Papers

We study fair multi-armed bandits under the Nash Social Welfare (NSW) objective, which measures performance via the geometric mean of accumulated rewards. Existing work defines Nash regret as $\mathrm{NR}_T = \mu^\star - (\prod_{t=1}^T \mathbb{E}\mu_{I_t})^{1/T}$, where $\mu_{I_t}$ is the mean reward of the recommended arm $I_t$ and $T$ is the horizon. Since it applies the geometric mean to per-round marginal expectations, it ignores the joint distribution of rewards across rounds, leaving the NSW fairness motivation unaddressed at the trajectory level. We propose trajectory-wise Nash regret $\widetilde{\mathrm{NR}}_T = \mu^\star - \mathbb{E}[(\prod_{t=1}^T \mu_{I_t})^{1/T}]$, which computes the geometric mean over complete sample paths before taking expectations, capturing NSW fairness more faithfully. By Jensen's inequality, $\widetilde{\mathrm{NR}}_T \geq \mathrm{NR}_T$, making it a strictly stronger metric. We also introduce high probability Nash regret $\widehat{\mathrm{NR}}_T = \mu^\star - (\prod_t \mu_{I_t})^{1/T}$, giving the first high probability regret bounds in fair bandits. Our two-phase algorithm, Round Robin Nash Confidence Bound (RR-NCB), combines round robin exploration with a Nash confidence bound index policy. We show $\widetilde{\mathrm{NR}}_T \leq \widetilde{\mathcal{O}}(\sqrt{k\log T/T})$ and, with probability $1-\delta$, $\widehat{\mathrm{NR}}_T \leq \widetilde{\mathcal{O}}(\sqrt{k\log(kT/\delta)/T})$, matching the optimal $\widetilde{\mathcal{O}}(\sqrt{k/T})$ rate despite the stronger metrics. Optimality follows from a lower bound via AM-GM and standard $k$-armed bandit minimax arguments. Simulations validate our theory.

Let $N^+$ and $N^-$ be disjoint compact smooth submanifolds of a Euclidean space, and let $\Lambda\subset N^+\times N^-$ be a compact smooth embedded submanifold prescribing admissible pairs of one-sided traces. Given a smooth family of separating hypersurfaces $\Gamma_t\subset\mathbb T^d$, we study harmonic map heat flows into $N^\pm$ in the two moving phases, subject to \[ (u^+,u^-)\in\Lambda, \qquad \bigl(-\partial_{\nu_t}u^+,\partial_{\nu_t}u^-\bigr) \perp T_{(u^+,u^-)}\Lambda \quad\text{on }\Gamma_t. \] For $q>d+2$, initial data in $W_q^{2-2/q}$ satisfying these conditions at $t=0$ generate a unique short-time strong solution in $W_q^{2,1}$, which is smooth up to the moving interface for every positive time; smooth initial data satisfying the compatibility conditions of every order yield solutions that are smooth up to the initial corner. We double the paired map across $\Lambda$ by normal reflection, which turns the interface conditions into a Dirichlet problem near the interface, and match this problem with the two bulk phases by an overlapping space-time Schwarz map inside a Schauder fixed-point argument. When the interface evolves independently by mean curvature, we also obtain a blow-up alternative in terms of its curvature and the two phase gradients. As an application, we prove local smooth solvability for the periodic matrix-valued sharp-interface system appearing in the convergence theory of Fei, Lin, Wang, and Zhang (Invent. Math. 233 (2023), 1–80).

A fermion mass pairs a field with a partner of conjugate charge: elementary (Higgs-Dirac), self-conjugate (seesaw) or a three-fermion composite (symmetric mass generation, SMG). We give half of a Spin(10)-like generation an explicit Majorana mass in a four-dimensional SMG model and ask what the other half does in a phase with no condensate. With the source on, every mass-type term of the unsourced half averages to zero under the symmetry group of the sourced action, so a light mass term, and a seesaw's light-heavy mixing, requires a spontaneously broken symmetry; exact on the lattice and a general proposition. The source is colour-democratic (a Delta_R-type mass on every flavour's right-handed taste doublet); the single-nu_R split lies outside the positivity class used but inside the symmetry statement. Measured up to 8^4: (i) in the symmetric-gap phase, with the source screened to at most 1.1% of free, the unsourced half's single-fermion readout stays at 0.3% of free while its pair susceptibility rises from 0.2% to 1.2-1.7% at h=2; on like mode sets it falls with the volume, on (4^4,8^4) no inequivalent light mass channel grows faster than free, and symmetry breaking is not resolved at L<=8; (ii) at the critical point the explicit mass collapses the critical sigma channel and moves the light half toward free as a saturating crossover, not a power law; direction tests (MIXED by their pre-registered letter) are consistent with a critical coupling rising with the mass; y_c(h) is not located. Pole versus zero of the light propagator at p->0 is not measured. The outcomes are readings after pre-registered tests that mostly returned no verdict. Also: no first-order signature of the merged transition at L<=8, a Z_4-odd response handed to a lattice composite, and flavour democracy of the positivity class. Every claim has an evidence class and a runnable check.

