Papers

Interactive 3D head generation requires coordinated speaking and listening motion that responds to an evolving conversation. Existing generators use incoming observations as context but keep their parameters fixed, leaving conversational patterns unused as a learning signal. We introduce EvolvingAvatar, a causal generator that uses test-time training to adapt to user face video and dyadic audio during interaction. Its dyadic context prediction objective provides a self-supervised learning signal from audiovisual context without target motion labels at test time. Persistent fast weights accumulate these updates within each conversation to guide motion generation, while transient jaw adaptation responds to current audiovisual context. Predicted speech activity controls how persistent adaptation guides motion. We also introduce InterHead-Bench, a unified 455.95-hour benchmark built from single-view and dual-view conversation videos. Experiments show improved conversational motion statistics over strong baselines. On the hardest out-of-distribution split, generation improves as conversations unfold, reducing mismatch with recorded user-avatar expression statistics by up to 11.1% from the first interval.

Behavioral Foundation Models (BFMs) are an emerging paradigm in reinforcement learning, playing a role analogous to large language models in natural language processing: they have shown remarkable versatility, enabling zero-shot performance, fast imitation, and online adaptation, all by exploiting the structure of a latent space. In this work, we investigate whether the latent behavioral space induced by BFMs can serve as an effective search space to discover large repertoires of behaviorally diverse and high-performing policies through Quality-Diversity (QD) methods. While QD methods generally search directly in high-dimensional policy parameter space, in this paper, we present BFM-QD, a framework that performs QD search in the compact latent space of a BFM. We further show that the BFM-QD framework provides a closed-form, gradient-free policy improvement operator that approximates a policy gradient update, but requires no critic training and no backpropagation. Across continuous-control benchmarks spanning dense locomotion, sparse navigation, and contact-rich manipulation, BFM-QD consistently outperforms parameter-space baselines, with particularly stark gains in sparse and deceptive settings, where all tested parameter-space QD methods collapse to near-zero performance. These results show the effectiveness of the BFM-QD framework, benefiting from the synergy between dimensionality reduction of the search space and offline pretraining from diverse behavioral data. This positions BFMs as a general-purpose backbone for QD optimization, extending their utility beyond zero-shot task solving to the discovery of diverse behavioral repertoires.

Adam and its variants dominate neural network training, but a single run only reveals whether a configuration works well after most of its budget is spent, a poor fit for hyperparameter or architecture search, where configurations must be ranked cheaply and pruned early. We introduce EvE (Evolutionary Explorer), a steady-state, population-of-four differential evolution (DE) optimizer with a targeted Adam fallback: each iteration proposes one candidate via DE, running a short burst of gradient descent only if the DE step fails to improve on the incumbent. Selection is greedy, so on a deterministic objective the best-so-far value is provably monotone non-increasing, and since gradients are used only as a targeted rescue, per-iteration cost stays within a constant factor of a single Adam step regardless of dimension. Under a fixed, evaluation-cost-matched budget, EvE wins or ties Adam on 76% of 70 (problem, dimension) cells across seven scalable benchmarks up to one million variables. On three real neural-network tasks (an MLP on MNIST, and LoRA fine-tuning of a 1.5B-parameter language model on two datasets) EvE finishes the same charged budget 1.7-3.9x faster, at a modest cost in final quality (about one accuracy point on MNIST, 9-11% higher relative test loss on the two fine-tuning tasks; on GSM8K, Adam is about 5 accuracy points more accurate, and fine-tuning lowers accuracy below the base model for both). Inside successive halving on UCI Adult, EvE completes hyperparameter and architecture searches 3.1-3.5x faster, ranking configurations about as consistently with Adam as Adam does with itself across seeds (Kendall's tau 0.66-0.69). EvE is not a total replacement for Adam as a final-stage trainer, but a fast, gradient-aware proxy for the search-heavy, budget-constrained regime one level up.

