Papers

The Tile Calorimeter (TileCal) is a sampling hadronic calorimeter covering the central region of the ATLAS experiment at the CERN Large Hadron Collider (LHC). It employs steel as the absorber material and plastic scintillators as the active medium. The High-Luminosity LHC (HL-LHC), scheduled to start operation in 2030, will deliver instantaneous luminosities significantly exceeding the baseline LHC design, imposing more stringent requirements on detector readout and trigger systems. Consequently, TileCal has to be capable of reliable operation under increased radiation levels and very high particle flux, while maintaining full compatibility with the upgraded ATLAS trigger architecture. During the Long Shutdown period (2026-2030), the TileCal readout electronics will be entirely replaced with radiation-tolerant systems designed to handle data rates approximately an order of magnitude higher than those of the baseline LHC configuration. The photomultiplier tubes (PMTs) in the most highly irradiated regions will also be replaced with improved devices exhibiting enhanced stability and radiation tolerance. To meet these challenges, the system design has been correspondingly optimized to ensure improved performance, efficiency and robustness in high-radiation environments, and an extensive irradiation testing program has been carried out. This contribution presents the resulting design developments of the TileCal system, together with the results obtained from the irradiation tests.

Video games offer scalable environments for studying perception and control in embodied agents. Abundant online gameplay videos could supply demonstrations, but they rarely include player inputs for training. Inverse Dynamics Models (IDMs) have thus been proposed to infer inputs from frames. Large (up to 1B parameters) IDMs trained on $\sim$1K-2K gameplay hours demonstrate feasibility and cross-environment generalization at this scale, but researchers do not clarify what the key components are to recover individual actions and often report only aggregate accuracy that can mask rare-action failures. We study the problem in a data-constrained scenario to evaluate how spatial motion features, model architectures, and training objectives affect an IDM's outcome and we analyse our models on per-key and balanced metrics such as $F_1^{macro}$. Our experiments on Trackmania highlight the importance of factors like the model architecture and motion flow extraction in preprocessing, while also showing the limits of evaluation through unbalanced metrics. The application of the same architecture and training recipe to Cyberpunk 2077 reveals uneven performance across game mechanics. Our per-action evaluation and failure analysis highlight ambiguities from camera motion, delayed effects and imbalanced key-press frequencies that call for explicit modeling of 3D scene structure, long-term state and the adoption of proper losses in future implementations.

Changes in principal eigenvalues and eigendirections provide complementary diagnostics of structural instability in factor models, but covariance-based inference can be unreliable under heavy tails. We develop two-sample tests for equality of these features of trace-normalized shape matrices under high-dimensional elliptical factor models. Our approach combines Tyler's identity with orthogonalization and cross-fitting to accommodate general location and precision pilots. We derive a spectral limit theory that yields asymptotically valid calibration without upper-tail moment assumptions on the radial variables, allowing the two populations to have different radial distributions and factor ranks. Simulations demonstrate good size control and gains in size-adjusted power over covariance-based benchmarks under heavy-tailed elliptical distributions. An application to S&P~500 stock returns illustrates how the tests distinguish changes in relative component strength from changes in component orientation.

Click-Through Rate prediction, a core task in recommendation and advertising systems, relies on modeling interactions among sparse categorical features. Explicit cross networks are a central paradigm for CTR prediction, and recent progress has largely come from increasing the interaction capacity of a single predictor through deeper cross networks and more expressive cross operators. We revisit whether continually increasing interaction capacity remains the most effective way to improve predictive performance, and find that its benefits quickly exhibit diminishing returns even as capacity continues to grow. This motivates a complementary scaling direction that we call estimator scaling, where additional resources are used to incorporate multiple related estimators rather than only enlarging a single predictor. Through theoretical analysis, we show that the gains from estimator scaling are governed by the amount of non-shared predictive variation available across estimators. However, exploiting this variation naively can be expensive: independently trained models provide substantial estimator diversity but require deployment cost to grow with ensemble size. This motivates a parameter-efficient realization of estimator scaling that can incorporate diversity from multiple estimator sources without maintaining multiple full models. Building on this view, we introduce RECursive Averaged Predictor (RECAP), a parameter-efficient recursive CTR model that operationalizes estimator scaling at three levels: distillation across independently trained models, exponential moving averaging over training trajectories, and aggregation over inference-time routes within a weight-shared recursive backbone. Experiments across multiple benchmarks establish new state-of-the-art predictive performance on standard benchmarks, while placing the RECAP on a favorable performance-parameter Pareto frontier.