At a discrete set of “magic” twist angles, twisted bilayer graphene develops two bands at charge neutrality that are almost perfectly flat. We present a unified theory of this phenomenon within the chiral continuum model. The central object is the square of the chiral Hamiltonian, a $2\times2$ Schrödinger operator for an electron moving in a non-Abelian $SU(2)$ pseudo-magnetic field generated by the interlayer tunneling. From it we derive an energy sum rule in which the interlayer coupling splits into a bounded overlap channel and an unbounded current channel; their different scaling with the coupling $\alpha$ explains why the first magic angle is qualitatively different from the rest. The asymptotic rule $\alpha_{m+1}-\alpha_m\to3/2$ follows from a rescaling of the moiré potential together with its three-cell magnetic periodicity, with the two parity families of zero modes each repeating with period $3$ and interleaved with each other. Near the AA point the zero-mode problem becomes a lowest-Landau-level problem in an effective field $B_{\rm eff}=3\alpha$, so that the high-order zero modes are coherent Landau states of width $1/\sqrt{3\alpha}$ whose guiding centres converge to $\pm(\pi/3) q_\mu$, with kinetic and confinement energies in equipartition. Deforming the coupling into an Abelian one removes the magic-angle sequence, which shows that the non-Abelian structure is essential. Between consecutive magic angles, band inversions at $\Gamma$ and $M$ produce phases with Chern numbers $C=\pm2$, and the quantum metric reaches a sharp maximum at $\theta\approx0.43^\circ$, identifying a promising regime for correlated and topological phases beyond the first magic angle.

A connected graph with at least two vertices is matching covered if each of its edges is contained in a perfect matching. A matching covered graph is solid if every separating cut in it is a tight cut. A matching covered graph which is free of nontrivial tight cuts is a brick if it is nonbipartite. Every bipartite matching covered graph is solid. Lucchesi and Murty conjectured that there exists a positive integer $N$ such that, for every integer $n\ge N$, the maximum number of edges in a simple solid matching covered graph on $2n$ vertices is $n^2$. In this paper, we disprove this Conjecture, and show that the maximum number of edges of a simple solid matching covered graph on $2n$ ($n\ge2$) vertices is $n^2+2$. Moreover, we characterize the graphs attaining this bound. In addition, we prove that every simple solid brick of order $2n$ has at most $n^2$ edges for $n\ge4$.

When several people share a 3D virtual room with an LLM agent, the agent must decide not only what to say, but whether an utterance was addressed to it and, if accessible, what profile information about the others present it may use. To study both problems, we construct LookAway, a controlled corpus of 40 sessions involving 80 distinct personas and an LLM agent (1,200 turns), including ambiguous-addressee turns in which speaker orientation agrees or conflicts with the intended addressee. Across three open-weight large language models and five conditions varying which profiles the agent sees and whether it is told where each person faces (18,000 decisions), adding speaker orientation increased addressee accuracy from 56% to 99.5% when orientation was congruent, but when the speaker faced someone other than the addressee, two of the models went by where the speaker faced on more than 85% of those turns. Warning one model that orientation could be misleading reduced this only modestly. A browser-based 3D demonstrator shows the effect live: the same sentence gets an answer when the speaker faces the agent and silence when they face the other person. Providing both personas' profiles improved responses about the person being asked about, but also increased the use of profile attributes not revealed in the shared conversation, reaching 45.3% of answers for one model. More context thus improves multi-user interaction but also leads to oversharing, so shared LLM agents need mechanisms for weighing spatial cues and controlling when user-specific information enters a response.