Target Speaker Extraction (TSE) is pivotal in speech communication and human-computer interaction, enabling the isolation of a specific speaker's voice from complex acoustic environments, i.e., the cocktail party scenario. Although traditional TSE systems conditioned on enrollment speech have progressed substantially, enrollment speech as a cue has inherent limitations. Its reliability degrades when the target and interfering speakers have similar voice characteristics, when intra-speaker variability (e.g. changes in emotion or speaking style) creates a mismatch between the enrollment and target speech, or when the enrollment itself is contaminated by noise or competing speakers. This review surveys deep-learning-based TSE from the perspective of auxiliary target cues drawn from multiple modalities. We organize existing methods according to five types of information used to isolate the target speaker: audio enrollment, visual, spatial, textual/semantic, and neural cues. We also trace the evolution from discriminative estimators to variational, diffusion, flow, codec, and foundation-model-based systems and summarize representative datasets and evaluation metrics. We review the benefits and limitations of different cues and discuss challenges involving synchronization, missing or unreliable observations, data scarcity, privacy, computational cost, and real-time operation. Finally, we summarize future directions concerning adaptive cue fusion, instruction-driven extraction, realistic evaluation, and trustworthy deployment. By jointly reviewing cue design, model architecture, training objectives, datasets, and evaluation metrics, this article provides an overview of the current landscape and open problems in multimodal TSE.

Remote sensing novel view synthesis under sparse observations remains challenging due to insufficient geometric constraints and limited cross-view supervision. Existing Neural Radiance Fields (NeRF) and 3D Gaussian Splatting (3DGS) methods are prone to overfitting and face challenges of depth ambiguities, missing cross-view information, and insufficient constraints in under-observed regions. To address these challenges, we propose DIBR-GS, a neural Gaussian Splatting framework that exploits Depth Image-Based Rendering (DIBR) to generate pseudo views for cross-view consistency supervision. Specifically, reliable geometric initialization is constructed by aligning monocular depth priors with sparse SfM reconstruction, and cross-view appearance priors are incorporated into neural Gaussian representations to enhance appearance modeling under sparse observations. Furthermore, we introduce a progressive DIBR-based pseudo-view supervision strategy to provide additional geometric and appearance constraints, enabling more complete reconstruction of weakly observed regions. In addition, a height-constrained anchor growth strategy is designed to suppress unreasonable Gaussian expansion. Experiments demonstrate that the proposed method achieves superior performance over existing approaches when training with only 3 input views. Compared with the previous best-performing method, it improves PSNR by 6.83 dB, with relative gains of 14% in SSIM and 60% in LPIPS, while maintaining competitive computational efficiency. Our code is available at https://github.com/kanehub/DIBR-GS

Instruction-based image editing has achieved strong performance in single-turn settings, yet practical editing is often iterative, with each instruction applied to the output of the previous turn. We find that existing editing models degrade rapidly under recursive editing and attribute this failure to a train-test mismatch in the conditioning distribution: models are trained on clean source images but must repeatedly condition on their own imperfect outputs at inference time. To address this, we propose MT-OPSD, an on-policy self-distillation framework that trains the model on self-generated conditioning states with editing supervision from a clean-conditioned teacher, without requiring multi-turn annotations. We further introduce LME-Bench, a benchmark of 100 ten-turn editing sessions for evaluating long-horizon robustness. Experiments across three editing backbones show that MT-OPSD substantially improves long-horizon editing success and reduces multi-turn collapse while largely preserving single-turn editing quality.

We prove that each of the inequalities $P^{+}(p+1)>P^{+}(p-1)$ and $P^{+}(p-1)>P^{+}(p+1)$ holds for a positive proportion of primes. The argument combines a logarithmic balance identity with a uniform Selberg sieve over a thin cofactor strip. The same transfer mechanism applies to either shift and converts a one-sided large-prime-factor reservoir into an unconditional ordering result in both directions.