We study tail dependence of a $d$-dimensional random vector whose coordinates are subject to random right censoring. Along each fixed direction the censored problem reduces exactly to a univariate one, and the observed data determine the radius and whether it was produced by the event or censoring vector. An ordinary Kaplan–Meier product limit therefore estimates the joint tail probability in that direction, in every dimension, and with no multivariate survival function, no smoothing and no tuning parameter beyond the threshold. The theory of this directional estimator is formulated under an arbitrary marginal standardization and conditions only imposed on the standardized laws, in particular for any max-domain of attraction. We prove uniform consistency and functional weak convergence at the square root of the effective number of joint extremes, allowing the standardization to be estimated. A multiplicative standardization recovers the heavy-tailed theory, whereas a standardization built from the marginal (non-directional) Kaplan–Meier estimators requires no marginal tail model and targets the normalized tail copula itself. The standardization error is negligible for the former, and for the latter under a mild condition on the joint censoring. Simulation studies validate the finite-sample performance of the estimator. An application to the National Flood Insurance Program dataset comprised of claims generated by Hurricane Ian estimates the joint upper tail of building and contents losses from indemnities, which are subject to capping, simultaneously in both coordinates.

Power systems with increasing variable renewable generation face greater uncertainty in scheduling and balancing. Intraday and balancing electricity markets facilitate position adjustments and real-time balancing close to delivery. As delivery approaches, continuous intraday market participants exposed to imbalance settlement adjust their positions by trading additional volumes to reduce their imbalance exposure. We conjecture that positions remaining open after intraday trading, together with demand and supply uncertainties affecting physical market participants, influence price formation in the balancing market. This cross-market interaction is, however, rarely studied. To understand this interaction, this paper uses probabilistic modeling to examine how intraday orderbook information reflects subsequent imbalance price formation in Germany and Austria. We compare orderbook representations based on open, high, low, close, and volume, Volume-Weighted Average Price (VWAP), and last mid price across multiple horizons. Each representation is evaluated using the self product, neighboring products, and the product from the neighboring country. We then compare the best orderbook setting with fundamental feature sets and their combinations, followed by an ablation study of the available training history. We show that VWAP with neighboring products provides the best performance in both countries. Combining orderbook and fundamental information reduces testing loss in Germany but increases it in Austria. Using all available observations provides the best overall performance, while excluding 2022 can reduce loss for extreme price samples. These results reveal and help explain country-dependent interactions between the intraday and balancing markets.

Existing LLM routers choose among models using static per-model costs. We show that open-weight inference markets introduce a second, largely ignored decision axis: after choosing a model, a client must still choose which provider serves it. Measuring live endpoints across [nummodels] open models, competing providers, multiple task types, and three measurement waves, we find that provider choice cannot be inferred from the price list. The same model can vary sharply in quality, latency, availability, and price across providers; higher-priced providers are consistently faster, but price does not reliably predict quality or availability; and provider feasibility is task-selective, with one deployment nearly normal on knowledge tasks but catastrophically degraded on multi-step reasoning. We formulate same-model provider selection as a price-taker market-aware routing problem. A simple measured-map policy routes to the cheapest provider that is both quality-equivalent and healthy, yielding matched-quality savings while avoiding degraded endpoints. Because the map drifts, we introduce FACET, an online provider router that certifies per-(provider x task) feasibility facets and fails safe to an anchor before serving uncertified arms. Across relaxed deployment assumptions, FACET tolerates imperfect task assignment and sparse feedback, while systematic evaluator bias exposes a quality-signal trust boundary that can be mitigated with ground-truth probes or audits. Live provider runs further confirm that certification can move real traffic from a premium anchor to a substantially cheaper certified endpoint. Our results suggest that market-aware LLM routing must measure not only which model to use, but also who serves it.