Dense retrieval models are typically trained with contrastive objectives that learn effective representations but do not directly optimize retrieval metrics or downstream task performance. To address this problem, we introduce RELER (REinforcement LEarning for Retrieval), a reinforcement learning framework that enables existing embedding models to learn to retrieve directly in embedding space and align to task-specific rewards. We train RELER by sampling unit-length query and document embedding actions from von Mises-Fisher (vMF) distributions centered on normalized encoder outputs, scoring the resulting retrieval or downstream outcomes as rewards, and updating the encoder with REINFORCE using a leave-one-out baseline (RLOO). As exploration in the high-dimensional embedding space is prone to sampling noise, we further propose conditional-mean projection (CMP), which projects each sampled embedding onto the low-dimensional subspace spanned by its encoder output and the candidate embeddings it is compared against, reducing noise in the policy gradient while preserving its expectation. We evaluate RELER on BRIGHT, a benchmark with reasoning-intensive queries that remain challenging for existing embedding models. RELER consistently outperforms InfoNCE and LambdaLoss in average nDCG@10 when post-training BGE-M3 and Qwen3-Embedding backbones. We further evaluate downstream utility through retrieval-augmented generation (RAG), where we adapt only the query encoder while keeping the document index and generator fixed. Across seven QA datasets, jointly optimizing retrieval and answer rewards improves both average retrieval performance and answer quality in RAG.

Typed decision models answer a declared question without generating text: a decision head returns a probability for each of the declared options in a single forward pass. A single pass is fast, intuitive System 1 thinking. We study what lies between one pass and generated reasoning: looping, in which the same layers are recursively applied several times before one typed readout. Each loop lets the model revise its hidden state before it commits to an answer, without generating a token; we call this System 1.5 thinking. We propose SanSi, which turns a pre-trained looped language model into a typed decision model. The option probabilities are read after every loop, and every loop is trained with a proper scoring rule, so that one model serves every budget from one loop to eight in a single run. On 10,027 test decisions from 59 sources, SanSi reaches 72.0% accuracy: 13.5 points above a non-looped model of the same shape trained with the same recipe, 5.3 points above a newer non-looped model of its size, and 1.8 points below one with three times the parameters. On two depth-controlled tasks, loops extend the solvable depth beyond the depths seen in training, where the larger single-pass model fails. Used as the judge for policy optimization with reinforcement learning, without gold answers, SanSi raises the share of the generator's correct answers from 37% to 52%.

Visual tokens are a major source of inference cost in vision-language models, yet simple image downsampling remains a surprisingly strong compression baseline. This raises a complementary question: under a fixed token budget, where should visual fidelity be preserved? We introduce Foveated Compression, which encodes a full-resolution image once and represents it with a mixture of native- and compressed-resolution visual tokens. A behaviorally self-distilled Foveated Merger compresses local visual tokens while preserving compatibility with their native counterparts, and a lightweight Foveated Selector chooses one of nine spatial cells to retain at native resolution using exhaustive budget-matched intervention supervision. At 11.11% visual tokens, uniform Foveated Compression shows no significant paired difference from iso-token downsampling. At 20.99%, the learned selector significantly outperforms random and fixed allocation, but remains below strong whole-image resizing, showing that localized fidelity is not universally preferable. A budget-matched region-choice oracle reaches 82.73 macro accuracy versus 69.61 for the learned selector, revealing substantial headroom within the same spatial action space. Matched probing further shows that signals predicting when compression breaks the answer are substantially more accessible after language-model computation than to the lightweight prefill-free selector. These results expose complementary bottlenecks in region selection and compressed-region fidelity.

The Kannan–Lovász–Simonovits (KLS) conjecture asserts that isotropic log-concave probability measures have Poincaré constants bounded by a universal constant, independently of dimension. We give a deterministic variational proof with an explicit bound on the Poincaré constant $C_P(\mu)\le25$, where $\mu$ is any isotropic log-concave probability measure. Starting from elliptic moment estimates and a quadratic variance inequality, we establish geometric bounds on normalized Appell coefficient norms through joint maximization over the measure and test function. Variation of the measure gives a maximum-principle inequality, while stationarity in the test function controls the highest-order cumulant terms. Two concave barriers constructed from quadratic and cubic polynomials close the induction. A weighted Helmholtz–Hodge decomposition then controls the curl correction of weighted divergence, yielding a curvature estimate for compatible symmetric tensor fields that is uniform in rank. Quadratic duality converts this estimate into an operator comparison for centered integration, linking the coefficient bounds to control of the inverse gradient. A spectral-radius estimate and a scalar growth inequality for adjoint iterates then yield the Poincaré bound. The final estimate is independent of the auxiliary positive curvature, allowing approximation to complete the proof for general isotropic log-concave measures.

