Papers

Movable agents, such as autonomous vehicles and robots, should be able to autonomously adapt their pre-trained object recognition models to new environments without human annotations. While existing test-time adaptation (TTA) methods address label-free model adaptation, they typically treat test data as independent snapshots, without constructively exploiting a rich, unique source of supervision: the significant variance in prediction quality as an agent observes the same object from different distances and viewpoints. To capitalize on this, we propose MoCaFe, a model-agnostic and hyperparameter-insensitive paradigm that leverages motion-induced prediction variance for unsupervised adaptation. Specifically, we first develop mobility-calibrated filtering of pseudo-labels, which constructs reliable pseudo-labels by fusing cross-view predictions using inverse-variance weights. The filtered pseudo-labels then guide the selection of “hard samples” for effective learning. To further suppress pseudo-label corruption, we introduce p-MoCaFe, an optional extension that uses a public dataset to assign weighting factors to data samples, yielding an estimator of the clean loss with bounded bias. Extensive experiments on autonomous driving (nuScenes, KITTI) and embodied-agent datasets show that MoCaFe significantly outperforms state-of-the-art TTA schemes, achieving up to approximately 20% accuracy gain.

We study the Iwasawa cohomology complex attached to a pseudorigid family of $(\varphi, \Gamma)$-modules and prove coadmissibility of its cohomology groups, perfectness and compatibility with base change. We apply this result to give another proof of perfectness of the Herr complex in pseudorigid family. We also use it to prove perfectness of Selmer complexes and obtain a result on variation of ranks of Selmer groups in analytic family.

We establish the first partial regularity results for minimizers of a class of suitably quasiconvex variational integrals defined on anisotropic Sobolev spaces. These variational integrals are related to higher gradient continuum models for pantographic metamaterials.

A fundamental challenge in cognitive science and neural computation is the binding problem. Compositional generalization can be achieved by factorizing representations into roles, the structural slots of a representation (e.g., serial position or syntactic function), and fillers, the contents occupying them (e.g., a phoneme or a word), which can be recombined freely to represent novel combinations. How neural systems implement role–filler binding, however, remains unknown. One of its simplest cases is phoneme sequencing, where phoneme identity (filler) must be bound to position (role) so that /gum/ and /mug/ are represented differently. A proposal from NLP, the `onion hypothesis' (Csordas et al., 2024), holds that the direction of the neural population state encodes token identity, while its magnitude encodes position. It was formulated for random token sequences; we extend it to natural language and test it in neural models and the human brain. We first evaluated it in an encoder-decoder trained to repeat English words, using representational geometry analyses and causal interventions. Magnitude alone proves incomplete: position is encoded by magnitude together with a systematic rotation of the state direction, a scheme we formalize as the `spiral hypothesis'. We then analyzed intracranial recordings from the auditory cortex of 20 participants listening to short sentences. Across superior temporal gyrus electrodes, the change in population response between consecutive phonemes decreases in magnitude as position advances, and its direction is aligned within consonants and within vowels but near orthogonal across the two classes, supporting the magnitude coding shared by both accounts. These results provide a geometric account of how neural systems bind phoneme identity to position, and show how neural-model hypotheses can yield testable predictions about human neural computation.

We numerically study spectral and wave-function properties, as well as time evolution, in finite-size commensurate approximations of the 3D Aubry-André model. We explicitly show, through scaling analysis, the existence of two critical points. One of the critical points is a localization-delocalization transition in real-space, similar to the critical point in the 3D Anderson model. The other is a localization-delocalization transition in a dual momentum space, which does not have any analog in the 3D Anderson model. We estimate their values from spectral measures, such as the gap ratio and the spectral form factor, as well as from wave-function measures, such as the inverse participation ratio and the participation entropy. Additionally, we demonstrate that both critical points exhibit hallmarks of critical points between quantum ergodicity and localization. First, the eigenstates and the eigenspectrum at the critical point fulfill the mutual universal relation between the eigenspectrum compressibility $\chi$ and the eigenstate fractal dimension $d^{(1)}$ [S. Jiricek et al., Proc. Nat. Acad. Sci. 123, e2518027123 (2026)]. Second, the dynamics of the wave packet at the critical point is governed by the critical dynamical exponent $z$, characterized by the spectral fractal dimension and the dimensionality of the lattice [M. Hopjan and L. Vidmar, Phys. Rev. Lett. 135, 060401 (2025)]. Thus, similarly to the 3D Anderson model, the critical dynamical exponent is sub-diffusive with the value of $z=3$.

