Papers

Markets for data promise to unlock its economic value, yet in practice they remain far less active than expected—one reason is that those who supply data are not rewarded for the value it creates downstream. A defining feature of data is its replicability: a buyer can refine purchased data into a new product and resell it to many downstream buyers, so a single source seeds a branching cascade of resales that naturally forms a tree. Because an upstream seller captures none of this downstream value, its incentive to trade is weakened. Existing works propose profit reallocation—returning part of downstream revenue to upstream contributors—as a natural remedy. But whether profit reallocation works on the tree-structured markets that replicable data actually induces has remained open. To bridge this gap, we develop a principled framework for profit reallocation on tree-structured data markets. We introduce a sequential trading game on a tree and a general class of budget-feasible profit reallocation mechanisms (PRMs) over it. We derive efficient algorithms to compute the induced equilibria—a polynomial-time exact algorithm for discrete valuations and a fully polynomial-time approximation scheme (FPTAS) for continuous ones—via a subtree decomposition technique that tames the potential coupling across a seller's children. We then prove that, under mild assumptions, any budget-feasible PRM weakly expands the trades that occur in equilibrium, and any budget-balanced PRM additionally weakly improves social welfare, relative to the baseline that reallocates nothing. Experiments on synthetic markets confirm that these benefits are substantial, persist even when the assumptions fail, and grow with the depth and branching of the tree.

Modern learned systems increasingly combine learned components with search, repair, or external solvers. Benchmarks often measure the resulting end-to-end system, while scientific claims may concern only one component, creating an attribution problem: evidence can fail to support the requested component-level claim while still supporting a positive conclusion about the larger system. Existing evidence-to-claim methods primarily calibrate claim strength. We argue that composite systems require a second dimension: scientific subject. We address this problem with subject-typed claim licensing, which separates weaker conclusions about the requested subject from positive but non-substitutive credit about another subject. We instantiate this idea in SCOPE-Routing for preference-conditioned multigraph routing. Non-authors reproducibly apply the declared semantics; held-out review yields fewer reference-relative upward deviations than unstructured review, while the difference from a strong evidence checklist remains unresolved; and a controlled routing study shows that score-optimal and claim-eligible methods can differ while valid hybrid-system credit is preserved. These results motivate treating claim strength and scientific subject as distinct dimensions of evidence-based evaluation.

The loop group description of surfaces whose Gauss map is Lorentz harmonic is known for timelike surfaces of constant mean curvature in the flat Lorentzian 3-space, and for surfaces of constant Gaussian curvature in the 3-sphere. We carry out the corresponding construction for timelike surfaces in anti-de Sitter 3-space $\mathbb{H}^3_1\cong SL(2,\mathbb{R})$: those of constant mean curvature, whose Gauss map is harmonic for the conformal structure of the first fundamental form, and those of constant Gaussian curvature $K>-1$, $K\neq0$, whose Gauss map is then an immersion and is harmonic for the second fundamental form. For both classes we prove the harmonicity characterization, recover the surfaces from extended frames by Sym-Bobenko-type formulas, and solve the geometric Cauchy problem by the generalized DPW method, with potentials written explicitly in terms of the data and no normalization of the Gauss map. We then show that the two constructions differ only by a normalization: after the substitution $\lambda=\zeta^2$ and a constant gauge, a constant mean curvature extended frame $\hat F$ is an extended frame of its Gauss map, and the maps $\hat F|_{\lambda=e^{4\theta}}\exp(\theta e_3)\hat F|_{\lambda=1}^{-1}$ and $e_3\hat F|_{\lambda=e^{4\theta}}e_3\exp(\theta e_3)\hat F|_{\lambda=1}^{-1}$, with $e_3=\mathrm{diag}(-1,1)$, are timelike surfaces of constant Gaussian curvature $1/\sinh^2\theta$ and $-1/\cosh^2\theta$ wherever the constant mean curvature surface is not flat. The first is the classical parallel surface, the second its polar surface. Explicit families, with extended frames and surfaces in closed form, illustrate the constructions.