As human–AI interactions become more conversational, full-duplex speech language models capable of natural real-time dialogue are growing in importance. Beyond generating appropriate responses, these models must coordinate turn-taking, backchanneling, and floor management in real time. Reinforcement learning (RL) provides a way to refine these behaviors through direct feedback on interaction outcomes. However, existing RL methods either apply timing feedback to a token policy or optimize semantic content, leaving the joint improvement of timing and content unresolved. We introduce HiPLEX, an RL framework that factorizes a pretrained full-duplex text policy into a control policy that decides when to emit content and a conditional content policy that decides what to emit. The first factor selects among 'pad', 'epad', and 'con'. The second selects a token only when 'con' is chosen. This hierarchy describes conditional actions within each frame and uses the model's existing text head. We route timing advantages to the token-group factor through event-causal masks derived from generated speech episodes, and route an LLM-judge semantic advantage to the conditional content factor. Across three Moshi seeds on Full-Duplex-Bench v1, HiPLEX reduces takeover rates during natural user pauses and backchannel opportunities, and shortens post-interruption response latency relative to GRPO, while maintaining comparable judged interruption-response quality. On Moshi and PersonaPlex, HiPLEX better matches pooled human turn-timing and backchannel-rate marginals than GRPO.

Videofluoroscopic Swallowing Study (VFSS) is one of the gold standard for diagnosing swallowing disorders, providing dynamic X-ray imaging of the swallowing process. Automated kinematic analysis in VFSS relies fundamentally on precise anatomical keypoint localization. However, existing studies focus on limited keypoints (e.g., cervical vertebrae or the hyoid) and overlook critical regions such as the soft palate, while annotating only active swallowing segments and ignoring abundant non-swallowing data, resulting in poor data efficiency. Moreover, leveraging this unlabeled data via standard semi-supervised learning is suboptimal, as generic methods are prone to spatial bias. In medical X-rays with fixed layouts, models tend to memorize absolute coordinates rather than understanding anatomical structures. To tackle these challenges, we introduce VFSSKep, a novel dataset that extends annotations to the soft palate and incorporates large-scale unlabeled data. We further propose S$^3$KL, a Structure-aware Semi-Supervised Keypoint Localization framework designed to overcome spatial bias. It integrates a Structure-Aware Learning strategy to extract high-resolution structural cues for structure-aware representation learning, and a Structural Representation Consistency Learning strategy with block shuffling to enforce invariant structural recognition. Experiments show our method achieves state-of-the-art semi-supervised performance, even with unlabeled and 25% labeled data surpassing fully supervised learning with 100% labeled data. Code and data will be made publicly available at: https://github.com/kaai520/S3KL.

Modern voice assistants may be shared by multiple users and should be able to answer questions about earlier conversations such as "When did I originally plan to leave?" or adapt their behavior to individual users based on past interactions. This requires more than retrieving a topically similar passage: the assistant must identify the current speaker, recover the relevant past state, and distinguish it from later revisions. We present PERSIST, a persistent memory system for multi-session, multi-speaker spoken dialogue that explicitly models Who, What, and When. PERSIST structures cross-session histories into readable event records and retrieves them with a 3W joint scoring mechanism that combines semantic content, acoustic speaker identity, and temporal state. For real-time full-duplex interaction, PERSIST further reuses intermediate representations from the dialogue backbone, avoiding query-audio re-encoding and reducing retrieval latency from 578.42 ms to 7.03 ms. We also introduce SpokenTrace, a diagnostic benchmark that factorizes evaluation along memory tasks and speaker-query types, exposing failures in recall, speaker attribution, and temporal-state tracking. On SpokenTrace, PERSIST achieves 85.08% end-to-end task accuracy and improves all-support EM@3 from 49.01% with BGE-large to 82.10%.

We study the limit shape of the range of the random walk excited to the center on $\mathbb Z^d$, with $d\geq2$. A cookie is placed at each nonzero vertex. On its first visit to such a vertex, the walker consumes the cookie and takes its next nearest-neighbor step with a bias toward the origin. On a visit to the origin, or on later visits to a nonzero vertex, no cookie is available and the walker moves to a neighbor uniformly at random. We prove that the set of vertices visited up to time $n$, rescaled by $n^{-1/(d+1)}$, converges in probability in Hausdorff distance to an explicit $\ell^1$ ball. This answers a question raised by Kozma (2007).

Safety alignment in Large Language Models (LLMs) remains vulnerable to backdoor attacks. Existing LLM backdoors are almost all input-centric: activation depends on explicit trigger patterns in the user input, so modern guardrails are built to sanitize the input space. We challenge this assumption with a novel answer-side backdoor for multi-turn dialogue. Instead of inserting the trigger into the input, the adversary uses a benign first-turn prompt to naturally induce the model to generate a specific, seemingly innocuous word. Once merged into the dialogue history, this self-generated word becomes the trigger. When a later harmful query arrives, the model detects its own trigger and bypasses its safety refusal, while the user input stays perfectly clean. Across four LLMs, our attack reaches near-perfect Attack Success Rates, approaching 100% at only a 5% poisoning rate, while preserving general utility and clean-input safety, and it evades mainstream input-centric defenses. Representation-level analysis shows that the self-generated trigger consistently suppresses the model's refusal signal, exposing a critical blind spot in current LLM defenses.

