Papers

Continuous multimodal sentiment analysis estimates polarity and intensity from linguistic, acoustic, and visual cues that may disagree. Hard judgments compress sentiment alternatives, while learned fusion interfaces tie task adaptation to model representations. We introduce Shared Sentiment Evidence (SSE), an output-space interface with fixed view and sentiment-option semantics across frozen backbones. Four queries yield five-option distributions whose probabilities, entropy, and cross-view relations form a 28-dimensional vector for CatBoost regression. On CH-SIMS-v2 and CMU-MOSI, the Qwen-based interface improves on supervised joint-only readout. Matched Ridge and CatBoost controls assess the contributions of additional views, deterministic summaries, and nonlinear readout. With the same interface specification and fixed readout settings, separately fitted heads also improve on joint-only prediction for three additional frozen backbones. These results support learning continuous sentiment from reusable output coordinates.

Extremal constructions play a central role in the design and analysis of algorithms. Integrality-gap instances expose the limitations of relaxations, while hard configurations reveal structural sources of computational difficulty. Such constructions, however, are still typically discovered through a slow, manual process. This paper investigates how machine learning can accelerate their discovery to support algorithm design and analysis. We build on PatternBoost, a framework alternating local search with generation from a trained transformer, using its Axplorer implementation to investigate three problems: integrality gaps for maximum independent set of rectangles, integrality gaps for stabbing unit squares with axis-parallel lines, and hard instances for recursive guillotine cutting. By exploring candidate representations, local search operations, and surrogate models used to rank candidates before exact verification, we carefully adapt the framework to these combinatorial geometry problems.While naive representations and search strategies fail to find non-trivial instances, our tailored adaptation discovers numerous non-trivial constructions. For stabbing unit squares, the method reaches a gap of $20/13\approx 1.54$, improving on the literature's best known lower bound of $3/2$. Purely automated search converges rapidly and then plateaus, prompting the question of what is required to push the bound higher still. We find that initial instance diversity plays an important role: with modest expert input via a structured staircase construction, the system reaches an improved integrality gap of $14/9\approx 1.555$. These results demonstrate that machine learning and domain expertise can be combined to discover new extremal constructions that advance algorithmic lower bounds.

Identifying the neural underpinnings of intelligence is one of the major goals of modern intelligence research. However, few imaging studies explore the high extremes of intelligence, and most use only a single composite IQ score. This study used quantitative EEG recordings to investigate correlations between the EEG variables of individual alpha peak frequency, relative power, and coherence, and scores on verbal and perceptual reasoning tests in participants with IQs from the low-average to exceptionally gifted ranges. Overall, the results did not reveal any pattern of significant relationships between these EEG measures and the two psychometric tests. Since this study had only a small sample, heavily skewed towards the high-IQ end of the scale, no definitive conclusions about the EEG measures and verbal and perceptual reasoning can be drawn. Nevertheless, it reveals many opportunities for further research, and suggestions are made for progressing this topic in the future.

Four-dimensional scanning transmission electron microscopy provides access to rich diffraction information at every probe position, but the high data rates associated with pixelated detectors remain a major challenge for interactive operation. Event-driven detectors offer an efficient alternative by representing the measurement as a sparse stream of individual incidences, substantially reducing requirements related to data handling and enabling on-the-fly processing. Here, we develop a high-throughput, real-time, 4D-STEM workflow based on the Timepix4 detector and demonstrate its operation at microsecond dwell times and standard beam currents. A common clock shared by the scan unit and detector allows the probe position of each electron event to be determined directly from its time-of-arrival, eliminating the need for inter-stream synchronization and enabling fully concurrent and independent multi-stream processing. The resulting pipeline continuously processes the detector data during acquisition, with the reconstructed images directly available. We demonstrate live virtual annular detector imaging, Real-Time Integration Center of Mass and direct electron ptychography within the guided progressive reconstructive imaging framework. The workflow sustains the high event rates of Timepix4 while maintaining zero latency for live interactive operation, thus extending event-driven 4D-STEM towards beam currents and acquisition conditions beyond those previously demonstrated with Timepix3-based systems. These results demonstrate that the combination of high-bandwidth event-driven detection, hardware-level synchronization and parallel processing can transform 4D-STEM from an offline technique into an interactive imaging modality, in which dose-efficient phase contrast and diffraction-based signals can serve directly as immediate feedback during STEM experiments.

Facial gestures can enable access for people with motor impairments (PwM), yet recognizers may not reliably interpret individual facial movement patterns. Existing approaches either constrain agency by requiring predefined templates or impose repeated calibration, data collection, and computation through user-specific retraining. We present AdaptaFace, an input-level compatibility layer using bounded, proxy-dependent adversarial perturbations to translate user-compatible gestures into inputs for an unchanged facial action unit (AU)-based recognizer. Designed around six personalization principles informed by interviews with 12 PwM, AdaptaFace supports both recognition enhancement and gesture vocabulary extension. In a within-subject study with 16 participants, AdaptaFace increased task completion from 59.7% to 90.5% and reduced workload from 5.61 to 4.21. Offline validation showed strong steering with aligned perturbation generation and evaluation but weaker cross-recognizer transfer, defining the approach's boundary. These findings frame adversarial assistance as input-side accessibility mediation for personalized facial-gesture interaction.