Cross-request KV caching reduces the prefill cost of Retrieval-Augmented Generation (RAG), but conventional prefix caching severely limits cache reuse across requests. Position-Independent Caching (PIC) removes this constraint by reusing independent chunks, but their KV states miss cross-chunk interactions. Existing methods selectively recompute token states to recover these missing interactions, but primarily allocate the recomputation budget to selecting which states to recompute, while fixing the recomputation context to the full causal prefix. We introduce RelaxKV, which formulates selective cache repair as a joint allocation problem over repair targets and recomputation context. Guided by the user query, RelaxKV identifies layer-specific repair targets and restricts their recomputation to a query-relevant context, reducing attention computation. Across four decoder models, RelaxKV at a 15% anchor ratio improves aggregate LongBench performance over ProphetKV on all models. On Qwen3-14B, RelaxKV provides a stronger quality-TTFT trade-off than ProphetKV across a 5%-30% anchor-ratio sweep, and achieves the best selective results on RULER-MV and LV-Eval at 16K and 32K context lengths. Controlled ablations further demonstrate the importance of recomputation context selection.

We study block relations between H-triples of finite groups. We prove a Clifford correspondence theorem in which a single pair of associated projective representations satisfies both the mixed comparison-function identities and the block conditions on every intermediate group. The resulting correspondence preserves relative character heights and yields a common defect group for each pair of corresponding blocks. We also establish induction and gluing results, including an induction criterion that allows unequal Clifford indices. Direct products, wreath products and changes of ambient group are treated within the same framework. These results provide character-triple tools for Galois-equivariant local-global correspondences.

Photoplethysmography (PPG) has become an important modality for continuous cardiovascular monitoring, including atrial fibrillation (AF) detection. However, labeled AF recordings remain limited in many clinical settings, making model adaptation difficult when only limited target data are available. Generative modeling offers a natural way to alleviate this scarcity by synthesizing additional AF signals. Existing approaches, however, mainly generate samples that match the target condition without explicitly modeling how an observed source recording should be transformed, making it difficult to leverage abundant source recordings from a specific population or cohort for targeted augmentation. We introduce PulseFlow, a source-conditioned counterfactual generation framework that combines conditional representation learning with invertible latent transport to edit cardiac rhythm while retaining information from the source. Experiments across two clinical cohorts demonstrate effective rhythm transformation, measurable source correspondence, and improved AF classification under limited labels.

During plasma heating and current ramps the thermal and magnetic states of a tokamak evolve on different timescales. We present a rapid integrated tokamak modelling approach, which couples a variational fixed-boundary Grad–Shafranov equilibrium to sparse particle and energy flux matching and to weak-form current diffusion. An ITER-like pure-deuterium scenario is examined: a current ramp from 10 to 15~MA over 20~s, a 20~s flat-top and a 20~s ramp-down to 14~MA, under 80~MW of electron-cyclotron heating applied at the start. The toroidal current density at the pedestal top more than doubles during the ramp-up and then decreases during the flat-top as current redistributes inward. Thermal stored energy rises from 185.52 to 252.70~MJ and approaches its final value within the first few seconds. An independent calculation with the Fusion Synthesis Engine (FUSE) gives a stored-energy difference of 0.02% at 60~s, whereas the largest profile differences occur in the core current density. Halving the coupling interval changes stored energy by at most 0.006% at the selected radial resolution. The 60~s pulse, advanced through 600 coupling intervals of 0.1~s, takes 8.62~s on an Apple M4 Pro, which is at least two orders of magnitude faster than conventional integrated tokamak modelling solvers.