Let $F/\mathbf Q_p$ and $E/\mathbf Q_p$ be finite extensions, and let $G=\mathrm{GL}_2(F)$ or $D_F^\times$, where $D_F$ is the quaternion division algebra over $F$. Let $\Pi$ be an admissible Banach $E$-representation of $G$ whose locally $\mathbf Q_p$-analytic vectors $\Pi^{\mathrm{an}}$ have an infinitesimal character. If $p>2$ or $F=\mathbf Q_p$, we prove that $\Pi^{\mathrm{an}}$ and $\Pi$ have finite length in their respective admissible categories.

Reinforcement learning (RL) for large language model (LLM) agents remains challenging in long-horizon tasks with sparse outcome rewards, where assigning credit to individual actions is difficult. Methods such as GRPO assign the same trajectory-level advantage to all actions, while critic-based methods require learning an additional value function that can be costly and unstable. We introduce LLM Value Function RL (LVRL), which uses the pretrained knowledge and in-context learning ability of an LLM to estimate policy-aware state values without finetuning a separate critic. LVRL conditions the value model on group context and calibrates its predictions using known values at the initial and terminal states, enabling step-level credit assignment from estimated value differences. We further extend this idea to learning from an expert policy through on-policy distillation (OPD), introducing LLM Value Function OPD (LVOPD), which focuses teacher supervision on actions associated with decreases in estimated value. We evaluate our approach across diverse agentic benchmarks: AppWorld, BabyAI, and SWE-bench Verified. Across policy scales (4B to 32B), LVRL consistently and substantially outperforms both GRPO and PPO. On AppWorld and SWE-bench Verified, LVRL yields absolute improvements of up to 13.6 and 8.6 percentage points over GRPO. Notably, on tasks requiring extended exploration like BabyAI, LVRL bridges the gap from total failure to 75.0% success. Furthermore, LVOPD yields consistent improvements over standard distillation baselines on AppWorld. Finally, Monte-Carlo analysis confirms that our frozen critic accurately identifies semantic pitfalls and recoveries, proving that LVRL extracts robust, policy-aware step-level credit from sparse terminal outcomes.

A model-independent measurement of the CKM angle $\beta$ can be performed using a time-dependent analysis of $B^0 \to D \pi^+ \pi^-$, $D \to K_S^0 \pi^+ \pi^-$ decays, where the Dalitz plots of both the $B$ and $D$ decays are divided into bins. The choice of binning scheme for the $B^0 \to D \pi^+ \pi^-$ Dalitz plot directly impacts the statistical sensitivity to $\beta$. This paper presents an optimization of this binning using a Fisher information-based quality factor $Q^2$ and simulated annealing. The optimized binning improves the sensitivity to $\beta$ by approximately $10\%$ relative to the equal-phase-difference baseline, as validated by toy Monte Carlo studies without experimental effects. The robustness of this improvement against decay time acceptance, Dalitz plot efficiency, Dalitz plot resolution, and background contributions is also assessed.

Area metrics arise as effective description at intermediate scales in a number of approaches to quantum gravity, including string theory, holography and loop quantum gravity. Recently, it has been shown that area metric actions can be derived from the modified Plebanski framework on the linearized level. Surprisingly these actions avoid extra poles in the propagator for the effective length dynamics, and hence constitute interesting deformations of linearized Einstein gravity. To be able to study whether this property persist for the full theory, we construct here non-linear area metric dynamics from modified Plebanski actions. We provide the geometric tools for area metrics that do not rely on perturbation theory and allow a systematic construction and study of general non-linear area metric actions: an algorithm that extracts a length metric from an area metric and a connection on two-forms that is uniquely determined by the area metric, together with its curvature and curvature invariants. We derive area metric actions from modified Plebanski actions in first and second order versions. We also find that area metric actions can be reformulated as Poincare gauge theories. We determine the effective length metric action, which on a flat background describes a graviton and a massive spin-two field with parity-violating couplings set by the Barbero–Immirzi parameter. Additionally we discuss cosmological backgrounds and the role of the matter coupling, which together open the way to cosmological applications.

