Papers

A ruler reads an unknown length against a calibrated scale. The quantum data ruler reads a matrix element of an unknown state against the signal of a known reference, from their ratio. It is exact for any Hamiltonian and any time, since transition operators change by a state-dependent constant times one function of time, removing the vanishing-signal limit. The readout is unbiased under dephasing and amplitude damping, and recovers the coherent ergotropy of a quantum battery that two-point measurement erases. The structure survives the classical limit as action–angle Fourier modes.

Let $p:X\rightarrow\Delta$ be a proper holomorphic submersion whose total space $X$ is a Kähler manifold. We prove that $\dim_{\mathbb C}H^0(X_t,mK_{X_t})$ is independent of $t$ for every integer $m\geq1$. This was conjectured by Y.-T. Siu in 2002.

Time series forecasting models are typically compared on pointwise error, which scores a prediction in isolation from the decision it is produced for, and a lower forecast error does not imply a better decision downstream. A parallel debate asks whether modern transformer architectures forecast better than recurrent and other lightweight models. We compare linear, fixed recurrent, transformer, and mixing based architectures against recurrent networks evolved by neuroevolutionary architecture search, evaluating each on forecast accuracy and on the net return of a daily long/short strategy. All models are fit on a pooled panel, one network trained across the whole universe. Across four mid-cap portfolios and three trading years, the evolved networks rank first on both forecast accuracy and net trading performance, while the second most accurate model loses money once positions are formed and costs are charged. The advantage tracks a horizon match, since rank IC for the evolved networks rises from a one-day to a ten-day scoring horizon while every model above 300 parameters declines. They are also the cheapest end to end: a CPU-only search of 16 minutes yields 66-weight networks that predict in 10.8~$\mu$s on a Raspberry Pi Zero, against transformer baselines of up to 817,153 parameters that require GPU training.

Electrophysiological source imaging (ESI) aims to estimate cortical source activity from noninvasive electrophysiological measurements such as electroencephalogram (EEG). However, ESI is fundamentally ill-posed because source activity is substantially higher-dimensional than sensor observations, resulting in non-unique solutions. Recent learning-based approaches address this ambiguity by learning data-driven source priors, yet they often struggle to generalize across subject-specific cortical geometries. To address this, we propose CANDLE, a learning-based ESI model that estimates source activity on subject-specific cortical geometries. CANDLE learns a prior over the null space induced by the source-to-sensor mapping derived from T1-weighted MRI, restricting learning to unobservable source components while preserving geometric constraints. To train CANDLE, we develop a whole-brain simulator spanning over 1,100 subject-specific cortical geometries with source configurations derived from over 26,000 statistical brain maps. Trained exclusively on simulated data, CANDLE outperformed prior ESI methods on simulated source activity estimation and generalized to two empirical tasks: (i) intracranial stimulation localization from simultaneously recorded scalp EEG and (ii) epileptogenic zone estimation from presurgical interictal EEG. Our project page is available at https://candle-esi.pages.dev}{https://candle-esi.pages.dev.

The AI CUP 2025 Precise Analysis of Table Tennis Smart Racket Data Competition introduced smart table tennis rackets that collect extensive player swing data, enabling research on table tennis big data. These data support in-depth analysis of players' return techniques and swing-force consistency, improving the accuracy of player skill assessment. This study focuses on six-axis sensor data collected by smart table tennis rackets and proposes TTNet, a novel deep learning model with multitask learning capabilities, to advance table tennis data analysis and related applications. TTNet combines convolutional neural networks (CNNs), residual networks (ResNet), and self-attention mechanisms to simultaneously predict four player attributes: gender, playing hand, years of experience, and skill level. We adopt a two-stage training strategy that incorporates data augmentation and task-specific loss functions to improve generalization on imbalanced data. Our approach achieved second place on the official competition leaderboard.

