditional noise predictor (CNP) to produce an isotropic Gaussian source for each temporal condition. The CNP is supervised by source samples obtained through flow reversal, which maps observed targets backward through a pretrained FM model. A three-stage pipeline pretrains the FM model, trains the CNP, and fine-tunes the FM model using the learned source distribution, while preserving the FM backbone architecture. Across video prediction, video interpolation, and 7-DoF Franka robot motion planning, CNP-Flow consistently improves generation quality. It also matches baseline performance with fewer function evaluations. Project page: https://embodiedai-ntu.github.io/cnpflow

A search tool never says no: it returns its top-k passages even when the index holds no answer, so the agent sees irrelevant text instead of a miss signal. We ask what frozen search agents do when the tool refuses instead. On an index-hole testbed (257 NQ and 300 HotpotQA questions run with and without their gold passages in a 21M-passage BM25 index), seven agents receive one of five refusal wordings. An un-announced one-sentence refusal raises abstention on unanswerable questions from 23% to 97% on average for Qwen3-8B/32B and from 28% to 57% for Claude Haiku 4.5, cutting wrong answers almost one-for-one and beating a system-prompt instruction by 51 points on average. Search-R1 ignores the refusal and fabricates retrievals; Claude Sonnet 5.5 and Opus 5.5 answer from memory (abstention +2 points) and obey a system-prompt directive instead (+16). We also found that wording matters: an explanation beats a bare token; a directive inside the observation is decisive for Haiku; a soft warning is useless. Realistic triggers, from a lightweight score-based predictor to an LLM grounding judge, fall well short of the oracle, and all land on a benefit-versus-signal-quality curve that prices any trigger by its recall at a fixed false-refusal budget: for compliant agents the bottleneck is the detector inside the tool, not the agent, and the curve tells future detector work what each point of recall is worth.

We determine the sharp uniform constant in the quartic stability estimate for the logarithmic Sobolev inequality on finite cycles. We equip $C_{n}=\mathbb{Z}/n\mathbb{Z}$ with the uniform probability measure, and we let $\mathcal{E}_{n}$ be the Dirichlet form of the simple random walk on $C_{n}$, normalized so that its spectral gap is one. Frank and Ivanisvili recently proved the sharp logarithmic Sobolev inequality $2\mathcal{E}_{n}(u)\geq \mathrm{Ent}(u^{2})$ for all $n\geq 4$. We prove that $2\mathcal{E}_{n}(u)-\mathrm{Ent}(u^{2})\geq \frac{1}{3}\Vert u-1\Vert _{2}^{4}$ for all $n\geq 4$ and all nonnegative $u$ with $\Vert u\Vert _{2}=1$. This is the sharp form, uniformly in $n$, of the quartic stability estimate of Xie and Zhang, who obtained the constant $\frac{1}{12}$. The same estimate holds on the circle and for the word-length energy on $C_{n}$. Among these models, the four-cycle is the only extremal one: on $C_{4}$ the constant $\frac{1}{3}$ is sharp but not attained, while on $C_{n}$ with $n\geq 5$ and on the circle the sharp constant is at least $\frac{1}{3}+c$, where $c>0$ does not depend on $n$. We also give explicit upper bounds for these sharp constants. Our second main result is a stability estimate for the cubic Sobolev inequality of Frank and Ivanisvili, which is the main step in their proof. It gives the quantitative version of this inequality expected by Frank and Ivanisvili, with the optimal powers of $\Vert u-1\Vert _{2}$: four on $C_{n}$ with $n\geq 5$ and on the circle, and six on $C_{4}$. Two key new ingredients of the proofs are a bound for the first Fourier coefficient of $u$ in terms of its mean, which holds because $u$ is nonnegative, and a sharp stability estimate for Gross's two-point logarithmic Sobolev inequality, with sharp constants in both the fourth and the sixth powers of the distance.

Self-play red-teaming improves language-model safety by pitting attacker and defender roles against each other in a zero-sum game. However, real adversaries increasingly use mosaic attacks: multi-turn sequences whose individual fragments are innocuous in isolation yet assemble into a harmful payload. We develop a theory of mosaic defense that characterizes what is required to prevent such attacks without sacrificing helpfulness. We first show that no fixed bounded window of recent prompts is sufficient in general: safety-relevant information may occur arbitrarily far back in the interaction. We formalize a watchman, an online state mechanism that carries this information forward, and show that under explicit assumptions it enables zero-failure defense with positive benign helpfulness. Under stronger conditions, it is also optimal among zero-failure defenders. An exact watchman may nevertheless require exponentially many states, while exact maliciousness detection can require exponentially many queries in an unstructured black-box model. These state and query lower bounds do not by themselves imply hard learning: the construction underlying the state lower bound is efficiently learnable from labeled examples, whereas certifying worst-case safety can require substantially more information under restricted access. We also show that self-play equilibrium alone does not certify usefulness, motivating a constrained formulation that maximizes worst-case benign helpfulness among zero-failure defenders. Empirically, training role-specific attacker and defender LoRA adapters over frozen LLMs via multi-turn self-play strengthens both roles: attackers become more effective at eliciting harmful responses, while defenders become more robust to attack, with improvements also observed on unseen attack objectives.