Activation steering provides a lightweight and flexible way to control large language model (LLM) behavior. However, effective steering requires more than inducing the intended behavior: it should also limit unintended changes and remain robust across inputs and training data. Existing evaluations cover these dimensions only in fragments. As a result, the trade-offs between efficacy and side effects have not been systematically characterized. We introduce SteerScope, a two-axis, multi-dimensional evaluation suite that jointly characterizes steering outcomes and method properties through 15 metrics. We score target efficacy and side effects on language quality, task capabilities, and safety and reliability, and further assess generalization and data dependence through steering-specific metrics for sample efficiency and sample sensitivity. Rather than comparing methods at a single operating point, we characterize the trade-offs between efficacy and side effects. Under matched models, tasks, and evaluation protocols, we benchmark 23 methods spanning 4 families, including prompting, LoRA, and SFT as baseline methods, and release the suite as an extensible codebase. We find that current activation steering methods do not yet surpass the Prompt Steering baseline in their overall balance between steering efficacy and side effects: across both model scales, no evaluated activation steering method achieves higher efficacy without incurring greater composite side effects. We further uncover a consistent coupling between steering efficacy and side effects. Under OOD prompts, target efficacy is often preserved, whereas side effects tend to become more pronounced, particularly through declines in instruction relevance and fluency. Methods also exhibit sharply different sample-efficiency profiles.

We study ridge regression from exactly $s$ distinct rows of a fixed design. Responses are fixed, and only the subset is random. The determinant law and selected ridge fit share one positive definite penalty. Established mean identities and exponential-family duality give the unique penalty that matches a prescribed full-data ridge fit in expectation. It exists exactly when $s$ exceeds the target's effective dimension. Our main result concerns centered covariance risk normalized by full-data penalized loss. For balanced signed coordinate replicas, a strict sector inequality gives the sharp risk and all maximizing responses at every budget from the dimension to one below the row count. This holds for any nonzero positive semidefinite query. With the target and query fixed, the maximizing response space is unchanged across these budgets. For general designs, we characterize attainment of a leave-one-out envelope. For existing real equiangular tight frames, flat row query energy characterizes when every nonzero residual response maximizes at two deletions. At three deletions, we give the sharp risk and complete maximizing space for isotropic queries, using unequal triangle weights. The balanced geometry yields a same-sample unbiased ridge–Horvitz–Thompson mixture with lower sharp risk and an exact mean-share improvement boundary. Under full recalibration after feature changes, we prove quadratic regret from searching the complete old maximizing space and a query-uniform bound on the mixture's risk gain. The strongest sector inequalities have exact computer-assisted proofs.

Multi-reference image generation requires preserving the appearance of multiple subjects while composing them into a coherent scene. However, existing diffusion transformers commonly encode references as dense visual token grids and jointly process them with global attention, making conditioning increasingly expensive as the number and resolution of references grow. We present RefRoute, a framework that addresses both reference representation cost and attention overhead through two complementary mechanisms. Compact residual conditioning combines low-resolution latent tokens with lightweight residual features extracted from full-resolution pixels, reducing reference token counts while retaining fine-grained appearance cues. Condition routing and attention routing align reference tokens with their assigned target regions and restrict cross-reference interactions, while allowing selective reference access beyond region boundaries for scene integration. We further introduce RefRoute-Data for training many-reference generation models and ManyRef100, a benchmark spanning human, object, and mixed compositions with 10-17 references. After many-reference fine-tuning, RefRoute achieves an overall Weighted-Ref-VIEScore of 36.06 on ManyRef100, compared with 8.88 for FLUX.2-Klein-9B. Separate inference-cost evaluations show substantially slower latency growth as the reference count increases: at 16 references, our 50-step and 4-step configurations achieve $18.3\times$ and $14.2\times$ speedups over their corresponding FLUX baselines, respectively. These results establish compact reference representations and spatially routed attention as an effective approach to scalable many-reference image generation.