Constrained decoding for Masked Diffusion Language Models (MDLMs) aims to ensure that generated outputs satisfy a specified structure or syntax constraint. MDLMs generate outputs by repeatedly unmasking masked positions present in their current state. Recent strategies for constrained decoding constrain the model's per-step mean-field posterior (which factorizes over masked positions) by enforcing the desired constraint with an automaton. The resulting chain-structured factor graph allows exact constrained sampling via dynamic programming. However, despite each draw being exact and constraint-satisfying, we prove that their composition, in general, tilts away from the model's relative probabilities over valid trajectories, thus leading to trajectory bias. We derive an exact expression for this bias as a product of ratios measuring how valid continuation mass changes when the denoiser is reconditioned, and characterize when the bias vanishes. We then correct the bias by introducing TWISTER, the first automaton-twisted Sequential Monte Carlo decoder for MDLMs, using the step-exact decoder as the proposal. We show that for regular language constraints, the Feynman-Kac correction is exactly computable, with the twists obtained efficiently using quantities pre-computed for step-exact sampling. We prove that the resulting Feynman-Kac model targets the unbiased Doob h-transformed path law conditioned on constraint satisfaction.

Deaf and hard-of-hearing (DHH) signers cannot converse in real time across different sign languages today: existing sign-to-sign translation systems run offline, requiring the full source clip before any target sign is emitted. Live use cases - e.g. broadcast interpretation and two-way video calls - instead demand simultaneous output, while the source signer is still signing. We present, to our knowledge, the first simultaneous sign-to-sign (S2S) translation system, with two wait-k regimes: test-time wait-k inference applied directly to a full-sentence model, and a trained wait-k model via stochastic multi-path supervision. We further introduce ca-Stream-AL, a computation-aware latency metric for streaming output. Averaged across six S2S directions on both a smaller human-verified test set and a larger synthetic S2S corpus, our streaming system achieves a 38% ca-Stream-AL reduction while staying within a 9% DTW-PA-MPJPE increase and a 2.1 BLEU-4 drop compared to the full-sentence baseline. A word-order case study probes how the streaming model handles word order mismatch between different sign languages - a consequence of simultaneous translation.

The James Webb Space Telescope (JWST) has enabled the first in-depth characterisations of sub-Neptune atmospheres, revealing a diversity of chemical compositions and cloud properties that challenge current models. Multi-planet systems provide an opportunity to compare planetary atmospheres while controlling for formation conditions within the same protoplanetary disk. We present JWST NIRSpec G395H 3-5 um observations of two similarly-sized sub-Neptunes orbiting a sun-like star within the TOI-125 system: TOI-125 b ($P=4.65$ d, $R_p=2.7~R_\oplus$, $M_p=10~M_\oplus$, $T_\mathrm{eq}=1100$ K) and TOI-125 c ($P=9.15$ d, $R_p=2.85~R_\oplus$, $M_p=6.8~M_\oplus$, $T_\mathrm{eq}=825$ K), comprising of one full transit of TOI-125 b but only 70% of TOI-125 c's transit due to larger than predicted TTVs. We obtain precise R~100 transmission spectra for both planets, with median errorbars of 50 ppm for TOI-125 b and 85 ppm for TOI-125 c. Atmospheric retrievals are compatible with a ~150x solar metallicity atmosphere or clouds above ~3 mbar for TOI-125 b, and a ~100x solar metallicity atmosphere or clouds above ~10 mbar for TOI-125 c. Our results may support recent evidence for metal enrichment in sub-Neptunes, while also further complicating the proposed trend in atmospheric feature size with planet temperature. However, shorter wavelength follow-up observations of both planets are needed to establish whether their spectra are truly muted or feature-rich, with implications for the nature of sub-Neptunes around sun-like stars.