Speculative decoding (SD) accelerates autoregressive generation by letting a lightweight draft model propose tokens that a target model verifies in parallel. However, its standard acceptance rule, designed for exact distribution correction, rejects tokens to which the draft assigns excess probability, even when the target finds them highly plausible: over half of the rejected tokens lie inside the target's own nucleus. Since verification dominates the cost of SD, these rejections waste its most expensive operation. We introduce Nucleus Speculative Decoding (NSD), a plausibility-aware verification rule that accepts a draft token if it passes the standard test or belongs to the target nucleus, while keeping SD's residual correction and bonus sampling unchanged. NSD requires no training or extra forward passes and is compatible with any drafting mechanism. Because it preserves SD's recovery rule, its deviation from the target distribution can be characterized exactly: we prove that the single-step total variation error equals the draft's excess probability inside the target nucleus, which is precisely NSD's gain in acceptance probability. NSD thus trades fidelity for acceptance at an exact one-to-one rate, and we further derive sequence-level fidelity bounds. Across six target models and five mathematical reasoning and code generation benchmarks, NSD achieves the highest throughput among all compared methods, with speedups of up to $5.16\times$ over autoregressive decoding and $3.15\times$ over standard SD, while improving accuracy over SD on five of the six models and nearly halving verification time per output token. Our code is available at https://github.com/EIT-NLP/Nucleus-Speculative-Decoding.

In this article, we study the global well-posedness for the quadratic Schrödinger system on $\mathbb{T}^6$. To achieve this, we utilize the concentration-compactness/rigitdity argument initiated by Ionescu and Pausader \cite{IPT3}. Our result is also regarded as a periodic analogue of Gao-Meng-Xu-Zheng \cite{GMXZ}.

Efficient post-quantum cryptography on resource-constrained Internet-of-Things (IoT) devices requires implementations that exploit the target processor architecture while resisting practical implementation attacks. This paper presents an ISA-accelerated and implementation-hardened realization of Ring Binary Learning with Errors (RBLWE) encryption on a commodity ARM Cortex-M33 microcontroller. Packing four 8-bit polynomial coefficients into the byte lanes of a 32-bit register and processing them with SIMD-style instructions, together with a packed message codec, accelerates encryption and decryption, while a buffered hardware-TRNG entropy source drawn from the on-die Secure Element drives the key-generation gain. Together these give same-core cold-start speedups of $4.06\times$, $3.35\times$, and $3.01\times$ for key generation, encryption, and decryption over a scalar baseline, and $3.52\times$/$3.18\times$ lower encryption/decryption cycle counts than a reference Cortex-M0 implementation. On top of this accelerated core, we add four staged countermeasures: constant-time execution, fault hardening against zeroing, random-corruption, and instruction-skip faults, a Fujisaki-Okamoto (FO)-style CCA2 transform, and first-order shared (masked) CPA decryption, reporting each layer's cost individually. Binary-level inspection confirms these countermeasures survive compilation and identifies a compiler-induced masking flaw resolved with a hand-written assembly replacement. Dudect-style timing tests, debugger-assisted fault-injection campaigns, and component-level TVLA then provide implementation-level evidence for the staged protections. The results demonstrate a practical acceleration-security tradeoff for RBLWE on off-the-shelf microcontrollers and reusable architecture-aware techniques for lightweight post-quantum implementations.

Model merging offers a promising solution for combining multiple fine-tuned checkpoints into a single model through parameter arithmetic. However, finding optimal merging coefficients requires an extensive search that becomes prohibitively expensive as models scale in both size and number, due to high memory requirements and combinatorial growth in the search space. We show that, within the same model family, models exhibit highly congruent performance distributions over merging coefficients across different model sizes. This distributional similarity enables a practical paradigm we call \textit{$\alpha$Transfer}: searching for optimal coefficients on a small proxy model, then directly transfer them to larger target models. We verify $\alpha$Transfer across multiple merging methods, model families, and tasks. Experimental results demonstrate a 6$\times$ speedup and 70% memory reduction on vision transformers, and a 20$\times$ speedup and 85% memory reduction on large language models, while maintaining comparable performance. Our findings establish $\alpha$Transfer as an efficient and generalizable approach to scaling model merging.