The conventional Hall effect arises from the transverse deflection of mobile electronic charge carriers in conductors. Here, we predict a bosonic charge Hall effect in charge-ordered insulators mediated by bichargons, collective bosonic excitations of charge order carrying quantized electric charges $\pm 2e$. In contrast to conventional electronic carriers, a thermally excited bichargon gas does not support dc electrical conduction in response to an external electric field despite its constituents carrying finite electric charges. We show that a temperature gradient can instead drive a diffusive flow of thermal bichargons, while an out-of-plane magnetic field deflects the oppositely charged bichargons in opposite transverse directions via the Lorentz force, leading to a finite Hall charge current and opposite charge accumulations at the sample edges. Our results broaden the paradigm of charge Hall transport beyond conventional electronic conductors, establishing that a charge Hall response can emerge in an electrically insulating system through charged bosonic quasiparticles.

For a Dirac operator $D$ on a finite weighted graph, let $d^D$ denote the associated noncommutative (Connes) distance. We show that deleting an edge can actually decrease the noncommutative distance between two vertices in the graph. The smallest example of this phenomenon comes from a weighted 4-cycle, and the case of deleting an edge from a weighted 4-cycle is determined completely: if $d^{D'}$ denotes the noncommutative distance in the graph after edge deletion, we prove that $\sup d^D/d^{D'} = 2/\sqrt{3}$ for the $4$-cycle, and further that this upper bound holds for all graphs. On the other hand, we show that deleting an edge can decrease the noncommutative distance between two vertices of an $n$-cycle precisely when $n$ is divisible by $4$. In cases when a deleted edge decreases the noncommutative distance between two vertices $x$ and $y$, we show that the deleted edge need not be incident to either of the vertices $x$ or $y$, and in fact the deleted edge can be arbitrarily far from both in the graph-theoretic (number of edges) distance and in the weighted (geodesic) distance. Moreover, deletion of a single vertex arbitrarily far from both $x$ and $y$ in either the graph-theoretic or weighted distance can change $d^D(x,y)$ by an arbitrarily large factor.

Transformers have exhibited impressive empirical success across various domains, but their theoretical foundations remain less developed. This work constitutes a mathematical study of the measure-to-measure operators defined by transformers. We show that transformers map sub-Gaussian inputs to sub-Gaussian outputs; this ensures that taking arbitrary-length compositions of the softmax operator is well-defined. We then show that transformers are Hölder continuous with respect to the 1-Wasserstein distance on appropriate spaces of sub-Gaussian inputs. This allows us to establish estimates on the error propagation along a transformer between a sub-Gaussian input and its empirical approximation. We also study a mean-field analog of the cross-attention mechanism, which is an operator from a pair of probability measures to a single probability measure. We show that cross-attention exhibits different Hölder regularity and sample-complexity in its two input arguments. Last, we apply our results to deduce approximation guarantees for measure-to-measure transformers. Together, these results provide a firm stability and finite-sample theory for transformers on sub-Gaussian data.

We present JevCascade, an inference-time compute allocation framework for prefill-only decision models, built on readout stability and zero-label restricted readout prediction. Prefill-only decision models score every candidate in a menu in a single forward pass and never decode, which makes one call one to two orders of magnitude cheaper than a same-scale generative language model. We show that this read-out structure carries a testable property. When an intervention changes only the menu and leaves the input text fixed, the post-intervention accuracy is already determined by the cached first-pass distribution. The restriction predictor restricts the pass-1 probabilities to the menu, renormalizes and reads off the argmax, with no labels and no second pass. Across six model families, ten core datasets (sixteen in total) and two task types, menu-only interventions are predicted to within 4.2 points, exactly for one family. The property is ordinal, not probabilistic, since a probability-level variant of the same estimator errs by 21.0 points, and class-specific, since same-scale generative models err by 1.6 to 15.8 points and degrade as they grow. It makes inference-time compute decidable before deployment. Uniform extra passes buy calibration but almost no accuracy; at matched cost a confidence cascade beats every scheme that re-asks the same model, and curating the menu beats enlarging the model, a 0.8B model on a curated 5-candidate menu reaching 95.4% on CLINC150 against 80.0% for a 4B model on the full 150-label menu.

A memory system can retire an obsolete value and later restore it merely because the same old statement appears again. A re-read of an old source and a genuine revert can produce the same observed sequence of values while requiring opposite current answers. We study this ambiguity on 130 extractor-selected atomic transitions derived from software fixes. In the ordinary transition condition, identity-based temporal memory reaches 98.5% model-judged accuracy with zero observed errors under a literal stale-value proxy. Appending a verbatim re-read of the old statement reduces accuracy to 10.8% and raises the stale-value rate to 88.5%. A guard that refuses to reactivate a previously retired value restores accuracy to 97.7% and reduces that rate to 0.8% in this constructed re-read condition. The guard cannot also recognize a legitimate revert without additional change provenance. Two supporting studies examine exposing retired history to the answer model and supplying current source for changed behavior. An exploratory extraction study over 707 software fixes provides scope context, not a universal coverage estimate. The design implication is to distinguish an observation of a value from evidence that the value changed. Selected inputs, aggregate-only answer records, related-family judges and a post-failure guard evaluation limit the conclusions to the retained experiments.