Large language models perform strongly on competition mathematics, but their research-level reasoning remains difficult to evaluate systematically. Theoretical computer science (TCS) connects algorithm design to explicit guarantees and fundamental limits, providing a setting for evaluating whether models can justify computational improvements with arguments humans can inspect. We introduce TCSAlgBench, a benchmark and reusable pipeline for natural-language proof discovery, comprising 398 theorem-level challenges from 138 STOC and COLT 2026 papers. Expert-designed rules complete paper-specific context, preserve computational assumptions and quantitative guarantees, and withhold constructions when discovering an algorithm is part of the task. For each task, prover systems receive theorem statements and access to cited prior work. The pipeline supports fresh, versioned challenge batches from newly released papers. We evaluate ten model configurations from four families under direct inference and prover-verifier discussion, and compare four agent workflows under matched model-call opportunities. All evaluations use the full benchmark. In the model comparison, GPT-5.6 Sol max achieves the highest five-run verifier-accepted coverage at 23.6% after 10-round discussion. Discussion and repeated sampling improve coverage. In the separate agent comparison using GPT-5.5 xhigh, decomposition improves coverage over discussion, and agentic planning achieves the highest five-run verifier-accepted coverage at 25.4%. TCSAlgBench provides a refreshable testbed for measuring progress in model reasoning and studying how agent workflows support research-level proof discovery.

LVMB manifolds are a large class of compact complex non-Kähler and non-algebraic manifolds, constructed from an algebro-combinatorial datum. We provide an upper bound on their algebraic dimension and prove it to be sharp. Comparing our result with the lower bound found by Meersseman, we obtain the exact algebraic dimension of an LVMB manifold in many relevant cases. Pursuing our analysis further, we also obtain a description of the algebraic reduction of an LVMB manifold. From this, it emerges that Meersseman's lower bound coincides with the dimension of the rational component. This bimeromorphic invariant of an LVMB manifold is then computed in terms of the nonrationality degree of the associated toric quasifold. This is an invariant recently introduced by Battaglia and Prato, for which we provide an explicit formula.

For every pair of integers $0\leq k\leq N,$ and and every subgroup of $D_N\times\mathbb{Z}_2$, we construct the nonnegative symmetric Grassmannian, which is the subspace of the nonnegative Grassmannian fixed under that group, where the dihedral part acts on columns (with a sign correction to keep nonnegativity) and the $\mathbb{Z}_2$ factor exchanges a space with its orthocomplement (again, with a sign correction). This construction generalizes the earlier constructions of \cite{Karpman2018,Fraser2020,Shevchenko2025}. We study the geometry of this space. Then, when $k$ is further restricted to the range $[2,N-2]$ we also define a symmetric amplituhedron. We analyze its basic properties and its conjectural BCFW decomposition. The ABJM and reflected Lagrangian amplituhedra are the special cases corresponding to the groups $\{1\}\times\mathbb{Z}_2,$ and the group generated by a reflection combined with the exchange,

Joint-embedding predictive architectures enable planning with latent world models, but accurate transition prediction alone does not ensure that the planning objective is easy to optimize. We introduce Control-Geometry Straightening (CGS), a single auxiliary loss that learns planner-friendly representations by directly straightening control geometry for sampling-efficient planning. CGS matches pairwise cosine similarities among actions to those among corresponding latent differences only using local transitions from pixel-action pairs. The loss can be applied across world-model architectures using end-to-end learned or pretrained representations. Under linear-dynamics, our theoretical analysis connects this objective to temporal straightening and more balanced terminal-cost curvature across the full planning horizon, yielding finite-budget guarantees for MPPI, local contraction results for CEM, and convergence bounds for gradient descent. Across four control environments and multiple planners, CGS improves planning with fewer sampled candidates and refinement steps, achieving success-rate gains up to 20 and 12.6 percentage points over LeWorldModel (LeWM) and its temporal-straightening variant (LeWM+TS), respectively, with sampling-based planners using 128 candidates per update. Probes, comparisons with DINO-WM architecture, and planner-side ablations clarify how latent motion organization, state dependence, and dynamical context shape planning behavior. Straightening control geometry thus makes good action sequences easier to find under limited planning budgets.