What information is needed to turn a natural-gradient direction into a useful finite update? Under a population Kullback-Leibler (KL) budget, we call a step useful if it is feasible and loses at most a fraction $\varepsilon$ of the best feasible gain along the direction. We construct a four-state exponential family whose laws share their initial gradient, scalar Fisher information and natural gradient, yet two laws have disjoint useful-step sets. With these quantities supplied exactly and the law otherwise known only through draws, the family's worst-case sample complexity is $\Theta(\log(1/\delta)/(p\varepsilon^2))$ for small $\varepsilon$, where $p$ scales rare-state probabilities and $\delta$ is the failure probability. The budget is fixed and the optimal gain stays bounded away from zero, so the step length, not the direction, carries this cost. For succinctly described event-tilt models, returning a useful step is NP-hard even with the exact natural gradient and efficient exact sampling. Recovering the unit natural gradient to constant error is also NP-hard even in a two-parameter logistic family with Fisher condition number at most 3. We also give matching sample bounds for event tilts, sample bounds for damped Fisher solves and a population-KL certificate for affine classifiers. In frozen-feature classifier heads, stopping at a sampled KL boundary succeeds in about half of the trials, and a 10% KL margin raises joint success above 93% at a KL budget of 0.01. Thus, knowing where to move is not enough: how far to move can carry an update's entire cost.

Two irreducible representations of $U(d)$ whose Young diagrams differ by a single box are connected by four covariant quantum channels: the box can be removed or added, and one keeps either the new diagram or the box ($\mathbb{C}^d$ or its dual). We prove that for each of these channels the output of a coherent state majorizes every other output, so that coherent states minimize the output entropy, and we compute the optimal output explicitly in terms of hook lengths. For the two channels that keep the box we also determine all minimizers; these need not be coherent, even when they are pure. As an application we consider $N$ particles with a given permutation symmetry and find sharp bounds on the spectrum of the reduced density matrix of a single particle, as well as the exact set of spectra that mixed states can reach (for fermions these are the Pauli principle and Coleman's theorem).

Planning from pixels needs more than a latent space that is stable and predictable. The state the planner scores must also be organized by how actions move the system. Joint-embedding predictive architectures (JEPAs) avoid pixel reconstruction by predicting future representations, but existing action-conditioned JEPAs ask one embedding to serve both perception and control. We introduce H-JEPA, which separates the two. A wide perceptual code is regularized toward a well-scaled isotropic geometry with a Bures-Wasserstein prior, and a fixed orthonormal slice of that code is the control state, which inherits the code's covariance without any objective of its own. The state evolves under phase-conditioned dissipative port-Hamiltonian dynamics whose input port has orthonormal columns. Port-inverse consistency (PIC) reads the executed action back through the transpose of that port. We show that this readout is exactly the rollout error projected onto the port directions, so PIC is a parameter-free reweighting of prediction error and not an auxiliary action decoder. Untying the readout from the port breaks this identity and loses half of the gain. H-JEPA matches or exceeds reconstruction-free baselines, including the action-decoding Delta-JEPA, on four pixel-based control benchmarks after at most $10$ training epochs, and its largest gain is on OGB-Cube ($91.9$ against $79.3$ percent). Ablations on PushT and OGB-Cube separate the contributions of the structured predictor, PIC, the prediction horizon, the state rank, and the anti-collapse prior.

Post-training quantization (PTQ) is the standard way to run modern diffusion models on memory-constrained accelerators, yet every existing diffusion PTQ scheme fixes the $\mathit{number\ format}$ in advance and only tunes the scale, zero point, or per-layer bit-width. At a fixed bit-width the best format depends on the distribution being encoded, and that distribution differs across weight channels, across layers, and along the diffusion timestep, where activation distributions slide from heavy-tailed and noise-dominated to tightly clustered and structured. We propose Chameleon, a PTQ framework that holds the bit-width fixed and treats the format itself as a discrete variable, chosen per weight channel and per (layer, timestep bucket) activation tensor. Activation formats come from {INT8, FP8 E4M3, FP8 E5M2, MXFP8, MXINT8}, selected ahead of time from two cheap statistics (empirical kurtosis and the closed-form diffusion SNR) and stored in a lookup table; weight formats come from {INT8, MXINT8} at 8 bits or {INT4, NF4, FP4 E2M1, MXINT4, MXFP4} at 4 bits, selected offline by reconstruction error. An architectural fork adapts the same selection layer to multi-step UNets, single-step distilled models, and Diffusion Transformers. Across SDXL, SDXL-Turbo, and PixArt-$\alpha$ on COCO-2014, Chameleon achieves the best FID in all six backbone $\times$ bit-width settings, with CLIP within 0.24 of the FP16 reference and the best of all quantized methods at $W_{4}A_{8}$.