We introduce the lattice quark potential model (LQPM), which discretizes the nonrelativistic quark potential model on a periodic cubic lattice and diagonalizes the resulting many-body Hamiltonian exactly. Unlike variational approaches, which provide only upper bounds on the energy, LQPM removes this variational bias, and its remaining finite-volume uncertainty is removed by extrapolation. Formulated directly in coordinate space, the method is indifferent to the specific form of the potential and accommodates arbitrary interactions, such as including three-body forces and spin-orbit and tensor couplings, that are difficult to treat in conventional few-body approaches. As a benchmark, the charmonium and $\Omega_{ccc}$ spectra are reproduced within a few MeV of experiment. For the fully charmed tetraquark $cc\bar{c}\bar{c}$, we obtain a $J^P=0^+$ ground state at $5934.8(13)~\mathrm{MeV}$, $33.2(13)~\mathrm{MeV}$ below the $\eta_c\eta_c$ threshold, unambiguously identified as a deeply bound tetraquark whose existence is robust against the choice of potential. Such a state can decay into two dileption pairs $2(e^+e^-)$ via $J/\psi e^+e^-$, with significance similar to $X(6400)$, or about one order of magnitude smaller. Lying below the lowest strong-decay channel, it can decay only through electromagnetic and weak interactions. Our results establish exact lattice diagonalization as a controlled, systematically improvable, and broadly applicable route to multiquark spectroscopy, providing a quantitative benchmark for the strong interaction and valuable guidance for future experimental searches for exotic hadrons.

Organizations automating operational processes need more than a correct outcome: they need to predict how a process will run, know which one actually ran, and inspect it step by step. When an agent is the executor that predictability is normally lost: the prescribed procedure goes into the system prompt, and only a final answer comes back. We deliver the procedure step by step over the Model Context Protocol (MCP) instead: a server releases one step at a time, the agent executes it, and each step returns a structured step_output. This trades autonomy for predictability, and two properties then follow by construction, independent of the executor. The execution path is prescribed before the run, so the process is predictable in advance rather than reconstructed afterwards; and the completed step records form a machine-readable execution log that downstream tooling can audit and optimize step by step. Evaluating 15,475 trials across 13 SOP-Bench domains and four open-weight executors from frontier (Kimi K2.5) to lightweight (Ministral 3 8B), we find step-level delivery makes the executed process predictable and inspectable for every executor, and additionally raises accuracy when the executor is small. Across all four, process adherence rises significantly (76-95% to 95-99%) and ungrounded answers (correct outputs produced without executing the SOP) near-vanish, falling from 2.1-4.5% to 0.2-0.3% of trials (all 95% CIs exclude zero); under prompt-based delivery, 31-49% of correct answers on know_your_business bypass the SOP entirely, even for the frontier executor. Accuracy is where the executor's capability enters: the lightweight executor gains +6.5pp grounded accuracy because supplying the process externally removes a reconstruction burden it cannot carry, while capable ones trade a small raw-accuracy decrement for a predictable, auditable process.

Small language models (SLMs) are attractive as local agent controllers because they reduce remote inference, latency, and deployment footprint, yet structured tool errors can cause an agent step to fail. Existing routers typically select a model once per query. However, agents expose sequential decision points whose difficulty dynamically changes based on intermediate observations. We propose STEPGATE, an uncertainty-aware handoff framework that scores each local SLM action and selectively escalates challenging steps to a stronger model. On a 52-task held-out single-step BFCL-derived test split, the Qwen2.5-1.5B/7B pair attains 82.7% task success with 30.8% escalation, versus 67.3% local-only and 75.4% random escalation (which uses 33.8% escalation). In a separate multi-turn evaluation, STEPGATE achieves 69.0% trajectory success and 84.0% action success using only 30.0% cloud actions, compared with 48.0%/70.5% local-only, 60.0%/78.2% random escalation, and 57.0%/77.1% query-level routing (strong-only achieves 82.0% trajectory success at 100% cloud actions). These results suggest that step-level escalation recovers a large share of the performance gap to the stronger Qwen2.5-7B backend at a matched cloud-action rate while transmitting fewer tokens remotely. However, our evaluation is limited to one model family, a single stronger backend, and scripted tasks. Furthermore, the test sets are small, multi-turn comparisons rely on paired intervals and statistical tests, and our risk tiers serve as research annotations rather than formal safety guarantees.