Beauty-hadron production in proton-nucleus collisions is a particularly powerful probe of cold nuclear matter (CNM) effects: thanks to the large beauty-quark mass, the production is initiated in early hard scatterings and is calculable in perturbative QCD, while the modifications observed in nuclear collisions directly constrain the nuclear parton distribution functions (nPDFs) in a kinematic region complementary to that accessed by charm. Precisely quantifying these effects is a prerequisite for isolating possible signatures of quark-gluon plasma formation in heavy-ion collisions. In this work, the production of open beauty hadrons in p-Pb collisions at $\sqrt{s_{\mathrm{NN}}} = 5.02$ and $8.16$~TeV is studied via a data-driven Bayesian unfolding of ALICE and LHCb measurements of non-prompt $D^{0}$ and J/$\psi$ mesons. The unfolded $p_{T}$- and $y$-differential cross sections are mutually consistent across decay channels and compatible with directly reconstructed beauty-hadron measurements. The nuclear modification factor $R_{pPb}$ is reported as a function of transverse momentum and rapidity, providing the first unfolding-based result spanning $-4.0 < y < 4.0$ of beauty-hadron $R_{pPb}$ covering the full rapidity range, with a precision comparable to or better than that of existing data. The results are compared with calculations based on nPDFs and can provide valuable constraints for future global nPDF fits. The total inclusive B hadron production cross section in p-Pb collisions is also reported. A weaker CNM suppression is observed for beauty hadrons than for charm hadrons, consistent with the expected mass hierarchy of cold-nuclear-matter effects.

In this paper, we construct a series of smooth affine varieties of dimension $n \geqslant 3$ that are generically flexible but not flexible. Moreover, these varieties admit a nontrivial divisor invariant under the subgroup of special automorphisms.

An adequate conversational answer may differ from a short or incomplete benchmark reference. To measure adequacy against the recorded history we prefer source-aware grading, in which the judge checks the reference against the full source before assessing system-blinded answers; original reference-only grading is reported alongside. With a local Qwen 3.8 27B Q4_K_M reader and a 24,000-token evidence ceiling, MemStrata CL1 scores 475/500 (95.0%) on LongMemEval-S and 1,400/1,540 (90.91%) on LoCoMo categories 1-4 under source-aware GPT-5.5 adjudication, against 463/500 (92.6%) and 1,205/1,540 (78.25%) under reference-only grading of the same answers. It preserves a retrieval backbone and adds nonduplicated, dated, speaker-attributed source spans. A same-reader full-history control with about 4.7 times the evidence scores 464/500 reference-only and 470/500 (94.0%) source-aware; neither difference is decisive. Keyword-only selection at the same budget scores 425, and a matched-reader Letta arm 438. On LongMemEval-M, where the packet holds about 1.6% of each history, MemStrata CL1 scores 427/500, with losses concentrated in multi-session and temporal questions. On 300 BEAM-1M questions it outscores dense retrieval, 0.738 to 0.706 (Wilcoxon p = 0.011). A same-seed replay of unchanged requests changed 1.5-2.3% of labels. On identical packets GLM 5.3 flash is non-inferior within 3 points (462 versus 463); Muse Spark 1.3 did not show non-inferiority on 269 questions. None of four pre-registered interventions met all of its registered advancement or feasibility criteria. Signed read-side artifacts support inspection but do not regenerate the private retrieval pipeline. The superiority of source-aware grading to human adjudication is not established, and development exposure, automated-judge dependence and the absence of held-out data preclude an independent-replication or leaderboard claim.