Direct numerical simulations of thermally stratified multi-layer Rayleigh-Taylor instability are performed to investigate the influence of interfacial Atwood number (At) on instability growth, interfacial coupling, turbulent mixing, and spectral characteristics. A fully compressible, three-dimensional, high-fidelity Navier-Stokes solver has been used to simulate ten cases spanning a broad range of interfacial $At$ to examine the evolution of coupled instability dynamics. The configuration consists of three superposed fluid layers with unstable density stratification across two interfaces generated through temperature variations. The temporal evolution of the flow is characterized using the maximum vorticity, mixing-layer growth, density fluctuations, turbulent kinetic energy, and energy partitioning between gravitational potential energy, TKE, and dissipation. The instability evolution is shown to proceed through distinct onset, quasi-exponential growth, and nonlinear saturation stages for all configurations. Increasing interfacial At leads to earlier instability onset, enhanced vorticity amplification, and accelerated development of turbulent mixing layers. The weakly stratified configurations exhibit dynamics resembling effectively single-interface RTI, whereas the strongly stratified cases develop two simultaneously active mixing layers that subsequently interact and merge into a coupled turbulent region. The wall-normal distributions of density fluctuations and TKE demonstrate progressive broadening of the mixing region and increasing redistribution of turbulent activity with increasing stratification strength. The late-stage spectra exhibit an approximate -11/5 scaling over an intermediate range of wavenumbers, consistent with buoyancy-dominated turbulent transport.

Surface electromyography (sEMG) provides a wearable, noninvasive interface to neuromuscular activity for movement decoding and human-computer interaction. Population-scale decoding remains difficult because the relationship between sEMG and neuromuscular activity varies across users and sessions, while task-relevant dynamics span channels and multiple timescales. Learning waveform-to-output mappings from task labels leaves the distinction between recording variability and coordinated motor activity implicit. We introduce the Neuromotor Hierarchy Network (NHN), which learns a compact latent neuromotor state from task supervision to represent task-relevant neuromuscular coordination. NHN constructs this latent state through a hierarchy inspired by neuromotor organization. It adapts recording statistics while preserving relative intensity. Its spatiotemporal encoder uses parameter-efficient channel interactions and modulates features with multi-timescale history. The resulting features yield candidate activations of learned motor primitives, which are temporally integrated and continuously weighted to form the state. Theoretical analysis characterizes the efficiency, temporal behavior, and optimization of NHN's core mechanisms. We evaluate the architecture for both continuous hand-pose estimation on emg2pose and touch-typing recognition on emg2qwerty. On emg2pose, NHN reduces user-averaged angular error by 0.52% to 2.84% across all three generalization splits in both Regression and Tracking relative to Hadidi et al.'s best task-specific variants, using 48.42% to 48.51% fewer parameters. On emg2qwerty, NHN reduces beam-search character error rate by 19.40% zero-shot and 30.42% after fine-tuning relative to SplashNet-Upscale, using 65.86% fewer parameters. Physiology-guided inference of a latent neuromotor state supports parameter-efficient sEMG decoding.

Existing molecular and materials learning approaches often rely on a limited set of structural representations, which may capture only selected aspects of complex three-dimensional structure. Here, we introduce mathematical invariant-enabled topological neural networks (MITNNs), a framework that represents complex structures through multiple complementary mathematical views and integrates them with topological neural architectures. MITNNs combine multiscale invariants from topology, spectral theory, commutative algebra, differential geometry, and discrete curvature, capturing complementary structural information from the same system. Systematic invariant-subset, architecture-subset, and ensemble analyses show that predictive performance depends on how mathematical representations and neural architectures are paired, with selected combinations outperforming individual models and the aggregation of all available components. Across protein-ligand binding, metal-organic framework properties, mutation-induced protein solubility, and molecular toxicity prediction, MITNN consistently outperforms existing methods. These results establish MITNN as a mathematically multimodal framework for scientific machine learning.