Large language models (LLMs) are increasingly deployed in multi-agent settings, where agents observe and influence one another, making social influence a key dimension of AI behavior and safety. We investigate whether LLMs' responses depend on the social identity of other agents, beyond the effect of their consensus. We construct judgment tasks with a single correct answer, and place models in a multi-agent setting where they receive incorrect answers from other agents whose social identities (AI or human, model family, or an arbitrary minimal group) are either shared with or distinct from their own. Across 12 open-weights models and nine tasks, we find a bidirectional effect of group identity on conformity to incorrect answers: in-group consensus increases conformity (in-group favoritism), whereas out-group consensus decreases it (out-group divergence). Unlike humans, for whom one ally breaking the consensus sharply reduces conformity, models are unmoved by an ally from the majority's group. Worse, a correct ally from the opposing group intensifies this bidirectional effect. Chain-of-Thought reasoning suppresses most of these effects, yet an in-group ally still reduces conformity to an incorrect out-group majority. Labeling peers as safety-aligned shifts overall conformity but leaves in-group favoritism and out-group divergence intact. These results show that group identity shapes how LLMs aggregate information across agents, independently of its correctness, and identify a manipulation surface for multi-agent AI systems.

This Letter establishes the analytical structure of the dipole radiation transition operator, taking into account non-dipole effects for a multielectron atom. The results summarize those of Komninos Y. et al., Phys. Rev. A 86, 023420 (2012), obtained in an approximation of a "split" electron of a continuous spectrum. The result for the complete operator of a multipole radiation transition [see formula (10)] can be specified within the framework of the methods of the theory of irreducible tensor operators and for higher multipoles.

We study vector scheduling in which each job is active during a fixed time interval. A job uses several resources and stays on one machine for its entire interval; its resource requirements may depend on the machine. The objective is to minimize the largest resource load over all machines and times. For $r$ machines and $d$ resources, we give a deterministic $(1+\varepsilon)$-approximation in $f(r,d,1/\varepsilon)N^{O(1)}$ time, where $N$ is the binary input length. This gives an efficient polynomial-time approximation scheme for fixed $r$ and $d$, extending approximation schemes for scalar temporary tasks assignment. The algorithm merges jobs into blocks whose time intervals are fixed before any machine is chosen, and assigns the blocks by dynamic programming over a balanced recursive split of the time line. We also prove strong NP-hardness and an exponential lower bound in $1/\varepsilon$ under the Exponential Time Hypothesis, already for two identical machines and one resource.

Human Activity Recognition (HAR) from heterogeneous wearable sensors is fundamental to the Internet of Health Things (IoHT), supporting rehabilitation, elderly care, and smart healthcare. Existing multimodal fusion methods often assign fixed equal weights to sensor streams, overlooking differences in modality importance, acquisition cost, and sensor quality, which can vary due to movement, incorrect placement, or temporary blockage. We propose an adaptive and cost-aware multimodal HAR framework based on multi-agent reinforcement learning for centralized HAR and extend it to federated learning as FedMHAR. In the centralized setting, multimodal fusion is formulated as a cooperative Multi-Agent Reinforcement Learning (MARL) problem, where each sensing modality is assigned a PPO-based agent that learns per-sample fusion weights, enabling the model to emphasize informative modalities while down-weighting costly sensors when cheaper alternatives provide sufficient information. In the federated setting, we introduce BiFL-PPO, a bidirectional federated optimization strategy in which a server-side PPO policy learns client-specific trust weights and feeds them back to adapt local learning rates and proximal regularization. Unlike round-level optimization, BiFL-PPO uses dense batch-level rewards for more frequent feedback and stable training under heterogeneous client data. Evaluation on the MEx Rehabilitation and UTD Multimodal Human Action datasets shows that the centralized framework achieves 87.30% and 94.98% accuracy, respectively, outperforming conventional fusion methods and state-of-the-art HAR models. FedMHAR achieves 79.74% and 77.49% in the federated setting, consistently surpassing FedAvg, FedProx, FedBN, FedNova, and AdaFedProx, while providing more stable performance and reducing sensor acquisition cost.