We use multipoint semidefinite programming to prove the nonexistence of strongly regular graphs. A normalized eigenspace projection of a primitive strongly regular graph gives a spherical two-distance set with one point for each vertex. A bound smaller than the required number of points therefore rules out the graph. Following the formulations of de Laat et al. and Kao and Yu, we use, for each reference type, coefficient matrices indexed by the feasible inner-product labels of the selected points. In degree zero, we combine the matrix coordinates indexed by the reference points into a single coordinate. The resulting programs use configurations of up to six points, with matrix orders at most $2^m+1$ for a reference set of $m$ points. Feasible dual solutions, verified in exact rational arithmetic, exclude strongly regular graphs with parameters $(351,140,73,44)$, $(550,162,75,36)$, $(703,182,81,35)$ and $(1344,221,88,26)$.

Efficient end-to-end entanglement distribution in quantum information networks requires routing under limited resources and fidelity constraints. We study entanglement routing as a fidelity-constrained unsplittable multicommodity flow problem that maximizes the number of admitted requests. As a proof of concept, we integrate neutral-atom quantum optimization into a hybrid classical–quantum column-generation framework. A classical restricted master problem selects routes, while a pricing problem generates fidelity-feasible paths. We formulate this NP-hard constrained shortest-path pricing problem as a quadratic unconstrained binary optimization (QUBO) problem and address it with hardware-aware register embedding and instance-driven pulse shaping. To our knowledge, this is the first study of neutral-atom quantum optimization as a pricing oracle for fidelity-constrained entanglement routing. On small benchmark instances evaluated with neutral-atom processor emulators, the method, combined with warm-start and post-processing, achieves an optimality gap below 1% across all tested sizes; the selected simulated-annealing route-generation baseline exhibits gaps of up to 6%. These results indicate that the generated bitstrings can provide useful candidate routes for classical refinement within column generation. This proof of concept does not establish quantum utility or scalability; further evaluation on larger instances, against stronger classical baselines, and on quantum hardware is needed.

Zero-order optimization (ZO) trains without backpropagation, making it relevant to forward-only hardware and non-differentiable loss, but its gradient variance grows with perturbed dimension, inhibiting large-model training. Sharded Optimization Mixture of Assemblies (SOMA) trains LSTM experts independently on $N$ data clusters using simultaneous perturbation stochastic approximation (SPSA), without exchanging gradients, activations or optimizer state. Its separable loss removes cross-expert perturbation noise at the cost of jointly learned representations across domains. Using 80,000 estimated RTX 5090 GPU-hours, we show modest sharding improves training compute efficiency over all tested monolithic ZO controls. At 8.44M parameters and 150 aggregate GPU-hours, SOMA $N=2$ with 64 perturbations reaches 1.76 test nats/byte, versus 2.00–2.11 for monolithic SPSA at 64, 256 or 1,024 perturbations and 2.21 for EGGROLL. On WikiText-103, these frozen checkpoints reach 2.07, 2.25–2.36 and 2.49, respectively. On a fixed separable objective with equal-size blocks, we prove independent losses reduce relative gradient variance to approximately $1/N$ of a shared-loss estimator's. Holding starting weights, data, perturbations and compute fixed, independent rather than summed losses lower SOMA $N=4$ test loss by 0.035 nats/byte after 1,000 updates across three seeds. Larger ensembles offer a separate inference benefit: at similar model size with top-$k$ routing ($k=4$), SOMA $N=256$ achieves 2.36M tokens/s versus 257k for SOMA $N=8$ ($9.19\times$, including routing), at lower test loss (1.68 versus 1.71), albeit using $59.9\times$ as much aggregate training compute. We release all training and evaluation code and checkpoints.

Reinforcement learning for long-horizon agents typically relies on sparse outcome-based rewards. This leads to a severe cold-start problem, as early-stage policies often fail to solve sampled tasks, leaving little useful reward signal for learning. To mitigate this problem, we use on-policy distillation (OPD) to provide token-level guidance on the student's own rollouts. We find that the benefit of this guidance depends on the performance gap between the teacher and the student. When the teacher substantially outperforms the student, distillation helps guide the student through the early training stage where outcome rewards provide little learning signal. As the gap narrows and eventually reverses, however, continued distillation becomes less beneficial and may hinder further improvement. Motivated by this observation, we propose Gap-Adaptive Teacher Scheduling (GATS), which augments the student's RL objective with an OPD term whose weight adapts to the teacher-student performance gap. Specifically, GATS gradually reduces teacher guidance as the student approaches the teacher's reference performance and withdraws it once that reference is reached. This enables GATS to leverage task-trained teachers smaller than the student, since teacher guidance is primarily needed during early training. Across ALFWorld, WebShop, and ScienceWorld with three Qwen2.5 teacher-student configurations, GATS achieves the highest average success rate among the compared methods in all three configurations, improving over reward-only GRPO by 4.37%-11.87% under matched student rollout budgets. Code is available at https://github.com/Ricardo-H/guide-then-let-go.