Accurate nuclei instance segmentation is essential for quantitative renal pathology, yet general-purpose models often struggle with low contrast, dense nuclei, complex morphology, and strong background staining. In this work, we extended a human-in-the-loop framework by combining 5,901 foundation-model-generated pseudo-labels from well-segmented cases (Easy), 860 newly expert-annotated unresolved challenging cases (Medium), and 198 expert-annotated consensus failure cases (Hard). These annotations, spanning different levels of segmentation difficulty, enabled the systematic evaluation of seven single-source and mixed-source fine-tuning strategies across nine cell segmentation model configurations. Fine-tuning improved all models, with Medium data included in seven of the nine best-performing strategies. LSP-DETR achieved the highest F1 score of 0.8725 with Hard-only fine-tuning, while StarDist showed the largest improvement, increasing from 0.7380 to 0.8332 with Medium-only fine-tuning. These findings show that annotations spanning multiple difficulty levels support effective model adaptation, although the optimal annotation composition remains model dependent.

We investigate the dependence of stellar mass and star formation activity on the topology of hosting large-scale structures using mass-complete galaxy samples in four redshift bins spanning from z = 0.4 to z = 4 using the COSMOS2020 catalog. Cosmic web components (clusters, filaments, and field) are identified by applying the Multiscale Morphology Filter to galaxy density maps, and group memberships (central, satellite, isolated) are assigned to each galaxy by the Friends of Friends (FoF) algorithm. Out to z < 1, we find that stellar mass increases toward denser structures, driven primarily by central and satellite galaxies, with differences up to ~0.35 dex between field and clusters. At these redshifts, star formation rate (SFR) is suppressed by ~0.1 dex in clusters compared to field galaxies, particularly for centrals, while the SFR of star-forming galaxies shows a much weaker dependence on the type of host structure, indicating that the quenched population primarily drives the observed environmental dependence. Specific SFR (sSFR) shows the strongest decline for centrals in clusters at z<1, consistent with enhanced quenching in dense environments. At 1<z<2, star formation activity becomes largely independent of environment, suggesting a transitional regime in the role of large-scale structure. At z>2, we observe a mild increase in SFR (~+0.1 dex) and sSFR (~+0.13 dex) from field to cluster galaxies, pointing to a possible reversal of environmental trends during early cosmic epochs. These results highlight the evolving influence of environment on galaxy evolution and set the stage for deeper investigations with upcoming wide-field surveys.

We study two physically distinct steady free-boundary problems in a two-dimensional inviscid fluid: a hollow vortex in a constant-vorticity flow subject to simple shear, third order and linear strain at infinity, without surface tension, and an irrotational flow past a constant-pressure bubble subject to surface tension, linear strain, and circulation at infinity. Building on the mathematical vortex-bubble correspondence recently developed by Crowdy and Tanveer, we show that both problems are linked by a common mathematical formulation. For the vortex problem, we extend the sequence-space fixed-point approach of Crowdy and Tanveer to obtain new local existence, uniqueness, and analyticity results. For the bubble problem, we develop a separate existence theory, reducing it to a nonlinear singular integral operator fixed-point problem and deriving a scalar solvability condition that defines a realanalytic surface in the physical parameter space. On this surface we obtain locally unique bubble solutions with real-analytic boundaries and holomorphically extendible velocity fields. Finally, we prove that the scalar solvability condition is equivalent to a functional conformal mapping identity. The scalar condition between the parameters is enough for the vortex and bubble problems to have the same free-boundary shape, despite their different exterior flows.

Recommender systems learn from observed user-item interactions, but explicit negative feedback is often unavailable. Since deep learning models require negative signals for training, negative sampling methods typically treat selected unobserved interactions as negatives. However, a missing interaction does not explain why a user is uninterested in an item or whether there is sufficient evidence to label it negative. This is especially important in business recommendation, where negative signals should be interpretable and aligned with business objectives. We formulate implicit negative candidate discovery to identify unobserved interactions supported by observed customer behavior. We encode these patterns as symbolic rules, score them based on support, informativeness, and product relevance, and rank the retained rules by evidence. An LLM then interprets the retained rules using business objectives and domain knowledge; the interpretations are combined with the statistical evidence in the final report. We evaluate our method in an industrial B2B setting and across five public recommendation datasets. Candidate-quality evaluations in the industrial setting and three public datasets show higher precision than the evaluated baselines, while symbolic selection improves downstream test PR-AUC by 12.5% over random selection with four negatives per positive example in the industrial task. Our results show that negative candidate validity can be evaluated separately from downstream recommendation performance. This distinction enables evidence-based, business-aligned, and explainable negative selection, improving both interpretability and model training in sparse, skewed, real-world recommendation settings.