Chiral Weyl–Kondo semimetals (cWKSM) provide a setting in which chiral Weyl quasiparticles emerge in the immediate vicinity of the Fermi energy from a Kondo-driven reconstruction of the strongly correlated electronic states in chiral heavy fermion systems (K.-S. Lin et al., arXiv:2602.22185). A defining characteristic of this strongly correlated topological state is the Kramers chiral Weyl fermions in the low-energy quasiparticle states. Recently, experiments in CeGaGe have emerged as a concrete realization of the proposed effect (Arushi et al., preprint). Motivated by these findings, here we go beyond the materials-specific effects by constructing a prototype Kondo lattice model; it incorporates only the essential couplings that respect the associated tetragonal crystalline symmetries. This simplification allows us to robustly demonstrate the symmetry-enforced Kramers Weyl fermions and related topological nodal states in the spectrum of heavy quasiparticles. Furthermore, the simplification provides a tractable setting to determine the salient features in the system's nonlinear optical response, the circular photogalvanic effect, in chiral Weyl–Kondo semimetals. Both analytical and numerical calculations identify sharp peaks in the frequency domain as signatures of the Kondo-driven chiral Weyl nodes; the sharpness of the spectrum reflects the resonant nature of the underlying strongly correlated electronic excitations. Thus, cWKSM provides a unique setting to spectroscopically identify topological fermions that are induced by strong electron correlations. As such, our results are expected to bring about much needed new insights into the understanding of strongly correlated gapless topological matter.

We construct complete canonical logical bases for qubit CSS codes by assigning quaternary coefficients to binary circulant permutation matrix pair-partition (CPM-PP) checks, constructing and normalizing logical representatives, and expanding the result into binary matrices. When the two check systems have invertible submatrices on disjoint column sets, cofactor representatives are canonically paired by the inverse of a single pairing polynomial. The resulting pairs span the entire logical space. When the pairing polynomial is a cyclic-shift monomial with coefficient one, normalization preserves the binary weights of the representatives. We state the construction for general block dimensions and CPM size, work through a corresponding example, and report the parameters, check ranks, and basis weights of seven binary codes. Representative examples have parameters $[[320,80,14]]$, $[[448,112,18]]$, and $[[2048,512,24]]$. All three have maximum check weight 10 on both the X and Z sides. Their canonical logical representatives have binary weights 25, 27, and 27, respectively, on both the X and Z sides.

Let \(X\) be a rationally smooth complex affine variety with a torus action and an attractive fixed point \(x\). Suppose that \(X\setminus\{x\}\) is \(p\)-smooth and that its integral equivariant cohomology has no \(p\)-torsion. We prove that the order of its total \(p\)-primary cohomology torsion is the \(p\)-part of the reduced numerator of the equivariant multiplicity at \(x\). In particular, this resolves the torsion-order conjecture of Juteau–Williamson and its local version for normal slices in Schubert varieties, using the equivariant torsion-freeness result of Fiebig–Williamson.

When recalling lists of concepts (e.g., animals) during the semantic fluency task (SFT), both humans and large language models (LLMs) organise their output into clusters of related items (e.g., sea animals) that are punctuated by strategic switches between clusters. In humans, this pattern can be explained by a semantic foraging process, whereby distinct neural and behavioural signatures accompany within-cluster production ("exploit") and between-cluster switching ("explore"). Whether LLMs likewise represent these two search regimes within their internal states is unknown. Here, we apply a range of mechanistic interpretability techniques to provide evidence for this. In Study 1, we use the Jacobian lens (J-lens), which maps intermediate-layer residual-stream representations to token-level activations, to show that concept-level activations predict switching. First, we find that switching coincides with low next-token activations. Moreover, the probability of switching rises as the set of strongest J-lens activations (the J-space) becomes depleted of items from the category currently being produced, analogous to explore-exploit decision-making during patch foraging. We then show that middle-layer J-lens activations of abstract category-related labels (e.g., "water") increase in anticipation of switching into that category. We confirm these representations to causally influence switching by deriving steering vectors that target category switching. In Study 2, we identify generic residual stream directions that are activated during and in anticipation of switching. By steering activations along these directions, we bias increased or decreased rates of switching. Our study extends the semantic foraging framework to artificial intelligences and provides evidence that LLMs maintain distinct representational signatures for exploration and exploitation as they verbalise conceptual information.