We consider a gradient, speed-change, symmetric exclusion process on the discrete torus $T^d_n$, $d\le 3$, whose empirical measure evolves, on the diffusive scale, according to a non-linear parabolic equation. We prove that, starting from a sequence of initial states whose relative entropy with respect to the inhomogeneous product measure associated with the initial profile is $o(n^{d/2})$, and whose density fluctuation field converges, the density fluctuation field converges, in $L^1(0,T; H_{- r})$, to the solution of a linear stochastic partial differential equation with time-dependent coefficients driven by a conservative space-time white noise.

We introduce chiral rotational wavepackets: coherent superpositions of a few low-lying rotational states of a molecule for which the expectation value of a molecular axis traces a three-dimensional chiral trajectory in the laboratory frame. The handedness is a dynamical property of the quantum state rather than of the equilibrium structure, and we show that it can be imprinted on linear rotors as well as on spherical and symmetric tops. We derive the action of space inversion, time reversal, and their product on such wavepackets in the Wigner $D^J_{MK}$ basis, and define the rotational enantiomers of a given wavepacket. To quantify their handedness we introduce two derivative-based pseudoscalar measures: a geometrical measure built from the curvature and torsion of the trajectory, which is even under time reversal, and a dynamical measure, which is odd under time reversal. The latter is shown to be proportional to the geodesic curvature of the trajectory projected onto the unit sphere, which links it, via the Gauss–Bonnet theorem, to the solid angle enclosed by the projected trajectory and to the parallel-transport holonomy of a molecule-fixed vector. Finally we show that a nonzero geometrical measure is a sufficient condition for the wavepacket to exhibit true chirality through its orientation trajectory in the sense of Barron.

We report an improved measurement of neutrino oscillation parameters at the Jiangmen Underground Neutrino Observatory (JUNO) and the consequent indication of neutrino mass ordering. The analysis is based on 207.2 live days of data, comprising 8,294 inverse beta-decay candidates collected at an average reactor baseline of 52.5 km. A world-leading precision of approximately 1% was achieved for the atmospheric neutrino mass splitting $\Delta m^2_{31}$, with $\Delta m^2_{31}=+2.509^{+0.027}_{-0.025}\times10^{-3}\,\mathrm{eV}^2$ for normal ordering and $\Delta m^2_{31}=-2.482^{+0.025}_{-0.026}\times10^{-3}\,\mathrm{eV}^2$ for inverted ordering, using the Daya Bay constraint in the fit to resolve the correct physical minimum under each mass-ordering hypothesis. We further improved the world's most precise measurements of the solar oscillation parameters, obtaining $\sin^2\theta_{12}=0.3036\pm0.0064$ and $\Delta m^2_{21}=(7.388\pm0.078)\times10^{-5}\,\mathrm{eV}^2$, corresponding to relative precisions of 2.1% and 1.1%, respectively. Incorporating constraints on $\Delta m^2_{31}$ from long-baseline accelerator neutrino experiments into our analysis favored normal ordering over inverted ordering, with a one-sided significance of at least $2.1\sigma$ across all possible CP-violating phases; a Bayesian analysis yielded a Bayes factor of 10.18 in favor of normal ordering.

Optical anapoles have attracted significant interest as a promising platform for enhancing light-matter interactions at the nanoscale. An ideal anapole is a localized excitation of electromagnetic fields that does not produce any far-field radiation. In practice, anapoles are not ideal due to the parasitic scattered fields associated with higher-order multipoles. Here, we use the recently established exact current multipole expansion and the exact anapole condition to design an ideal anapole in which radiation due to the multipole orders up to the electric and magnetic octupoles is either eliminated or strongly suppressed, reducing the total radiated power by orders of magnitude. We also propose and study realistic photonic structures in which such anapoles can be excited by a uniform linearly polarized plane wave through second-harmonic generation that involves the off-diagonal elements of the second-order susceptibility tensor. In this case, the anapole condition is reached off-resonantly by adjusting the polarization angle of the incident field, which allows for the anapoles to be excited over a wide spectral range in scatterers of different sizes. Using this approach, we achieve scattering suppression on the order of $10^{-4}$ in photonic structures that are half a wavelength in size. The method offers the possibility to realize localized electromagnetic excitations that are truly isolated from the surroundings.