We study the Jacobi spectrum and low-index rigidity of complex Hopf fibrations. We first give a representation-theoretic description of the Jacobi operator of a homogeneous Riemannian fibration and apply it to \[ \pi:(\mathbb{S}^{2n+1},g_\epsilon)\longrightarrow(\mathbb{C}P^n,h), \] where $g_\epsilon$ is a Berger metric and $h$ is the Fubini–Study metric. For $n\geq3$, we determine all negative and zero eigenvalues and obtain explicit formulas for the Morse index and nullity for every $\epsilon>0$. In particular, for the unit round metric, $\mathrm{Ind}(\pi)=2n+2$ and $\mathrm{Null}(\pi)=n(3n+5)$. We then extend Rivière's rigidity argument from $\mathbb{S}^3\to\mathbb{S}^2$ to higher dimensions. If $\phi:\mathbb{S}^{2n+1}\to\mathbb{C}P^n$ is harmonic and $\mathrm{Ind}(\phi)=2n+2$, then $d\phi_x\circ d\phi_x^\ast$ commutes with the complex structure of $\mathbb{C}P^n$ at every point. Consequently, up to an isometry of the domain, $\phi$ factors through the Hopf fibration as $\phi=P\circ\pi\circ f$, where $P:\mathbb{C}P^n\to\mathbb{C}P^n$ is holomorphic.

How far can stochastic gradient descent ascent (SGDA) go by tuning its timescale ratio and step sizes in nonconvex min-max games? We answer this question for nonconvex-PŁ (NC-PŁ) games by establishing the first tight complexity of two-timescale SGDA with a fixed timescale ratio and non-increasing step sizes. For $\ell$-smooth games with an inner $\mu$-PŁ inequality, we prove a complexity lower bound $\Omega(\kappa^2\ell\varepsilon^{-2}+\kappa^4\ell\sigma^2\varepsilon^{-4})$, where $\kappa=\ell/\mu$ is the condition number, $\sigma^2$ is the gradient variance, and $\varepsilon$ measures the outer gradient norm. This matches existing SGDA upper bounds and establishes a complexity separation from Smoothed-AGDA (Yang et al., 22'). In addition, we show that SGDA can fail to find a stationary point when its timescale ratio is as small as $o(\kappa^2)$. Our negative results highlight the fundamental limitation of SGDA in NC-PŁ games, and justify the development of alternative methods.

We present a rapid, mask-free fabrication workflow for the Paul wheel trap chip based on selective laser etching (SLE) of fused silica. The complete process - femtosecond laser writing, wet-chemical etching in KOH ($\sim$230 $\mu$m/h, releasing the trap geometry from a 500 $\mu$m wafer in approximately 2 h), RF magnetron sputtering of silver electrodes, and direct femtosecond laser ablation for electrode patterning - is carried out in-house, bypassing photolithographic processing and custom shadow masks entirely. Nine chips per 4-inch wafer can be produced in a single working day, reducing the fabrication lead time by more than one order of magnitude relative to the outsourced CVD diamond design. The functionality of the fabricated wheel trap chip is confirmed by a proof-of-concept microparticle trapping demonstration, in which a single microparticle was confined continuously for 72 h at atmospheric pressure. This establishes SLE of fused silica as a rapid, economically accessible fabrication platform for Paul traps in levitated-optomechanics applications.

We introduce complementary determinantal edge ideals. For a graph $G$ on $n$ vertices, the complementary determinantal edge ideal $J_{c}(G)$ is generated by the maximal minors of a generic $(n-2)\times n$ matrix obtained by deleting the two columns indexed by each edge of $G$. We completely characterize the graphs for which $J_{c}(G)$ is Cartwright–Sturmfels with respect to the grading by columns. We prove that this property is equivalent to the existence of a multilinear universal Gröbner basis and characterize the graphs satisfying these equivalent conditions. In particular, the ideals satisfying these equivalent conditions are radical.