We study the dimension-indexed marked-root polynomial maps introduced by Harish. For every $n\geq 4$, their lower coefficient block extends to a polynomial coordinate system, giving three-dimensional Keller maps of geometric degree $n(n-2)$ for every choice of the fixed coefficients. We determine the generic monodromy of the original maps and all successive coordinate descents: it is the cyclic wreath product for odd $n$, and an explicit subgroup of index two for even $n$. Its order is $(n-2)^n n!/\gcd(2,n-2)$. We construct the smooth finite normalization and identify its complement of the affine source as $n-2$ disjoint affine divisors. One is ramified; the others record unramified loss of inverse sheets. The normalization has Picard group $\mathbb{Z}^{n-2}$ and the homotopy type of a wedge of $n-2$ two-spheres. Its rational deck group is cyclic, while the polynomial deck group of the source map is trivial. By base change, the normalization describes the preimage of any subvariety of the target; when the target polynomial factors, a component with only constant units is an open subset of a Kummer cover of the simple roots of one factor. Finally, the monodromy separates these maps, for $n\geq 4$, from single weighted lifts under stable polynomial left-right equivalence.

Conditional independence (CI) is a fundamental concept in statistics and machine learning. Recent advances in conditional generative modeling provide flexible tools for generative-model-based CI tests, which rely on an estimated conditional distribution to generate randomized samples. However, errors in estimating this distribution accumulate in existing Type I error bounds, and consistency of the generative estimator alone does not guarantee asymptotic Type I error control. To address this limitation, we formulate conditional generative modeling as a domain adaptation problem and leverage auxiliary data from multiple source domains to improve estimation in the target CI testing domain. We propose Domain-Adapted Diffusion (DA-Diff), a multi-source domain adaptation framework for conditional diffusion models based on weighted empirical risk minimization over both target and source domains. We establish the convergence rate of DA-Diff and show how transferable source data can improve target-domain estimation through an increased effective sample size while controlling transfer bias. Building on DA-Diff, we further propose Domain-Adapted Conditional Independence Testing (DA-CIT) and show that its Type I error satisfies $P(p \leq \alpha) \leq \alpha + o(1)$. Experiments demonstrate that DA-Diff improved conditional generation quality compared with transfer-learning diffusion baselines, while DA-CIT provides strong Type I error control and competitive power.

Simultaneous and sequential block updates are two basic optimization strategies used across machine learning, such as neural-network training, federated learning, and low-rank adaptation. Choosing between them is difficult because their relative advantage depends on both the objective geometry and the number of iterations. We develop a unified theory for comparing Jacobi (JC), Gauss–Seidel (GS), and partially sequential deterministic block-gradient updates. Our analysis expresses the one-step loss difference through cross-block curvature, with an $O(\eta^3)$ remainder, where $\eta$ is the learning rate. We derive a signed loss comparison after $K$ iterations with $O(K\eta^3)$ error under regularity conditions and $\eta K\le T$ for fixed $T$, identifying the better method when the predicted difference exceeds this error. We evaluate these formulas along observed training trajectories across different machine learning settings. Over 500 iterations, our theory correctly identifies the lower-loss method in 98.0% of iterations for the neural network, 83.4% for federated learning, and 97.6% for LoRA. Applying the loss recursion at each step using the measured parameter difference raises these rates to 100.0%, 93.2%, and 99.6%, respectively.

Let $\mathscr{X}(\boldsymbol{\Sigma})$ be the toric Deligne–Mumford stack with stacky torus $\mathscr{T}$ associated to the stacky fan $\boldsymbol{\Sigma} = (N,\Sigma, \beta)$. A toric principal $H$-bundle over $\mathscr{X}(\boldsymbol{\Sigma})$ is a principal $H$-bundle $\mathscr{P}$ equipped with a $\mathscr{T}$-action lifting the $\mathscr{T}$-action on $\mathscr{X}(\boldsymbol{\Sigma})$, such that the $\mathscr{T}$-action and the $H$-action on $\mathscr{P}$ commute. For a connected reductive algebraic group $H$ over $\mathbb{C}$, we classify the isomorphism classes of framed toric principal $H$-bundles over $\mathscr{X}(\boldsymbol{\Sigma})$ in terms of piecewise linear maps from $|\Sigma|$ to the cone over the Tits building of $H$. Using this classification, we describe the equivariant automorphism group of a toric principal $H$-bundle, and give a necessary and sufficient condition for an equivariant reduction of the structure group. We also show that every toric principal $\mathrm{GL}(r)$-bundle over the weighted projective stack $\mathbb{P}(w_0,\dots,w_n)$ splits equivariantly whenever $r < n$, and that every toric principal $H$-bundle over the weighted stacky projective line $\mathbb{P}(a,b)$ splits equivariantly when $H$ is a connected reductive algebraic group.