Infrared small-target detection plays an important role in maritime monitoring and aerial surveillance. Although multimodal large language models (MLLMs) offer promising capabilities for visual understanding, existing MLLM-based approaches struggle to precisely localize infrared small targets. In this paper, we propose IRSTD-Agent, an agentic framework for infrared small target detection through dynamic visual search. The framework enables an MLLM to adaptively determine where and at what scale to inspect an image and progressively gather fine-grained visual evidence for precise target localization. Five complementary visual tools (PROPOSAL, ZOOM, DETECT, DROP and REFINE) support object candidate discovery, adaptive observation, target localization, hypothesis rejection, and target extent refinement, together enabling a coordinated search process over original-resolution images. To teach the MLLMs to conduct this search, we introduce Zoom-guided Interaction Learning, which uses annotation-derived interaction trajectories to supervise tool selection and the corresponding arguments. Through extensive experiments on WideIRSTD-Full and IRSTD-1k datasets, we demonstrate that IRSTD-Agent outperforms the evaluated vision-language models and enhances the precise localization capabilities of MLLMs in IRSTD tasks.

Chronic wound management affects over 8.2 million patients in the United States and imposes substantial clinical and economic burden. Clinical wound assessment commonly involves three coupled tasks: identifying wound type, delineating wound boundaries, and localizing the wound region for measurement and monitoring. Despite this clinical coupling, existing machine learning approaches typically address wound classification, segmentation, and localization using separate models. We present WILLIE, a unified framework and benchmark for wound classification, segmentation and localization that enables systematic evaluation of multi-task wound analysis under a common protocol. WILLIE harmonizes three public wound datasets into a shared benchmark and compares unified models across three scaling configurations against 10 single-task baselines. The best model achieves 91.88% classification accuracy, 91.41% Dice, and 96.23% AP@0.5 while producing all three outputs in a single forward pass. Beyond aggregate performance, our results show that segmentation-derived localization outperforms dedicated detection baselines in this benchmark, suggesting that box-based localization may be unnecessary for spatially coherent wound targets. Our findings highlight that effective multi-task learning in healthcare imaging depends not only on shared representations, but also on task formulation, compatibility, and benchmark design.

Overlapping multi step forecasts often disagree, a form of vertical instability that we term cross origin incoherence. We propose a Bayesian reconciliation framework that treats overlapping forecasts as noisy, biased measurements of a common latent trajectory. Operating as a model agnostic post processing layer, it requires no access to model internals. Simulations demonstrate substantial incoherence reduction and robust latent trajectory recovery, remaining highly resilient (correlation 0.972) even under severe nonlinear stress tests. An empirical application to S&P 500 volatility evaluates AR(1), ETS, and LSTM models. The framework reduces incoherence by over 97% across all models while delivering fully calibrated probabilistic forecasts (93% to 94% coverage). Notably, it improves point accuracy for ETS and LSTM. Furthermore, the estimated horizon specific parameters act as a diagnostic X-ray, revealing hidden biases in neural networks without requiring access to their architecture

The CANDECOMP/PARAFAC (CP) decomposition is widely used for revealing the underlying patterns from multiway data (also referred to as a higher-order tensor). When the data is clipped or saturated, however, the linear CP model becomes unreliable. Several remedies exist such as treating the clipped entries as missing or imputation; however, both fall short in different scenarios. We propose a nonlinear CP model (NCP) for pattern discovery in this setting, extending ideas from nonlinear matrix decompositions to tensors, and solve it using a flexible ADMM (Alternating Direction Method of Multipliers)-based framework that can accommodate a variety of nonlinearities. Using synthetic data with known factors and simulated metabolomics data where clipping arises from instrument detection limits, we demonstrate that NCP recovers the underlying factors more accurately than CP fitted to only the observed entries or threshold-imputed data.

Hierarchical reinforcement learning uses temporally extended subtasks for exploration, yet committing to their execution can restrict both deployment and policy learning. We identify and separate the resulting execution and policy suboptimality. Task and execution trees distinguish reward objectives from policy choices and decision interruption. A Unified Value Function for HRL and a four-stage Generalized Hierarchical Bellman Equation then support a common analysis of both losses. Under bounded rewards and uniform termination, we establish hierarchical policy and execution improvement results. With the remaining node policies fixed, task-subtree compatibility and node-policy optimality under the original execution mode establish when Markov execution is optimal. The resulting decomposition leads to independent execution choices for behavior, targets, and deployment. We instantiate this principle through execution improvement and one-stage or two-stage policy improvement at arbitrary hierarchy depth. Option-based and goal-conditioned experiments demonstrate complementary gains from changing execution and changing the learning target. Controlled stochastic environments show how these gains depend on stochastic transition strength and spatial structure. This framework makes execution design an explicit component of hierarchical policy optimization.