We introduce the Functional Spectral-Newton Method (FSNM) for learning the leading singular structure of a conditional expectation operator without fixing a basis or reproducing kernel Hilbert space. FSNM fits a low-rank representation of the centered joint-to-product density ratio kernel by alternating functional Newton updates. Each update reduces to a preconditioned regression, which we approximate with vector-valued regression trees in a stagewise boosting procedure. At the population level, we establish descent and an $O(1/T)$ best-iterate block-stationarity rate under a relative weak-learner accuracy condition, and show that every nondegenerate local minimum over the full centered $L^2$ spaces is a globally optimal rank-$d$ approximation. Synthetic experiments show that FSNM recovers a low-rank density ratio and its leading spectral structure, and that the same learned kernel can answer multiple conditional queries without refitting.

We show that the degree $d$ Jouanolou foliation $\mathcal J_d$ on $\mathbb P^2$ is structurally stable for every $d \geq 2$. We prove the existence of a neighbourhood $\mathcal U_d$ of $\mathcal J_d$, such that every foliation $\mathcal F \in \mathcal U_d$ satisfies: the Fatou set is a connected disc bundle over a compact Riemann surface of genus $d(d+1)/2$, no leaf is dense in $\mathbb P^2$, and all but countably many regular leaves are biholomorphic to the unit disc. Finally, we prove transverse perfectness of the Julia set on the regular locus for $d \geq 2$.

Self-evolving LLM agents have gained prominence for their ability to improve after deployment by modifying their harness, including their controller instructions, memory management protocols, and reusable tools and skills, in response to user and environment feedback. However, locally useful updates may persist into later tasks where they produce unsafe behavior, even without direct adversarial influence. To study this risk, we introduce SEABench, a benchmark for studying endogenous misalignment arising from agent self-evolution, with 48 longitudinal task sequences that span multiple evolution surfaces, task domains, and harm types in a rich personal-assistant environment. To account for the stochasticity inherent in agentic operations, we provide an adaptive trajectory discovery pipeline that probes for failures while preserving original task intent and supports causal attribution through paired non-evolving agents and attribution scores. Our evaluation across multiple recent LLMs, evolution surfaces, and harm types reveals that self-evolution indeed increases task completion rates but often at the cost of safety failures that are absent for paired non-evolving baseline agents. We also show that qualitatively different safety behaviors emerge across evolution surfaces and harm types. Further, we show that this divergence in safety behavior is reflected in agents' chain-of-thought reasoning, which yields an effective monitoring strategy that can mitigate unsafe behavior with a low false positive rate.

We consider the problem of minimizing a sparse quadratic function over the unit hypercube. In binary quadratic programming, treewidth of the interaction graph is a central parameter for tractability: bounded treewidth yields polynomial-time solvability. Motivated by this fact, we investigate whether treewidth plays a similar role when the binary domain is replaced by the unit hypercube. We show that the situation is strikingly different. If the interaction graph is a forest, we give a strongly polynomial-time algorithm based on dynamic programming and a structural analysis of the resulting univariate value functions, which are shown to be concave and piecewise quadratic with linearly many pieces. However, the problem becomes strongly NP-hard already when the interaction graph has treewidth two. We then identify substantially more general polynomial-time solvable classes whose interaction graphs may have unbounded treewidth. Our approach exploits the fact that there exists an optimal solution in which every variable with a nonpositive coefficient for its square term is binary-valued, thereby separating the problem into a combinatorial part and a genuinely continuous part. We show that tractability can be recovered by controlling the complexity of these two parts and their interaction, rather than the treewidth of the entire interaction graph.