Scientific claims shared through social media platforms frequently reference research findings without explicitly linking to the corresponding scientific publications. Automatically retrieving the correct scientific source for such claims is a challenging multilingual retrieval problem involving semantic matching, paraphrasing, noisy social media text, and cross-domain language variation. In this work, we present a multilingual two-stage retrieval framework for CLEF 2026 CheckThat! Task 1 on Source Retrieval for Scientific Web Claims. Our system combines fine-tuned dense retrieval models with cross-encoder reranking for improving multilingual scientific document retrieval. We evaluate multiple transformer-based dense retrieval architectures including multilingual-E5, BGE, and Contriever under different metadata configurations. We further investigate multilingual joint training, retrieval depth analysis, metadata enrichment, and language balancing strategies for improving retrieval effectiveness. Experimental results demonstrate that metadata enrichment consistently improves retrieval effectiveness, while fine-tuned cross-encoder reranking provides additional gains in retrieval precision. Our final multilingual system achieves MRR@5 scores of 0.6222 for English, 0.5112 for German, and 0.6254 for French, with an overall average MRR@5 score of 0.5862.

When told that robins have sesamoid bones, people are far more prone to extend the property to sparrows than to whales. This behavior, called category-based property induction, is well documented in humans, but whether and how it develops in language models trained only to predict the next token is unclear. To shed light on this, we construct a hierarchical taxonomy of synthetic entities grouped by the properties they share. We then inject facts from this latent taxonomy into the continued pre-training of Pythia and OLMo 2 models from 70M to 7B parameters, and track the development of inductive behaviors. We find that taxonomically aligned induction emerges from next-token prediction alone: a property learned for one entity transfers more strongly within its taxonomic category than across categories. Internally, entities that share a deeper category become more similar in activation space, and clustering recovers the full taxonomic tree from entity representations. Contrary to the usual expectation that scale helps, we find that induction weakens with model size when the data budget is fixed, suggesting that larger models memorize individual facts rather than compress them into shared structure. Induction also strengthens with more pre-training before the taxonomy injection, transfers to novel in-context properties, and can be overridden by a latent taxonomy implied by the prompt. Together, these results show that a model's inductive generalization reflects the latent organization of its training data, with implications for data curation and for predicting how far a learned fact will spread.

We investigate a minimal visual perception-driven model of self-propelled particles that interact through purely position-based cohesive steering within a finite vision cone, in the absence of velocity alignment and physical volume exclusion. Building on a previously proposed minimal cognitive model, we extend the interaction range from the previously studied short-range and distance-independent limits to an intermediate regime, enabling a systematic investigation of how a finite vision range influences collective behavior. We find that this regime exhibits a rich state diagram that combines characteristics of both limiting cases while giving rise to qualitatively new collective states. Besides the gas, nematic-band, and polar file states, we uncover the emergence of active foams – system-spanning fractal-like networks sustained by dynamically evolving particle streams. These structures arise solely from non-reciprocal vision-based interactions and are absent in both the short and long vision-range limits. For larger vision angles, the system self-organizes into a variety of aggregate morphologies, including condensates, rings, and multi-twist filaments, revealing a strong interplay between interaction range and anisotropic perception in shaping collective organization.