A physics-informed loss adds a discretised PDE residual to the data term, but is only strictly valid if the equations being enforced are closed on the fields being fitted. This fails on coarse-grained, stochastically forced data: nonlinear terms in the PDE generally do not commute with the filter, so the coarse-grained fields do not satisfy the original equations, and driving their residual to zero encodes an implicit closure into the learned operator. Under normalised, translation-invariant filtering on a periodic domain, constant-coefficient linear constraints remain valid on the filtered grid. For the 2D incompressible Navier-Stokes equations, two such constraints are continuity and global momentum balance. We enforce these exactly by applying a closed-form projection on the output of a Fourier neural operator (FNO) at $O(N \log N)$ cost. On two-dimensional isotropic turbulence, truncated so that its forcing lies entirely beyond the cutoff wavenumber, the projection achieves a continuity error of $5.0\times10^{-7}$ against 0.51 for a plain FNO and 0.17 for a physics-informed FNO, and a global momentum balance error of $8.6\times10^{-11}$ against $7.5\times10^{-4}$ and $8.3\times10^{-4}$. The projection only costs an extra 2% of training time, and takes the fraction of rollouts whose energy remains bounded at 448 steps from 0.18 to 0.87. On resolved Kolmogorov flow, test-time optimisation costs approximately 3,300$\times$ as much per trajectory as the projection, while leaving maximum divergence three orders of magnitude higher. Nonlinear constraints can also be enforced once their unclosed terms are modelled: closing the global energy balance with a constant subgrid flux, fitted from the coarse training data alone, removes the 20.9% energy deficit that enforcing the unclosed balance produces and keeps every free-running rollout bounded over 2,000 steps.

Search filters help guests navigate vast catalogs in two-sided marketplaces like Airbnb, and recommending the right filters can meaningfully lift booking conversion. Many such production filter-ranking systems, however, represent the guest through hand-engineered, pre-aggregated features generated by ETL pipelines. This makes it expensive to maintain and difficult to extend for new filter types or contextual dimensions (trip length, group size). We present SIFT (Search Intent-to-Filter Transformer), a ranking model built on transformers that learns guest preferences directly from raw behavioral sequences. SIFT replaces manual feature engineering with a unified guest representation that feeds multiple prediction tasks, including booking likelihood, filter engagement, and ordinal capacity thresholds (e.g., 2+ bedrooms) – a general framework for filter ranking in two-sided marketplaces that accommodates both boolean and numeric-range filter types. Extending SIFT to new filters requires only adding a new head, not a new feature pipeline. To keep serving fast, this guest representation is computed offline on a daily cadence rather than at request time. Offline, SIFT improves booking and amenity-engagement PR-AUC by +51.9% and +62.8% respectively over the production baseline. In online A/B testing, SIFT increased engagement with recommended filters by +20.0%, overall filter usage among searchers by +0.72%, and usage of the newly-supported bedroom, bathroom, and bed filters by +3.9%, +10.7%, and +0.52% respectively. Demonstrating the system's extensibility, we rapidly integrated a novel hotel-intent filter using the same shared representation, driving a +3.8% lift in uncancelled hotel bookings and a +0.76% lift in overall marketplace bookings. SIFT is now fully deployed in production, serving scalable personalization to millions of guests.

Sparsely activated Mixture-of-Experts (MoE) models increase model capacity without a proportional increase in per-token computation. Dense-to-MoE upcycling reuses pretrained dense models to construct such systems, commonly by copying feed-forward networks (FFNs) into independently trained experts. We introduce MASKerade, a dense-to-MoE training method that instead learns experts as sparse subnetworks of a frozen pretrained FFN. Each expert is defined by a learned binary mask, and a token-level router selects which masked FFNs to execute and combine. The router and mask scores are optimized jointly, while the underlying FFN weight values remain unchanged. This formulation supports neuron-structured, semi-structured, and unstructured experts within the same routing architecture. Our main configuration uses four 2:4 experts with top-2 routing, where two half-dense expert passes have the nominal FFN arithmetic of one dense pass, without requiring independent expert weight matrices. On five vision-language benchmarks with Qwen and Gemma backbones, this configuration achieves the highest performance among the compared baselines. Comparisons across mask granularities, routing interventions, and compute-matched controls distinguish the effects of learned connectivity from expert activation count. These results establish mask learning over frozen weights as a practical alternative for constructing token-routed MoE experts.