The aim of the paper is to study Euclidean and l-finite Euclidean modules over a ring, submodules of their finite direct sums, reduced and strong reduced echelon forms of matrices with coefficients in Euclidean modules and bimodules. The concept of Euclidean module is a module-theoretic analogue of the concept of Euclidean ring. The class of (not necessarily commutative) Euclidean rings is a nice but `very small' class of rings that have arithmetic-like properties. On the contrary, surprisingly, the class of Euclidean modules is a `large class' of modules. The Euclidean modules exist for many constructions of rings that are defined over arbitrary rings. For example, for every skew polynomial ring $A=D[x;\s, \d]$ with coefficients in an arbitrary ring $D$, the generalized Weyl algebra $D[x,y;\s, a]$, the Weyl algebra $A_1=K[x][\der; \frac{d}{dx}]$, $U(\sl2)$ and many classical algebras, there exist Euclidean modules.

Multicomponent methods treat both electrons and nuclei quantum mechanically using the standard machinery of electronic structure theory. Previous work has demonstrated that quantitatively describing electron-nuclear correlation in multicomponent many-body perturbation theory methods requires large electronic basis sets with high-angular momentum atomic orbitals, and calculations on large systems can therefore become impractical. Similarly, the slow convergence of the electron-electron correlation energy with respect to highest atomic-orbital angular momentum is a well-known issue in standard electronic structure theory in which only the electrons are treated quantum mechanically, and numerous explicitly correlated methods have been introduced to mitigate this poor convergence. Motivated by the success of single-component explicitly correlated methods, we generalize the single-component MP2-F12/3C(FIX) approach for electron-electron correlation to electron-proton correlation to reduce the need for large electronic basis sets in multicomponent calculations. We also implement the complementary auxiliary basis set (CABS) singles correction for the electrons and protons. Our calculations show that the multicomponent MP2-F12 electron-proton correlation energy is within a few percent of the complete-basis-set (CBS) estimate obtained by QZ-5Z inverse-cubic extrapolation with PB4-D held fixed at every electronic basis-set cardinality tested, with the aug-cc-pVDZ basis set recovering 96-98% of the extrapolated CBS electron-proton correlation energy and exceeding the conventional multicomponent MP2 value at the aug-cc-pV5Z level. These results indicate that explicitly correlated methods can substantially reduce the electronic basis-set requirements of multicomponent calculations.

Current pre-training datasets are derived from web crawls, with all their issues, and were not designed to support mid- and post-training pipelines–for instance, they contain little explicit reasoning. Thus, many frontier labs have begun to develop their own internal datasets, starting from state-of-the-art models, to augment their pre-training data mix, eg, with reasoning traces to address cold-start problems. While demonstratively effective, none of these datasets are public, and the effect of this so-called synthetic data on knowledge and skill acquisition of language models, including small ones, remains poorly understood. We present SYNTH, the first open-source synthetic corpus derived from 58,698 Wikipedia articles that collapses pre-, mid-, and post-training into a single training stage via structured amplification of curated encyclopedic seeds. We evaluate SYNTH by training a suite of models: a 56M tiny model (Monad), 0.3B-0.6B dense models (Baguettotron), and a 13B / 1B-active MoE. At iso-compute, SYNTH outperforms filtered web data, and our models remain competitive with similarly-sized open-weight baselines. Because SYNTH is back-translated from grounded passages, SYNTH-trained models achieve high factual precision despite 10-140x fewer training tokens, with memorization targeted by the seed corpus. These results show that synthetic datasets, including our SYNTH dataset, are capable of producing competitive generalist models from a fraction of the training data, enabling rapid iteration as the frontier advances. These findings open up possibilities for both generalist models with significantly increased data efficiency, as well as domain-specific models where no instruction or conversational data is available. Finally, we publicly release our SYNTH dataset and the suite of Baguettotron models under a permissive license, thus supporting open-source language model development.