Bacteriophage Q$\beta$, first isolated in 1961, has served for more than six decades as a model system for molecular and viral evolution. The development of cell-free replication systems based on the Q$\beta$ replicase enabled the first demonstrations of Darwinian evolution in RNA molecules. In parallel, the phage's compact RNA genome, high mutation rate, and ease of propagation established Q$\beta$ as an exceptionally tractable model for studying viral evolution. The discovery of extensive genetic heterogeneity made of Q$\beta$ the first biological system in which molecular quasispecies theory found direct experimental support. Building on this foundation, decades of evolution experiments under thermal, ecological, and mutagenic pressures established how mutation, selection, epistasis, and population structure jointly shape adaptive trajectories. Deep sequencing has recently allowed the mutant spectrum of Q$\beta$ populations to be resolved as large, structured genotype networks, revealing a hierarchical organization around dominant sequences that generalizes classical mutation-selection balance to a dynamic process, and uncovering topological features shared with RNA viruses evolving within natural hosts. In parallel, the catalytic core of the Q$\beta$ replication system has been repurposed in synthetic biology to revive cell-free Darwinian evolution within compartmentalized, cell-like systems, opening new avenues for studying the origin and early evolution of life. Further recent work has pushed the phage into new experimental territories, including extreme, astrobiologically relevant environments and biotechnological platforms for peptide display. Together, these developments illustrate how a single bacteriophage has repeatedly anticipated and continues to clarify general principles of molecular, population, and ecological evolution.

3D vision transformers such as VGGT predict camera poses and scene geometry from multi-view images in a single forward pass, but their global attention over all concatenated view tokens dominates computation as the number of views grows. To reduce this cost, SparseVGGT and HeSS sparsify attention at the block level, and both retain blocks with high attention probability. However, we observe that attention probability poorly predicts how much the model's behavior actually changes when a block is removed, and we show that this mismatch is why performance collapses as sparsity increases. In this paper, we propose ReSS (ReSidual-ReStoring Sparse Attention), which recasts block selection from a problem of maximizing the retained attention mass to one of minimizing the drift that sparsification leaves in the residual stream. We introduce a drift score that quantifies how much each block shifts the residual, and, since the drift of a drop set depends on the directions of the contribution vectors rather than on their magnitudes alone, an iterative residual restoration procedure that refines the drop set as a whole. Across three backbones and five datasets, ReSS preserves dense performance better than prior methods at matched sparsity. Two further results support drift as the quantity that governs the cost of sparsification: maximizing drift degrades performance faster than random selection, and plotted against realized drift instead of sparsity, all methods fall approximately onto a single curve. Code is available at https://github.com/libary753/ReSS.

Non-local quantum computation (NLQC) consists on the implementation of a bipartite unitary $U_{AB}$ by two cooperating distant players by means of a two-round protocol with a single intermediate round of simultaneous communication. It is a major open question to know whether there exists a unitary $U_{AB}$ whose implementation in NLQC requires extra quantum systems with dimensions ${\rm exp}(n^{\Omega(1)})$, where $n$ is the dimension of systems $A$ and $B$. This type of exponential lower bound is essential for security of position-based quantum cryptography, since the capabilities of the adversaries are precisely described by NLQC. It has also been connected to many other problems, such as the optimality of universal quantum simulators, or the expected properties of holographic quantum gravity. Currently the best lower bounds are only sublinear in $n$. In this paper we consider the family of diagonal ${\pm 1}$ valued unitaries $U_{\varepsilon}$, indexed by an element of the Boolean hypercube $\varepsilon \in \{\pm 1\}^{n^2}$, i.e. $U_{\varepsilon}|i\rangle_A|j\rangle_B =\varepsilon_{ij} |i\rangle_A|j\rangle_B$. We show that if $U_{\varepsilon}$ can be implemented in NLQC with constant accuracy for all $\varepsilon$, and the dependency on $\varepsilon$ in the first round of the associated strategy is a polynomial of degree $O(n^{\frac{1}{4}-\delta})$, then the implementation of at least one $U_{\varepsilon}$ in NLQC requires resources scaling as $\exp\left(\Omega\left(\frac{n^{2\delta}}{(\log n)^2}\right)\right)$. The proof is based on geometric properties of particular Banach spaces, namely their type constants, together with random estimates of Boolean functions valued on them.