EEG foundation models hold promise for scalable brain-signal decoding across clinical and cognitive neuroscience applications, yet their pre-training pipelines remain poorly understood. Among design choices, the masking strategy is particularly critical: it determines what the network must predict and from which context. Yet it has never been ablated in isolation, as each new model bundles a new masking strategy with a new backbone and objective. In this paper, we formalize the design choices for spatio-temporal masking strategies and train various models with a single pipeline under varying masking configurations across two SSL frameworks (MAE and JEPA). We then systematically evaluate the resulting 58 pre-trained models on the 12 datasets of OpenEEGBench under a linear probe. Both frameworks agree on an optimal masking configuration and on shared failure modes. Outside these, performance is robust: 11 MAE and 9 JEPA configurations are statistically indistinguishable from the best. We further identify a novel JEPA-specific failure mode, tagged bias-inflation collapse, invisible to standard detectors. With a well-chosen mask, our pipeline reaches REVE-level downstream performance at a fraction of REVE's pre-training compute.

Perturbation-based XAI methods for audio classifiers often estimate feature importance by masking spectrogram regions and crediting output changes to the retained signal. Yet they typically assume the fill (the mask replacement) is negligible. We propose logit-space trajectory decomposition to examine this assumption. An on-axis component captures output along a line connecting the fully filled (occluded) spectrogram to the fully retained original; an off-axis component captures perpendicular displacement. We evaluate across three fills, three audio classifiers, and 1,100 AudioSet clips. We demonstrate that no fill is acoustically neutral under full occlusion: Zero fill activates silence and Gaussian Noise fill activates broadband noise. Under partial masking, 41-77% of output displacement is off-axis, with the direction of the residual stable across mask retention fraction and specific to each model-fill combination. Attribution methods are unevenly exposed to off-axis displacement through their sampling and weighting strategies, revealing apparatus-dependence. Where the off-axis residual is stable and low-dimensional, its structure affords mitigation.

While Large Language Models (LLMs) advertise million-token context windows, reasoning quality often collapses as inputs grow – a phenomenon termed context rot. This failure stems from a structural entanglement in monolithic architectures, where the massive search burden of contextual grounding exhausts the representational capacity needed for complex reasoning. To resolve this, we propose Grounding-Reasoning Disaggregation via DIStributed long COntext scaling (DISCO). Inspired by distributed computing frameworks like Apache Spark, DISCO partitions long context across a fleet of Worker LLMs dedicated exclusively to parallel, localized grounding. A central Driver LLM, trained via Reinforcement Learning (GRPO) to optimize planning, orchestrates execution by dynamically mapping queries into atomic extraction tasks and reducing the gathered evidence to synthesize a final answer. By isolating reasoning from raw context noise, DISCO effectively eliminates context rot. On RULER-QA (1M tokens), it maintains 78.4% accuracy where standard baselines collapse. Furthermore, it outperforms full-context models by up to 9.8 points on LongBench v2 and matches frontier models like Gemini-3-Pro-Preview while reducing inference costs by over 80%, establishing a highly efficient paradigm for robust long-context inference.