Demonstrating quantum advantage on current quantum hardware is a central goal of quantum computing, and random quantum circuits underpin many leading proposals. Yet sampling-based demonstrations are often difficult to verify, while observable-based approaches face a different challenge: concentration can suppress differences between circuit instances. Recent experiments have put forward the estimation of out-of-time-order correlators (OTOCs) in random circuits as a promising task for verifiable quantum advantage, yet whether their circuit-to-circuit fluctuations survive concentration as system size grows has remained open. Here we show that they do. For broad classes of local random circuits in any fixed spatial dimension, we prove inverse-polynomial fluctuations of fixed-order OTOCs at system-scale depths. In one-dimensional Haar-random brickwork circuits, we further show that macroscopically many gates contribute to these fluctuations, yet in each layer they remain confined to a sublinear-width region. As a byproduct, we develop a classical algorithm exhibiting the first rigorous improvement over brute-force classical simulation of OTOCs in 1D. Although classical hardness remains open, our results rule out strong concentration as an obstruction to OTOC-based proposals for verifiable quantum advantage.

Multimodal continual instruction tuning (MCIT) aims to enable multimodal large language models to acquire new capabilities from sequential tasks while preserving previously learned knowledge. Existing methods primarily mitigate catastrophic forgetting by constraining parameter updates or separating task-specific adaptations. However, continual adaptation can also benefit from external knowledge that provides domain-specific information and reusable reasoning patterns for solving diverse instructions. For example, to answer "How many red cubes are to the left of the sphere?", domain knowledge can provide relevant concepts about objects and spatial relations, while reasoning knowledge can specify ordered operations such as object recognition, spatial filtering, and counting. Despite this potential, how to leverage external knowledge for continual adaptation remains largely unexplored in existing MCIT methods. To this end, we propose ReCAP, a retrieval-guided framework that leverages external knowledge to guide capability reuse during continual adaptation. At each continual stage, ReCAP uses external search and an LLM to incrementally build a knowledge base of domain, reasoning, and format knowledge based on the current-stage training data. For each instruction, retrieved domain knowledge guides generation, while retrieved reasoning knowledge selects and orders capability modules to form an instance-specific capability path. As these capability modules are reused across stages, subsequent adaptation can overwrite previously learned parameters. To enable stable cross-stage reuse, ReCAP introduces adaptive subspace recycling, which parameterizes reusable capability modules with shared bases and stage-specific cores, protects historically important directions while recycling residual capacity. Extensive experiments on MCIT benchmarks show that ReCAP achieves SOTA performance.

Class-Incremental Learning (CIL) requires models to recognize new classes over time without forgetting previously learned ones. With the rise of vision-language pre-training, CLIP has become a strong foundation for CIL. A common design in CLIP-based CIL is to construct textual classifier weights by encoding class-name templates with the CLIP text encoder, and then classify visual features by image-text cosine similarity. This design is appealing: since CLIP aligns images and text in a shared embedding space, textual weights appear to provide an off-the-shelf classifier for incremental classes. However, we show that this seemingly natural design is not always beneficial, as a modality gap can still separate the two modalities and make textual classifier weights deviate from visual class distributions. Empirically, under identical task-wise CIL training, initializing the cosine classifier with visual class centers yields lower loss and better incremental accuracy than using CLIP textual features. Motivated by these observations, we propose VIS, a visual-only method for CLIP-based CIL that removes the deployed textual branch and constructs the incremental classifier entirely in the visual space. To obtain stronger task-adaptive visual representations, VIS uses only base-session data to enhance CLIP's final visual representation with informative visual-layer features. Built on the enhanced visual representation, VIS employs a simple kernelized incremental least-squares SVM, whose classifier weights are solved in closed form from additive sufficient statistics. When new classes arrive, VIS accumulates their sufficient statistics and recomputes the classifier weights for all seen classes, enabling efficient incremental updates while preserving historical class knowledge. Extensive experiments show that VIS achieves state-of-the-art performance without a textual branch.