Language models describe some internal states as good and others as bad. But whether models have a stake in them is an open question. Simply asking models is unlikely to be informative. Any answer may be consistent with genuine introspection, superficial pattern-matching, or with fixed scripts learned in character training. We therefore study revealed preference. Rather than asking about a state, we use activation steering to attach a positively or negatively valenced activation pattern to one of two otherwise meaningless 'zones', switch steering off, and then observe which zone the model prefers. A model with a stake in that state should choose accordingly. Across seven open-weight models from five families, this is indeed what we find. First, steering changes the passages models write about each zone, and those words shift later choice. Second, this shift persists when all surface-level tokens are held fixed and only the hidden KV cache differs. Third, the effect also remains when all text is generated without steering and valence is only injected during cache construction. Thus, the hidden state is sufficient to move choice in proportion to the steering dose. Fourth, the dependence of choice on hidden valence is nearly absent in a base model and emerges during DPO, consistent with a link between valence and goal-directed behaviour formed in training. Finally, given tools to self-steer, a model does not tend to induce a positive state, but it regularly removes an imposed negative state. It does so at a dose-dependent rate and significantly more often than it removes random-direction interventions. Overall we demonstrate that valence-related activation patterns leave hidden traces that predictably govern later choices, even when all visible tokens are identical across conditions. Whether these traces are accompanied by any subjective experience relevant to model welfare remains unclear.

We develop a high-order fully discrete ALE-SAV finite element method for sharp-interface two-phase Navier–Stokes flow that satisfies a discrete energy dissipation law. We introduce an SAV reformulation to ensure the stable treatment of the surface and gravitational potential energies, together with an energy-stable ALE transfer operator that controls the density-weighted kinetic energy across moving meshes. The resulting scheme is linear and satisfies a modified energy-dissipation inequality. Numerical experiments, including rising-bubble benchmarks, demonstrate the robustness of the method and confirm second-order convergence in time and arbitrarily high-order convergence in space.

In this note, we prove that for n > 2 a harmonic map $\mathbb{S}^n \to \mathbb{CP}^m$, of index n+1 is pseudo horizontally weakly conformal, that $n$ must be odd. In particular, for even n every non-constant harmonic map $\mathbb{S}^n \to \mathbb{CP}^m$ has index at least n+2. We also present a harmonic map from $\mathbb{S}^4$ to $\mathrm{Gr}_{\mathbb{C}}(2,4)$ of index 5 that is not pseudo horizontally weakly conformal, so the statement does not extend to Grassmannians.

Scientific information-extraction systems often return a claim with an evidence string, which users must locate in the original PDF. This is challenging because the extracted evidence and PDF text layer are different representations: line wrapping, Unicode variants, superscripts, citation markers, and fragmented items alter text sequences and geometry. We present a source-preserving alignment framework: normalize text for robust matching while preserving provenance for accurate localization. It aligns evidence with normalized page text, maps matches back to source-character spans, and renders only their geometry. When exact alignment fails, line-break-aware token alignment recovers supported spans while excluding unmatched noise. Experiments on 1,020 chemistry papers show that the framework achieves a 92.6% quote-level automatic localization rate, compared with 43.6% for text search and 19.1% for a precomputed bounding-box baseline. Component ablation confirms distinct contributions from normalization and approximate token alignment, while human verification assesses the visual correctness of returned highlights. Overall, these results demonstrate that reliable evidence verification requires robust matching and precise localization within a shared source-preserving alignment representation.

GPU libraries such as CUTLASS expose tens of thousands of semantically equivalent kernels for a single operation, making exhaustive autotuning expensive and execution-free selection difficult. Existing analytical selectors require hand-designed performance rules, while learned selectors operate on raw configuration parameters and must infer hardware consequences from data. We introduce a hardware-aware representation for CUTLASS kernel selection that augments candidate configurations with statically computable estimates of induced hardware behavior. We construct a dataset of 4.9 million CUTLASS kernels and train gradient-boosted and neural learning-to-rank models to rank candidates within each problem. On held-out exhaustive evaluation problems, hardware-aware representations reduce selection regret by up to 40% relative to structural baselines and 64.2% relative to NVIDIA's matrix-multiply heuristics. We further evaluate data-efficient cross-precision and epilogue-fusion transfer within CUTLASS GEMM, showing that explicitly representing candidate-induced hardware behavior provides a useful inductive bias for learned kernel selection.