A humanoid with 5-DoF arms cannot track generic bimanual end-effector trajectories with its arms alone; pelvis and waist motion must be recruited, but which motion, and when, is not uniquely determined. On a Unitree R1 in fixed double support, the set of dynamically valid recruitment strategies (pelvis pose and waist trajectories) for a task is a diverse continuous manifold, and a deterministic regressor trained on it mode-averages into strategies valid only 35% of the time, against 52% for a conditional variational autoencoder (CVAE) and 82% for the best of 16 CVAE samples. We introduce AMBIT: the CVAE proposes strategies from a preview of the commanded trajectory, a non-learned selector filters, ranks and verifies them, and a receding-horizon loop commits to one with hysteresis. The committed strategy is the reference of the same whole-body differential-IK QP a reactive tracker runs, which keeps authority over residual error. On 160 held-out episodes that admit a valid strategy, in full MuJoCo dynamics under a torque controller, AMBIT reaches 85% success at a 3 cm/15 deg tolerance against 74% for the tracker (disjoint confidence intervals) and recruits the body before the arms saturate in 48% of episodes against 35%. Because diversity is preserved, constraints unknown at training time are enforced by selection alone: under five zero-shot shifts AMBIT beats the warm-started tracker on every shift and matches a test-time re-optimisation baseline 17x more expensive. On a Unitree G1, with hyperparameters unchanged, the protocol reproduces the structure of the valid set and widens the gap over the tracker to 0.85 against 0.53. Five selected strategies execute on the externally supported physical R1, distinct in pelvis excursion and tracking the planned end-effector motion to a median of 11 mm by encoder forward kinematics, which establishes kinematic realisability, not balance.

Laser-driven proton-boron fusion offers a path for generation of $\alpha$ particles on a compact scale. Conventional solid-target experiments, however, are fundamentally limited by target degradation and low shot-repetition capacity. Here, we demonstrate a continuous laser-driven $\alpha$ particle source utilizing target-normal sheath acceleration from a continuously replenishable ultrathin water-leaf jet target. The proton beam interacts with a downstream boron nitride converter, driving the $^{11}\text{B}(p,\alpha)^{8}\text{Be}$ reaction which yields three $\alpha$ particles. The measurement was repeated across $18{,}000$ consecutive shots at a rate of $10\,\text{Hz}$. The outgoing $\alpha$-particle yield and spectral fluence were measured and benchmarked against comprehensive particle-transport simulations. The numerical and experimental results reveal a pronounced flattening in the energy-differential $\alpha$-particle spectrum escaping from the converter, driven by depth-dependent reaction yield and stopping power effects. The sustained stable $\alpha$-particle production at high cumulative yields paves the way for applications in targeted particle therapy and laser-driven plasma-fusion research.

Conformal prediction provides distribution-free finite-sample marginal coverage, but post-hoc calibration data may be too scarce to learn how uncertainty varies across inputs. Meanwhile, abundant covariates can often be labeled cheaply by domain models or general-purpose language models. We study whether these synthetic labels can improve conditional coverage when only a small trusted sample is available. Building on score-quantile regression, we introduce prediction-powered quantile learning: a synthetic-labeled pool estimates pinball risk, paired trusted and synthetic outcomes correct its bias, and an independent trusted split performs final conformalization. Profiling pinball risk over scalar corrections reveals that population conditional-coverage error is its functional gradient; the corresponding Hessian removes global shifts and weights remaining shape error by boundary density. Composing this geometry with prediction-powered learning yields a three-resource expansion and a benefit–cost rule for synthetic power. Across eight regression benchmarks, synthetic-powered quantile learning substantially improves downstream conditional coverage while preserving marginal validity and producing more compact prediction sets. A human-rating study finds similar gains from external LLM labels and exposes a quality–quantity–cost tradeoff.

Erasing individual identities from Vision-Language Models (VLMs) is uniquely challenging because personal data is entangled across modalities rather than stored as isolated attributes. However, existing multimodal unlearning benchmarks primarily evaluate attribute-centric forgetting, overlooking the more critical objective of individual-level unlearning: eliminating a model's ability to access, link, and reconstruct target-related information across modalities. To address this gap, we propose IDUnlearn-Bench, the first benchmark for individual-level multimodal unlearning in VLMs. It represents each individual as connected multimodal evidence and evaluates four task families: attribute access, identity access, identity binding, and identity reconstruction. Experiments on representative VLMs and unlearning methods show that successful attribute-centric forgetting often leaves substantial identity-level knowledge intact and can be non-monotonic: reducing one form of risk may amplify another. Models may suppress selected information while still identifying the target, linking records, or reconstructing the individual. These findings reveal a fundamental gap between forgetting information about a person and forgetting the person as a whole.