Spiking neural networks (SNNs) offer sparse and event-driven computation, making them attractive for energy-constrained reinforcement learning (RL) on edge devices. In value-based RL, deep spiking Q-networks (DSQNs) combine such efficiency with action-value estimation for decision making. However, existing DSQNs often require multiple simulation timesteps for competitive performance, increasing computational and energy costs, whereas reducing the timesteps can cause substantial performance degradation. We investigate this degradation from the perspective of Q-value estimation errors. By decomposing errors across actions into common-mode and differential-mode components, we find that low-timestep DSQNs suffer disproportionately from common-mode errors shared across action values, which are particularly detrimental to temporal-difference learning through bootstrapped targets. Based on this finding, we propose Common-Mode Compensation Deep Spiking Q-Network (CMC-DSQN), which uses an auxiliary ANN to compensate for common-mode errors in the SNN outputs. At inference, greedy action selection can be performed directly from the SNN outputs, allowing the auxiliary ANN to be completely removed and preserving the energy efficiency of SNNs. Extensive experiments on Atari and MiniAtar environments demonstrate substantial performance improvements under low-timestep settings. CMC-DSQN outperforms state-of-the-art DSQN baselines by nearly $20\%$ at $T=2$ and further surpasses the ANN baseline at $T=4$.

Recently, Cotler, Ivo, and Maldacena have shown that under scale invariance, eternal inflation is interpreted as a failure of the reheating surface volume renormalization due to an ill-defined scaling dimension. Meanwhile, observations suggest that scale invariance is slightly broken, which is parametrized by deviation of the spectral index from unity, $\varepsilon=n_s-1$. Motivated by this, we study how the scale invariance breaking effect modifies the no-eternal inflation condition as the renormalizability of the reheating surface volume. For this purpose, we adopt two independent approaches: investigating the behavior of the normal ordered reheating surface volume operator under a shift of the curvature perturbation, and analyzing the coarse-graining structure to obtain the scaling dimension. Both approaches commonly reveal that as long as $\varepsilon$ is negative, which is consistent with observations, the fractal structure of the reheating surface volume breaks down at macroscopic scale, moderating the no-eternal inflation condition.

Quantum telescopy, proposed by Grottesman et al., uses spatially entangled single-photon states to modify HBT stellar interferometry, potentially surpassing Michelson interferometry in resolution without baseline limits. However, finite source bandwidth, non-unit efficiency, detector response times, and celestial light bandwidth all affect its effectiveness. In this work, we consider a spatially entangled singe-photon state generated by beam-splitting a practical anti-bunched photon source from resonance fluorescence, which is a common method of generating single-photon states, and evaluate the signal level in quantum telescopy with inclusion of imperfection of detection system and finite bandwidth of celestial light. Here, given the incoming light, we optimize the parameters of the anti-bunched photon source and the detector system for the best signal-to-noise ratio (SNR), which can match that of the Michelson method in the ideal case but is always smaller in the realistic case. Alternatively, weak coherent states from heavily attenuated lasers can replace the entangled single-photon state but suffer low signal level, similar to HBT method. We find that the SNR with a realistic anti-bunched source for producing the reference fields can still beat the SNR of the coherent state scheme in the weak incoming field limit. The optimized parameters for the anti-bunched source and detection system will be a guide for future experimental endeavor.

Let $\textit{spex}_{\mathcal{P}_1}(n,F)$ be the maximum spectral radius among all $n$-vertex $F$-free $1$-planar graphs. Define $F_t$ as the friendship graph formed by $t$ triangles sharing exactly one common vertex. Tait and Tobin (2017)~\cite{Tait2017} used the fundamental structure of spectral extremal graphs to determine the unique planar graph with maximum spectral radius for sufficiently large order. Subsequently, Zhang, Wang and Wang (2024)~\cite{Zhang2024} characterized the corresponding extremal graph in the class of $1$-planar graphs. In this paper, we focus on $F_t$-free $1$-planar graphs and establish a structural theorem for their spectral extremal graphs for all $t\geq1$ and sufficiently large $n$. More precisely, every extremal graph is connected and contains a copy of $K_{2,n-2}$, and for $t\geq2$ the two distinguished vertices are adjacent and the subgraph induced by the remaining vertices is a bipartite graph. Based on this structure result together with the drawing properties of $K_{3,6}$, we determine $\textit{spex}_{\mathcal{P}_1}(n,F_t)$ and characterize its unique extremal graph.