Large language models (LLMs) raise new questions for instructors, among them how to integrate LLMs productively into coursework and what to evaluate in students' work when an LLM can produce much of it directly. LLM-guided homework assignments offer one answer. Instructors configure the LLM to guide students in ways that achieve specific pedagogical goals, such as recalling material, discovering new concepts, or critically evaluating deliberately flawed reasoning, and grade the full student–LLM conversation, and with it the student's reasoning, rather than only the final answer. In this paper, we report on the large-scale deployment of such assignments, implemented through LLteacher, an open-source tool that supports recall, discovery, and critical-thinking assignments, in a large introductory statistics course serving mostly pre-major undergraduates. Results on 134 students show meaningful gains in self-reported confidence, with over 80% agreeing that the assignments improved their comprehension of course material and their ability to interpret statistical results; gains were largest among students who started with lower confidence, suggesting this approach may help narrow gaps in preparation. Interaction patterns varied widely, from long single messages to rapid iterative exchanges, and hallucinations, when present, were rarely disruptive to learning.

Behavioral foundation models (BFMs) provide humanoids with reusable repertoires of whole-body behaviors; in real-world humanoid control, the same behavioral intent may require fundamentally different motions under different terrain constraints. Covering such variation with terrain-matched demonstrations requires enumerating a combinatorial space of behaviors and terrain geometries. We introduce P-BFM, a perceptive behavioral foundation model that factorizes humanoid control into terrain-invariant intent and terrain-conditioned realization. A forward-backward representation maps motion references, target states, and reward functions into a shared intent space without terrain information, while a perceptive policy learns how to realize each intent under the surrounding terrain geometry. We further identify a complementary limitation of purely latent control: behavioral latents can preserve local motion patterns while losing precise global progress. We therefore introduce Explicit Root Instructions (ERI), which separates global transport (e.g., heading and planar velocity) from behavioral intent, while leaving local whole-body adaptation to the perceptive policy. This decomposition leads to a characteristic capability absent from conventional BFMs: one fixed intent induces different, terrain-appropriate behaviors, including changes in step height, stride, posture, foothold placement, and contacts, without terrain-specific demonstrations. Across challenging terrains, P-BFM improves motion fidelity, root-control precision, and perturbation recovery over strong baselines. A single frozen policy further supports motion tracking, goal reaching, reward inference, teleoperation, and terrain-aware recovery, and transfers zero-shot to a Unitree G1 using onboard depth sensing.

Resolving correct citations can be a time-consuming task for research writers. We address local citation recommendation (LCR), where the goal is to retrieve appropriate references for a given sentence. Web tools generally depend on the existing citation graph, which may bias results toward citation count or more recent publications. LCR research using full paper texts has been limited by the lack of publicly available data. We present a new dataset, the Local Citation Recommendation Corpus (LCRC), containing 14,735 scientific statements derived from astrophysics review papers, each with one or more citation targets whose full text is accessible via API. Using this dataset we systematically compare retrieval methods and develop a citation recommendation system that avoids citation graph bias while achieving 8.0% improvement in Recall@25 and 6.9% improvement in NDCG@25 over dense retrieval baselines without model fine-tuning. To support reproducibility, we make our code and dataset publicly available.

For a smooth locally reductive stack admitting an adequate moduli space, we show that there are finitely many open substacks preserving the adequate moduli space, and give a complete classification of such opens. For $\mathbb{G}_m$-actions, this becomes an explicit description in terms of the codimension-one Bialynicki-Birula strata. Moreover, for a stable adequate moduli space, we show that the number of preserving opens are bounded by 3 raised to the relative Picard rank. As an application, the number of fixed components for $\mathbb{G}_m$-actions is at least the relative Picard rank.

When several predictions use the same internal representation, information about some targets can remain easier to recover than information about others. We study how this specialization forms, persists, and changes in minimal artificial learners. With reconstruction errors weighted equally during learning, changing which target is observed precisely selects the favored target and redirects an already specialized learner. Removing current support can reduce a formed bias, whereas state-following update feedback can maintain it. We then compare learners formed through different observation and update conditions but matched on specified reconstruction measurements. Both change under the same brief opposing intervention, yet their responses differ. Resetting Adam largely removes the ten-update difference; exchanging its second moment reverses which route is more susceptible. New interventions show that equalizing the mean second-moment scaling reduces but does not remove the difference: its coordinate-wise pattern also matters. With fresh Adam or calibrated SGD, smaller route differences emerge later, whereas 500 common opposing updates bring the selected allocation endpoints close. A further control produces response differences with identical acquisition and equal mean loss weights but jointly different weight variability and realized sequence. Acquisition-selected formation also extends to a symmetric three-target setting. These interventions distinguish specialization's formation, present support, and time-dependent latent susceptibility.