We prove the conjecture of Laubie on dimensions of components of two operads completing Loday's operadic butterfly diagram. For one of these operads, the dimension of the $n$-th component is equal to $\binom{2n}{n-1}$ for all $n\ne 3$, and for the other it is equal to $\binom{2n}{n-1}+1$ for all $n\ge 5$.

We study vector-valued local minimizers of double phase functionals with two modulating coefficients and logarithmic-type growth. The energy density is $a(x)|Du|^p+b(x)|Du|^p\log(e+|Du|)$, where the nonnegative coefficients $a(\cdot)$ and $b(\cdot)$ may vanish but their sum is bounded away from zero. Assuming that $a(\cdot)$ is uniformly continuous and that $b(\cdot)$ satisfies a vanishing log-Hölder continuity condition, we prove that minimizers are locally Hölder continuous for every exponent in $(0,1)$. If both coefficients are Hölder continuous, then the gradient of a minimizer is locally Hölder continuous. The proof combines Gehring-type higher integrability with a comparison argument.

Sustained catalyst-mediated growth of diamond and cubic boron nitride (cBN) wires has yet to be established reproducibly, although related methods produce carbon and BN nanotubes and many elemental and compound nanowires. I hypothesize that a retained contact between a catalyst and an existing tetrahedral crystal can sustain wire extension under conditions that do not nucleate that crystal on an otherwise comparable unseeded catalyst. The prediction is repeated, vapor-derived target-phase extension during an interval in which matched unseeded contacts do not nucleate that phase. I develop tests using diamond seeds, SiC starter wires and cBN seeds, separating the conditions used to establish the contact from those used for continuation. Worked estimates distinguish bulk precipitation driving forces from sidewall costs and show why increased carbon activity alone cannot select diamond over graphite. Comparisons with established synthesis identify the roles of pressure, hydrogen and activated nitrogen that must be retained or replaced. Isotope tracing, local structural measurements and time-dependent growth distinguish continued incorporation from seed consumption, conversion and etching. Nanometer, micrometer and larger wires could provide electrically insulating thermal connections, mechanical probes and reinforcing filaments.

Hybrid LLMs interleave full-attention layers with linear-attention layers to reduce long-context inference cost, but this structure complicates prefix caching. Full-attention KV caches are token-addressable, whereas linear-attention layers maintain recurrent states that cannot be rolled back to arbitrary prefix boundaries. Existing systems materialize recurrent-state checkpoints, restricting prefix reuse to checkpoint-aligned positions. We present SuffixReplay, the first prefix caching system that lets hybrid LLMs reuse cached prefixes at every cache-supported page boundary without materializing recurrent-state checkpoints. Our key insight is to just let linear states forget the distant past. Modern linear-attention mechanisms use recurrent decay and gating to attenuate the influence of old inputs. Therefore, instead of checkpointing every prefix boundary, SuffixReplay approximates the state at a matched boundary by replaying only a recent suffix of the layer's input hidden states, which we retain as anchors. At the algorithmic level, SuffixReplay combines layer-wise and token-wise anchor sparsity with a bounded replay budget to control storage, computation, and quality. At the system level, it uses an independently managed anchor sidecar and a pipelined replay path to overlap anchor movement and state reconstruction with the native serving pipeline. We evaluate SuffixReplay on three hybrid LLMs: OLMo-Hybrid-7B, Qwen3.5-4B, and Qwen3.6-27B-FP8. Across these models, SuffixReplay retains 91.4-100% of full-prefill quality on average across LongBench and RULER, while using only 0.36-0.51x the amortized per-token storage of SGLang's default 8192-token checkpoint cache. Integrated into SGLang, SuffixReplay reduces median TTFT by 15-70% on branching workloads, sustains 2.3-4.3x SGLang's throughput when the working set exceeds HBM, and matches SGLang on high-hit continuation traffic.