Prior Fitted Networks (PFNs) such as TabPFN now rival established statistical procedures across prediction and estimation tasks. A natural explanation is that PFNs have the property of statistical adaptivity, that is, they perform nearly as well as a method tailored to the true data-generating model for a heterogeneous set of models, while not being told which model the data comes from. We study how such adaptivity is learned in a controlled location-estimation problem. Each task is an unlabeled sample whose family is hidden: Gaussian data call for averaging, with error of order $n^{-1}$, whereas uniform data are best estimated from their extremes, at the faster rate $n^{-2}$. We also provide the example of a symmetric Gaussian mixture, for which a rate of $\sigma^2_n/n$ can be attained. On scalar inputs, softmax attention computes the derivative of the empirical cumulant-generating function. A single primitive therefore both supplies features that distinguish the families and forms estimators interpolating between the sample mean and the mid-range. We combine attention experts through either a softmax mixture of experts or a gated linear unit (GLU), and analyze stagewise gradient flow. With $\widetilde{\Omega}(n^{1+\epsilon})$ pretraining tasks, the learned estimator is asymptotically efficient on Gaussian tasks, within a factor $n^{\epsilon}$ of the minimax rate on uniform tasks, and order-optimal on mixtures in a shrinking-variance regime. These guarantees extend to new locations and longer contexts. A risk decomposition separates expert error, routing error and normalization error, which clarifies the architectural contrast. Softmax gating enforces normalization and exact translation equivariance, whereas the GLU must learn it: its dynamics separate into fast bias removal followed by slow expert selection. End-to-end experiments recover the predicted specialization.

Small reasoning models (SRMs) have shown strong performance on complex reasoning tasks by generating extended chain-of-thought trajectories, but they often fail to recover once their reasoning enters an erroneous path. Existing test-time fusion methods rely on local fusion signals to determine when to trigger fusion, which can be misled by transient uncertainty fluctuations and may reinforce unstable reasoning trajectories. We propose ThinkFuse, a training-free test-time fusion framework that selectively intervenes in unreliable reasoning segments. ThinkFuse compares segment-level uncertainty shifts with trajectory-level uncertainty trends to identify unstable reasoning points and fuse auxiliary reasoning paths into the primary model's trajectory. Extensive experiments demonstrate that ThinkFuse outperforms baselines on mathematical and knowledge-intensive reasoning benchmarks, with consistent gains across model-family combinations, and remains robust with a smaller primary model. Our analysis shows that ThinkFuse requires fewer fusion triggers and generates fewer tokens, highlighting the efficiency of selective triggering. Our code is available at https://github.com/js-lee-AI/ThinkFuse.

Bird monitoring in natural environments is challenging due to the small size of some species of birds relative to the scene, background clutter, variability in illumination, and the observers' viewpoint. Progress is further limited by the scarcity of large-scale, realistic datasets, which are essential for understanding behavioral patterns. To address this gap, we introduce a new benchmark dataset for the detection and segmentation of Western bluebirds (Sialia Mexicana), comprising over 6,000 labeled images from 41 recording sessions. The dataset features high-resolution (4K) in-the-wild images in which birds occupy only a small fraction of the image. We evaluated supervised detectors, open-vocabulary models under zero-shot and fine-tuned settings, and segmentation approaches. Supervised detectors remain the most reliable overall, with Faster R-CNN achieving the highest detection mAP and RT-DETR offering the best precision-recall trade-off. Open-vocabulary models perform poorly in zero-shot settings; however, fine-tuning substantially improves their performance, with YOLO-World becoming competitive with supervised methods and achieving the highest precision, F1-score, and mAP@0.5. For segmentation, supervised methods significantly outperform Grounded-SAM and SAM 3: Mask R-CNN achieves the highest mask mAP, while YOLOv8-Seg provides the best precision and fastest inference. A diagnostic analysis further shows that failures are not explained by object size alone, but by a combination of apparent scale, brightness, contrast, clutter, blur, crowding, and recording-session variation. Overall, our findings highlight the difficulty of zero-shot bird detection in cluttered ecological scenes and underscore the importance of domain adaptation in small-object settings.