Activation and key-value cache precision change what a quantized language model computes without altering its stored weights. Direct weight-code bounds, however, assign identical complexity to deployments that behave differently and charge separately for weight codes that behave identically. Behavioral Capacity Certificates (BCC) charge for behavior using the aggregate prior mass of complete implementations—weights, scales, activation and cache rules—that induce the same bounded loss. When quantization merges implementations, this shared mass lowers the complexity penalty, and a break-even law determines when the saving survives the cost of validating it. BCC supports a three-step deployment workflow, and our experiments verify each step. First, a forward-only screen shortlists per-layer bit-widths by how often candidate perturbations preserve the reference predictions, with quality comparable to Hessian-guided selection at lower preprocessing cost. Second, margin-certified cells identify weights that can be pruned or sign-flipped without changing the deployed behavior: every permitted combination preserves all declared predictions, and on OLMoE-1B-7B and SmolLM2-1.7B, independent probes bound the probability that any permitted combination changes a prediction on new text. Third, BCC bounds the population loss of the deployed model, nonvacuously for complete decoders and more tightly than the compressed-code route. At equal cache memory, giving keys higher precision than values yields lower NLL and higher prediction agreement on GPT-2, Qwen2.5, and SmolLM2, together with a tighter complexity bound in the GPT-2 audit.

We prove a conjecture of Smyth on the Mahler measure of non-reciprocal trinomials of height $1$, determining exactly when their Mahler measures are greater than or less than $M(x+y+1)=\rho=1.381356\ldots$, conjectured to be the smallest limit point of $M(P)$ for non-reciprocal polynomials. Conjecturally, our result gives the full spectrum of $M(P)<\rho$ for all non-reciprocal polynomials, not just for trinomials.

Flocking and schooling are thought to have evolved partly as defences against predation, but how prey should balance social and escape tendencies may depend on the predator's hunting strategy. We extend the predator-prey boids model of Ojo et al. (2023), itself based on Reynolds' boids, by combining six prey movement tendencies (alignment, cohesion, separation, dodge, repel and wiggle) into a single weighted acceleration update, and by reformulating wiggle as a sinusoidal manoeuvre. We then use an evolutionary strategy to optimise the six behaviour coefficients for collective prey survival against four predator hunting strategies: attack-centroid, attack-nearest, attack-random and attack-peripheral. Across five independent trials per strategy, coefficients converged within trials and mean fitness remained stable or increased, although trials often settled in different local optima. Prey survival was highest under attack-centroid and lowest under attack-nearest, in line with our hypotheses. Against attack-centroid, prey evolved individualistic predator avoidance with high escape coefficients, whereas against the other three strategies they largely kept their flock formation. Across all strategies, evolution favoured a low repel coefficient and relatively high dodge and wiggle coefficients. Our results suggest that optimal anti-predator behaviour depends on the interplay between escape tendencies and the predator's hunting strategy.

Topological structures such as simplicial complexes, hypergraphs, and cell complexes extend standard graph models by modeling higher-order relationships. These structures appear in many modern datasets and require specialized methods for generating meaningful embeddings. In this paper, we introduce TopoEmbedX, a unified framework for embedding a wide range of topological domains into Euclidean spaces. The package brings together several existing topological embedding algorithms—DeepCell, Cell2Vec, CellDiff2Vec, HOLE, and HOGLEE—and introduces five new algorithms: ComplexNetMF, ComplexRep, ComplexRandNE, ComplexWalklets, and ComplexHeat. These algorithms extend well-known graph embedding techniques to higher-order settings using the augmented Hasse graph of a topological domain. TopoEmbedX provides a clear, consistent, and easy-to-use framework for topological representation learning. Experiments show that the embeddings generated by TopoEmbedX support tasks such as classification and regression across multidimensional data.

Pre-trained language models (PLMs) with encoder-based architectures have shown impressive capabilities in zero-shot cross-lingual transfer for various language understanding tasks. However, applying this technique to dependency parsing remains a significant challenge due to its syntactic nature. To boost model generalizability across linguistic typologies, we propose a cross-lingual unsupervised bootstrapping method to improve syntactic knowledge within the PLM. We show that our method achieves a significant improvement in zero-shot parsing performance in low-resource languages. Analysis of these bootstrapped models uncovers increased robustness in recognizing syntactic structures, evidenced by higher scores in parameter-free tree probing tests.