We identify a mismatch between the physical role of transport fields in many PDEs and their usual role in neural operators: PDEs use them to select read coordinates, whereas neural operators typically treat them only as input values. We address this mismatch with the Green-Routed Neural Operator (GRNO), which uses the governing equation to determine where latent features are sampled. A parameter-free equation adapter evaluates the diagnostic relation and constructs a departure map whose values are the read coordinates. A multiscale encoder-decoder combines centered and routed reads of latent features to learn the complete finite-time update. Across five two- and three-dimensional PDE systems, GRNO achieves the lowest mean final relative $L^2$ error on four under 40-step autoregressive evaluation and remains competitive on Keller-Segel. Fixed-weight route interventions reveal strong dependence on direction and spatial alignment in four systems, with weak dependence in Keller-Segel. In independently trained ablations, GRNO achieves lower mean errors than variants that supply the transport field only as an input feature, substitute a learned displacement for the equation-specified route, or apply the route with a spatial misalignment, across all five systems. It also substantially outperforms directly advecting the physical state and learning the remaining update, indicating that equation-specified read coordinates provide an effective structural prior for long-horizon PDE forecasting.

Transcribing music into a human-readable score requires a coherent understanding of rhythm, harmony, melody, and form. Two obstacles limit this goal: annotated recordings are scarce, and accurate local predictions can still produce inconsistent musical sequences. We present SheetSage2, a unified music transcription framework that combines synthetic data, task-specific structured decoding, and autoregressive distillation. Automatically annotated MIDI, rendered into audio, provides scalable supervision across music understanding tasks. Task-specific structured decoders integrate complementary musical cues and their temporal dependencies to produce musically coherent scores. Autoregressive distillation further retains transcription accuracy without task-specific dynamic programming at inference. Across eight benchmark collections, a single SheetSage2-AR model exceeds the listed prior systems on 12 of 15 benchmark–metric pairs in our evaluation, substantially improving over SheetSage1 and surpassing task-specific models on several benchmarks. Model weights and inference code are publicly available.

The GKR soundness theorem bounds the acceptance of a false output claim for a fixed circuit and input. It does not say what the outputs of a compiled circuit mean for that input, and that has to be proved for each family of circuits. For a sparse Merkle tree over a compressing hash, heuristically almost every root admits a valid path for almost any leaf, so the needed statement concerns the witness as well as the claim. We prove per-input soundness for membership, non-membership and update claims, for trees of every depth, in the delegation setting of GKR: the verifier reads the circuit input in the clear and leaves the node hashes to the circuit. Assuming correct hash sub-circuits, every accepted input, honestly encoded or not, determines a valid witness, and the chain constraint cannot be dropped. If the witness read from an input fixed before the challenges is not valid, this verifier accepts with probability at most $\bigl(s_{\mathrm{out}}+\sum_i(8s_i+1)\bigr)/|\mathbb{F}|$ for a circuit with $2^{s_{\mathrm{out}}}$ outputs and $2^{s_i}$ wires read at layer $i$. This covers cube gates for the Poseidon2 S-box and, with $|\mathbb{F}| = p^4$, circuits over the 31-bit KoalaBear field with challenges from its quartic extension. The implemented node hash, a truncated permutation, is not collision resistant, so the statement that accepted runs for one key and root assert the same leaf assumes position binding of the tree. All our results are proved in the paper. Isabelle/HOL also checks a layer-chain bound, the exactness of the verifier's checks on encoded witnesses in a constraint-level model with abstract hash sub-circuits and, over one field, their composition for claims with no valid witness. All bounds concern the interactive public-coin protocol.

Frameworks that use large language models for scientific discovery typically rely on a fixed, human-designed algorithm that decides what the model sees at each step, leaving the model only the role of proposer. The model knows nothing of the search beyond what it is shown. As models grow more capable, a question arises: does a search strategy chosen by a human before the run scale better than promoting the model from proposer to planner and letting it own the search? The Bitter Lesson suggests that choosing the strategy in advance is the kind of hand-designed structure that general methods eventually outscale. We introduce AgentDiscover, in which a coding agent plans the search using its context as working memory, runs experiments, and records every attempt in a database of ideas, candidates, and their relations. This database serves as the agent's long-term memory and is structured so that the selection rules of classical algorithms such as MAP-Elites and Monte Carlo tree search each reduce to a single query, which the agent is free to use, combine, or replace. A server maintains the database and steers the agent after every submission, keeping it on course over long runs. In our experiments, AgentDiscover is more cost-efficient than existing frameworks, reaching better scores at lower cost. On tasks in kernel engineering, biology, algorithm design, and mathematics, AgentDiscover outperforms prior discovery frameworks. Its programs would have placed first among human competitors in seven past AtCoder heuristic contests, and on eleven mathematical and systems optimization tasks it matches or exceeds every baseline that uses the same model. Our code is available at https://github.com/mhdfb/AgentDiscover.