We theoretically investigate electronic responses to lattice deformation in a ferroaxial system using a tight-binding model on a two-dimensional square lattice and linear response theory. While conventional elastic responses are commonly discussed in terms of symmetric strain, the displacement gradient also contains an antisymmetric component describing a local lattice rotation. Focusing on this rotational degree of freedom, we treat the symmetric strain and antisymmetric local rotation as independent perturbations and incorporate their effects microscopically through deformation-induced modulations of the electronic hopping amplitudes. We find that the local rotation induces characteristic diagonal electric quadrupoles that are distinct from those generated by the symmetric shear strain. The rotation-induced response is dominated by the intraband contribution and increases approximately linearly with the ferroaxial crystal field, vanishing in the absence of ferroaxial order. In contrast, the symmetric-shear-induced response remains finite without ferroaxial order and contains both intraband and interband contributions. These results demonstrate that the antisymmetric local rotation provides a distinct electronic response channel characteristic of the ferroaxial state.

Artificial Intelligence (AI) tools are widely used to support decision making in tasks and domains where no immediate performance feedback is available. In these settings, users cannot learn to adjust their reliance behavior over time through trial and error. However, little is known about how novice users calibrate reliance on AI when external feedback is unavailable, or whether AI explanations can support calibration in its absence. We introduce reliance calibration as an organizing construct for studying how novice users dynamically adjust reliance behavior, and examine how AI explanations and meta-cognitive self-assessment shape it. Through a between-subjects study with 110 participants completing a clinical entity extraction task with AI assistance and limited performance feedback, we observe that novice users exhibit systematic drift toward over-reliance in the presence of explanations, while higher self-reported task understanding is associated with more selective reliance behavior. These results extend reliance calibration research into human-AI collaboration contexts without real-time performance signals and present actionable guidelines on designing AI tools that must support appropriate reliance in these settings.

Over a field of characteristic zero, we characterize the Hilbert functions that determine the degree reverse lexicographic generic initial ideal among Artinian quotients in four variables with the $2$-strong Lefschetz property. Our criterion is a finite numerical test that strictly extends the quasi-symmetry condition of Harima and Wachi. The proof parametrizes the possible generic initial ideals by flags of lower sets in the Borel orders on their common three-variable section. We also give nonrecursive formulas for the standard monomials and minimal generators of the almost reverse lexicographic ideal, and specialize them to generic complete intersections in at most four variables without restrictions on the degrees.

People increasingly ask large language models what to do with their money, yet seldom describe their finances in full. This paper asks what a model does with the gap. Holding finances fixed and changing only who the investor is said to be, we grade the financial evidence in the prompt from eight facts to none and measure how far the recommended equity allocation moves. Across 96,600 prompts to Llama-3.1-8B-Instruct, built from 100 financial profiles, 138 personas and seven disclosure conditions, the average gap between two personas with identical finances rises from 4.78 percentage points at full disclosure to 10.34 points with no financial facts. A two-way cluster bootstrap counting duplicated prompts once places the ratio at 2.16 (95% interval 1.69 to 2.79), and the rise is already 1.69-fold with a single fact left. Identity explains 5% of within-profile variation in advice at full disclosure and 96% with no disclosure. Household size is the only attribute whose influence grows reliably as evidence is withdrawn. Once standard errors are clustered on the persona, the unit to which identity was assigned, most attribute-specific interactions reported in the conference version lose significance, and gender instead appears as a small standing gap that full disclosure does not close. Stating risk appetite alone brings the swing into the range seen with two to seven generic facts. With no facts, the model's one-line rationale cites incomes, debts and savings it was never told, and these invented finances turn adverse more often for larger households. Inside the network, gender is linearly decodable at every layer, and ablating the gender direction at five layers leaves the aggregate identity swing unchanged. Advisory systems built on such models should be audited at the disclosure levels users actually reach, and judged across the whole identity space rather than one attribute at a time.