Every text classifier for an African language begins with a budgeting question: how many labelled examples are needed, and can labels from other African languages stand in for them? We answer both questions empirically for 28 language-task pairs, news topic classification in 16 languages (MasakhaNEWS) and tweet sentiment in 12 languages (AfriSenti), using a character n-gram linear model that trains in seconds on two CPU cores with no pretrained weights and no accelerator. Monolingual learning curves at budgets from 25 to several thousand labels show that topic classification reaches 90% of its full-data macro-F1 with about 400 labels in the median language, while sentiment is still improving at the full training size in 11 of 12 languages and needs thousands of labels. Pooling the full training data of the other languages in the benchmark is worth a great deal at small budgets and nothing at large ones: at 25 target labels it adds 0.20 macro-F1 on average for news (up to 0.43 for Lingala) and 0.08 for sentiment, the gain decays to zero by 800 labels, and at full size pooling hurts in 9 of 16 and 8 of 12 languages. Twenty-five target labels plus pooled data match what 100 to 400 monolingual labels achieve for most news languages. A complete zero-shot transfer matrix shows that transfer without any target labels recovers a median of only 13% (news) and 4% (sentiment) of the gap between a majority-class predictor and the in-language model, with the exceptions explained by shared script (Amharic and Tigrinya), shared lexicon (English and Nigerian Pidgin, the Arabic dialects), or a shared label prior rather than by language family. We release code that regenerates every number from the public benchmark files and translate the results into concrete annotation guidance for teams building African-language classifiers without GPUs.

To what extent does a local operator on smooth test functions determine a sub-Markov semigroup and its underlying structure of laws? Many existing approaches work with Feller semigroups on the space \(C_b\) of bounded continuous functions and rely on uniqueness, often established through a comparison principle for the associated evolution equation. However, even when the local operator is linear, uniqueness may fail and a \(C_b\)-Feller restriction may exclude the associated canonical semigroup. We discover that the space \(\operatorname{USC}_b\) of bounded upper semicontinuous functions offers a natural setting for this study. Within this framework, a complete description of the relationships among sublinear local operators, sublinear sub-Markov semigroups, and their underlying structures of laws is achieved without assuming uniqueness. Under suitable regularity and Lyapunov conditions, we construct the greatest semigroup compatible with a prescribed sublinear local operator and obtain a stochastic representation in terms of a Markov process under sublinear expectations. We characterize all sublinear sub-Markov semigroups dominated by this greatest semigroup in two ways: through a one-to-one correspondence with stable subfamilies of its representing laws, and through an order relation between their infinitesimal generators and the prescribed local operator. We further characterize the greatest semigroup via the greatest viscosity subsolution of the associated Hamilton–Jacobi–Bellman equation. These results clarify what information about global stochastic evolution can be recovered from local infinitesimal descriptions and what freedom remains in the absence of uniqueness. The resulting characterizations are new even when the local operator is linear.

A generative AI teaching partner should support reasoning over supplying conclusions; however, this has not been tested against learning in an authentic course. Drawing on design-based research, we specify the position as a conjecture map and report a first design cycle in two graduate-level research methods courses. Students used an AI teaching partner employing a constraint-first sequence requiring them to state and justify positions before receiving questions. Pre- and post-measures of AI literacy, critical thinking, and metacognitive awareness were collected alongside interaction records. AI literacy increased, concentrating in understanding AI, whereas critical thinking, awareness, and knowledge did not change. Since changes were limited to self-report measures, they may reflect growth in confidence instead of capacity. Interaction records, meanwhile, showed brief exchanges, uneven enactment of the constraint-first sequence, and missing records. These findings show why AI-supported learning requires interaction records to provide a more defensible basis for AI-supported designs than self-reports.

How many tokens from its context does a language model actually use, and what determines that number? We study this question through self-attention. Without retraining, we retain only the tokens with the highest attention weights at each head, layer, and query, keeping their original weights unchanged. By varying the selected set size and measuring the increase in negative log-likelihood (NLL), we estimate the effective attention set size needed to stay within a chosen loss tolerance. Relatively small selected sets can keep NLL close to the full-attention baseline, although the required size varies across models. Attention-based selection substantially outperforms random selection. Selected sets exhibit geometric structure, although geometric separation alone does not establish that model loss is preserved. Extending context while evaluating the same prediction targets increases the required set size, while its fraction of context decreases over the tested range. Experiments with a fixed supporting fact show that additional background pushes its tokens down the attention ranking and reduces their attention mass. Renormalizing the retained weights can substantially reduce the required set size, showing that it also depends on how selected representations are combined. Conditional theoretical models explain how competition and attention-mass retention can produce growing set sizes without more distinct information to retrieve. These results provide a way to measure effective attention set size in language models and investigate its dependence on context, competition, and aggregation.