Hard-margin SVM training is the distance problem between two convex hulls, which the Triangle Algorithm (TA) solves with a certified duality gap. We propose guarded block transfers: $k$ Mitchell–Demyanov–Malozemov (MDM) transfers per scan are aggregated into one exact line search, guarded by a comparison with the single best transfer at a cost independent of the number of points $n$, and replaced by an away step when the leading transfer is capacity-clipped. On the Minkowski-difference polytope, where the objective is $1$-strongly convex, we prove global linear convergence with explicit constants and no combinatorial swap-step bounds; the per-step contraction is $k$-independent and only the drop-count bound grows with $k$, so aggregation is provably safe while the saving in scans is measured, not proved. Since the TA certificate is the Frank–Wolfe gap divided by the current distance, gap-safe screening applies, and we bound the iteration after which it has removed every zero-weight point off the optimal faces by $O\!\left(\tfrac{k}{\rho}\log\tfrac{1}{\tau}\right)$ up to logarithmic factors in the geometry, $\rho$ the rate constant and $\tau$ the optimal-face margin. On five LIBSVM benchmarks, with fairer baselines than our submission, the solver matches the baselines to four or five digits wherever both converge, ties LIBSVM on sparse-support hard margins and beats our blended pairwise conditional gradients (BPCG). But our full-cache sequential minimal optimisation (SMO) code ties or beats it on kernel $L_2$ margins, LIBLINEAR's dual solver is up to $4.5\times$ faster on the separable $L_2$ margin, and our solver is one to three orders of magnitude slower than LIBLINEAR's Newton solver on dense-support $L_2$ margins and than LIBSVM on a nearly touching kernel hull. Its edge is the certificate, not speed.

Sorting is one of the most basic algorithmic problems. Adaptive sorting algorithms exploit features that make an input easier to sort, often captured by entropy measures. Many such measures have been studied, raising two natural questions: how do they relate to one another, and are there algorithms that are adaptive to them? We complete a hierarchy of relations between previously studied entropy measures and show that the classical measure Reg is a source of this hierarchy. We prove that an existing data structure yields a Reg-adaptive sorting algorithm, thereby achieving the adaptive bounds of every measure in the hierarchy. Following McIlroy's observation that Reg has a mathematically inconvenient definition, we study a slightly weaker but simpler measure, reg. For inputs without duplicates, we show that O(n + log reg) = O(n + log Reg), so this simplification preserves the adaptive bound. Finally, we do algorithms design and introduce SproutSort, a reg-adaptive algorithm in the offline binary search tree (BST) model. SproutSort achieves an access cost of O(n + log reg), making it the most adaptive algorithm in this model to date. We also introduce SkeletonSort, a simple randomised pointer-machine algorithm that sorts distinct keys in expected O(n + log reg) time, offering a considerably simpler implementation of a sorting algorithm this high in the adaptive hierarchy.

Optical cavity arrays are an emerging tool for efficiently interfacing optical photons to quantum emitters for applications such as quantum computing. In this work, we demonstrate a metrology technique for such cavity arrays by interfering cavity array outputs against a tilted reference beam on a camera, constituting a spatial heterodyne. Both the amplitude and phase of each cavity's transmitted field can be extracted from the resulting images. Enabled by the improved scaling of heterodyne detection over intensity detection in the presence of technical noise, we demonstrate signal-to-noise ratio greater than one down to the single detected photon level, even in the presence of hundreds of noise equivalent photons. This readout technique holds promise for fast, non-destructive imaging of atomic qubits in cavity arrays by requiring fewer scattered photons while allowing the use of fast cameras with higher electronic readout noise.

Motivated by recent work on $\lambda$-fold near-factorizations by Kreher, Li, and Stinson (Designs, Codes and Cryptography, 2026), we introduce and systematically investigate $(\lambda,\mu)$-fold factorizations as combinatorial structures with prescribed representation multiplicities. Such a factorization consists of two subsets of a finite group whose products represent each nonidentity element exactly $\lambda$ times and the identity exactly $\mu$ times. These structures generalize $\lambda$-fold near-factorizations and provide a common framework for several families arising in combinatorial design theory, including strong external difference families with two equal-sized subsets, as well as binary sequence pairs with two-level correlation. Their associated $\{0,1\}$-matrices satisfy the Bridges-Ryser equation $XY=\lambda(J-I)+\mu I$, linking the factorization problem to a classical matrix framework for combinatorial designs. We establish the foundational theory of $(\lambda,\mu)$-fold factorizations, provide two general constructions, and prove several nonexistence results for finite abelian groups.

Sequential statistical procedures are increasingly embedded in scientific systems in which observations arrive incrementally from heterogeneous sources. In such systems the statistical update is only one part of the computation: observations must also be acquired, aligned across inputs, ordered, delivered, persisted, and replayed, and results must be passed to systems that display them or act on them. Sequential methods are nevertheless missing from the general software toolkit. They run inside proprietary experimentation platforms and commercial statistical packages, or exist as offline functions over complete data, and the batch fit interface that dominates machine-learning libraries has no place for a procedure that listens, keeps state, and decides when to stop. We propose an architecture that separates statistical inference from data topology, execution runtime, run lifecycle, persistence, and external action. Its central abstraction is the Sequential Procedure: a state-transition function that maps an inferential state, a valid statistical input, and a statistical random state to a new state and a scientific output. The procedure does not define how observations are acquired, paired, scheduled, stored, or acted upon. We specify the architecture semantically rather than through an object model, derive seven conformance invariants that any implementation can be tested against (among them synchronous/asynchronous, checkpoint, replay, and batch equivalence), and describe a dependency-free reference implementation in which all seven hold bitwise. Lorden's 2-SPRT for the Kiefer-Weiss problem serves as the reference procedure; the same contract accommodates sequential estimators, Bayesian filters, change-point detectors, and stateful predictive models.

We present a time-dependent physical optics (TDPO) formulation for computing the acoustic scattered field of a stationary object in response to a moving source in three-dimensional space. Due to the motion of the source, which may be fast, the conventional frequency-domain PO method is not employed. Instead, a time-domain variant that explicitly accounts for the motion is formulated. The study focuses on the near-field regime, where source motion induces a complex wave field beyond a simple Doppler effect. The proposed algorithm accommodates arbitrary source trajectories and arbitrary signal bandwidth, as well as high source velocities relative to the speed of sound. Near and beyond the shadow boundary, where PO is least accurate, the formulation is supplemented by a Fock correction of the surface field, extended here to a moving source with a harmonic signal. The method matches or exceeds the accuracy of finite element simulations at a computational cost lower by orders of magnitude.

In this paper, we discuss equivariant formality for spaces equipped with a primary cyclic group action. We study the behavior of equivariant formality with some topological constructions. The algebraic complexity needs to deal with injectivity. In the end, we discuss equivariant intrinsic formality.

This paper proves the weak type (1,1) boundedness for maximal truncated singular integral operators with rough non-convolution kernels of the form $\Omega(x-y) K(x,y)$, where $\Omega$ is homogeneous of degree zero with $\Omega \in L\log L(\sS^{d-1})$ and $K$ is a standard Calderón-Zygmund kernel. This extends the recent resolution of the classical convolution case by Lai \cite{Lai2025weak} to a wider class of operators.

We investigate the long-term radial velocity (RV) stability of one of the Far-UV (FUV) modes on the Cosmic Origins Spectrograph (COS). We do so by using a standard white dwarf, WD~0308-565, that has been observed over a large fraction of COS's operational lifetime of 17 years. We demonstrate that for modest signal-to-noise COS can return an RV stability of $<$3 km s$^{-1}$ over a baseline of 15 years. For higher SNR and a smaller number of epochs, we obtain $\sigma_{\mathrm V}=600$ m s$^{-1}$. We also show that the absolute radial velocity accuracy for this target is consistent with results from ground-based optical spectroscopy. We discuss some observational strategies and astrophysical objects that may be well suited to pushing to the very RV limit of the instrument. Utilizing COS for precision RV work opens a new scientific avenue for space-based UV astronomy as COS approaches 20 years of operations and hints at what may be possible with the stability of a high-resolution UV spectrograph on future missions such as the Habitable Worlds Observatory.

Modern cloud platforms generate high-dimensional, noisy telemetry from thousands of microservices. Unlike classical anomaly detection benchmarks, cloud anomalies are short-lived, irregular, and largely non-periodic, making timely detection challenging. We present an empirical benchmark of deep learning models for anomaly detection using a real-world IBM Cloud Console dataset. We evaluate GRU, Transformer, TimesNet, and Autoformer architectures using the Numenta Anomaly Benchmark (NAB), a timing-aware metric that accounts for early detection and false alarms. TimesNet achieves the highest NAB scores due to strong early-detection sensitivity. Transformer models also detect anomalies early but incur higher false-positive rates. An improved GRU autoencoder, incorporating robust scoring and persistence rules, achieves competitive performance with a more stable false-alarm profile. Overall, the modest performance differences suggest that real cloud anomalies are dominated by short-term deviations rather than persistent periodic structure, emphasizing the importance of timing-aware evaluation and robust post-processing.

This article takes steps to show that an equivariant version of the well known phenomena of Koszul Duality can be formulated in a manner not considered prior: via dg (co)algebra valued functors on the orbit category. As such techniques used in this article mix traditional and modern categorical methods in homotopy theory.

Real-world datasets often exhibit severe class imbalance, degrading the performance of deep learning models, particularly on rare classes. While imbalance is well studied in binary and multiclass settings, it is substantially more challenging in multilabel problems due to complex label co-occurrence. In clinical applications such as ECG classification, this challenge is coupled with a second critical challenge: the need to prioritize high-risk conditions, regardless of their prevalence, to mitigate the high cost of false negatives. We introduce the Multilabel Class-Prioritized Probabilistic Sampler (ML-CLAPPS), a learnable sampler that optimizes a distribution over training instances to control the model's exposure to different classes. This approach addresses multilabel imbalance while enabling prioritization of significant conditions via a user-defined importance vector (IV). Empirical evaluation on a real-world multilabel ECG image dataset demonstrates that ML-CLAPPS achieves state-of-the-art performance. We show that it aligns class exposure with the specified IV, and that increasing a class's importance leads to corresponding improvements in its classification performance, enabling explicit prioritization of clinically critical conditions.

Recent work shows that ordinary Reed–Solomon codes over prime fields admit polynomial-size lists up to list-decoding capacity on every evaluation set. We show a contrasting phenomenon over binary extension fields. For every fixed rate $0<R<1$, there exists $\varepsilon_R>0$ such that, for all sufficiently large $h$, the full-field Reed–Solomon code over $\mathbb{F}_{2^h}$ has a received word with $n^{\Omega_R(\log n)}$ codewords within relative distance $1-R-\varepsilon_R$. To our knowledge, these are the first superpolynomial ordinary Reed–Solomon list-size lower bounds at fixed positive rate and a fixed positive agreement gap above the rate. Thus capacity-approaching polynomial list size for Reed–Solomon codes is not uniform over the underlying field, and the obstruction occurs at every fixed rate. As a puncturing consequence, the same holds for primitive Reed–Solomon codes; the obstruction is also robust under controlled dense puncturing. The proof begins with an exact correspondence that turns certain binary Bose–Chaudhuri–Hocquenghem weight-enumerator coefficients into sizes of single Reed–Solomon lists. A classical binary weight family gives the initial quarter-rate construction, while a quadratic-form enumeration supplies its superpolynomial multiplicity. A common-kernel quotient/descent argument and common-root padding then extend the construction to all rates. We also determine the optimized agreement envelope achieved by the construction.