We present a novel class of minimum energy estimation problems for positive linear systems with linear costs subject to coupled process and measurement disturbances, where the latter is bounded by the state and the former is bounded by the noise. Through dynamic programming we show that the problem admits explicit solutions. Remarkably, the Luenberger observer structure of the optimal estimator emerges from the optimization itself, with a switching gain that inherits the sparsity of the disturbance constraints, and it is obtained from a differential equation in the finite horizon case. In the infinite horizon case, an algebraic equation characterizes the limit of the finite-horizon solution and yields a stationary estimator with a static gain. We introduce two distinct notions of detectability to characterize when the static gain stabilizes the error dynamics while preserving their positivity, and analyze under which conditions the stationary solution can be formulated as a linear program. We further establish that a disturbance perturbation of finite L1-norm yields an estimation error of finite L1-norm. The framework is illustrated on a large-scale irrigation network.

Looped Mixture-of-Experts (MoE) models combine parameter reuse with sparse computation to improve performance under matched budgets. Prior work demonstrates that different loop visits can play different roles even when they share parameters. To probe the contributions of different loop visits, we learn separate residual coefficients in a model that applies a shared block twice, observing a smaller scale in the first visit. Fixed coefficient experiments show that reducing the first visit's scale preserves or improves performance, whereas the same reductions to the second hurt it. This asymmetry motivates us to explore asymmetric compute allocation. We propose LatentLoop, which compresses the first visit's sequence, retains full resolution in the second, and reallocates saved computation to increase the hidden size. We further learn how strongly the first visit updates the full sequence, and share MoE weights across visits while using separate attention parameters to accommodate their different sequence resolutions. Across 15 configurations spanning 1.3B–7B parameters, with the largest budget exceeding $10^{21}$ FLOPs, LatentLoop consistently lowers validation NLL. At a fitted NLL of 1.988, predicted compute savings are 19.0% and 7.9% relative to vanilla MoE and the looped baseline. It also improves average scores on nine benchmarks at all sizes in 0-shot and 5-shot settings. These results suggest asymmetric compute allocation is a promising direction for looped MoE models.

Association schemes induced on the shells of the Grassmann scheme $Gr_q(N,a)$ form an important family in the study of multivariate $P$- and $Q$-polynomial structures. For $a<N/2$, the scheme induced on the furthest shell $X_a$ is the known bivariate $P$- and $Q$-polynomial scheme arising from attenuated spaces. In this paper, we prove that, for every $1\leq i\leq a-1$, the association scheme induced on the interior shell $X_i$ is both trivariate $P$-polynomial and trivariate $Q$-polynomial. The two structures share a common index set consisting of the lattice points of a bounded non-simplicial polyhedron. We establish the $P$-polynomial property through combinatorial interpretations of the intersection numbers. Using Dunkl's coordinate description of $X_i$ and the addition theorem, together with recurrence relations for the $q$-Hahn and $q$-Krawtchouk polynomials, we obtain the required vanishing and nonvanishing conditions for the Krein parameters, and hence the $Q$-polynomial structure. Motivated by this index set, we extend the notion of an $A_M$-Leonard pair from simplicial to polyhedral domains and show that every interior shell carries a polyhedral $A_3$-Leonard pair.

Spiking neural networks (SNNs) offer great potential for low-power intelligent computing owing to their event-driven nature, yet their deployment is limited by high inference latency and inefficient hardware utilization caused by temporal dependencies. Existing accelerators struggle to balance timesteps, accuracy, and energy efficiency, while hardware-oriented timestep compression remains underexplored. To address these challenges, this work presents STISA, a unified algorithm-hardware co-design framework featuring: (i) a Temporal Splitter Compression (TSC) technique with a Temporal Split Structure (TSS) to reduce temporal redundancy while preserving network dynamics; (ii) a hardware-efficient spatiotemporal parallelism scheme, which co-optimizes dataflow and architecture through a Temporal-Prioritized Output-Stationary (TPOS) mapping and a flexible Block-Mux Streaming (BMS) architecture; and (iii) a joint TSC-TPOS-BMS co-optimization framework featuring a bandwidth-aware resource allocation strategy to achieve balanced accuracy, latency, and energy efficiency across diverse network architectures. On the algorithmic side, TSC reduces synaptic operations by 24.44%-51.71% while achieving competitive accuracies of 96.38%, 81.10%, 68.51%, and 82.40% on CIFAR-10, CIFAR-100, ImageNet, and DVS-CIFAR10, respectively. On the hardware side, FPGA prototypes deliver up to 7.99 speedup, 30.4% power reduction, and 30.1% LUT reduction. Compared with state-of-the-art SNN accelerators, STISA achieves 0.16 GOPS/W/PE, demonstrating its scalability and superior energy efficiency for real-time SNN inference under constrained hardware resources.

Two-dimensional infrared (2D IR) spectroscopy is a powerful nonlinear technique for probing vibrational couplings, anharmonicities, coherence, and molecular dynamics. Among the microscopic parameters encoded in 2D IR spectra, transition dipoles are fundamental quantities that characterize molecular structure and govern light-matter interactions. However, reconstructing these quantities from spectroscopic data remains a challenging inverse problem. Here, we introduce a physics-informed convolutional neural network (CNN), Spec2DipoleNet, trained on 2D IR spectra generated via the non-Hermitian Hamiltonian (NHH) method. This multi-task CNN reconstructs the transition dipole matrices under physically-motivated masking constraints. On the validation set, the model achieves a root-mean-square error (RMSE) of 0.085, an $R^2$ of 0.97, and a normalized cross-correlation of 0.98. It reliably recovers matrix elements associated with allowed transitions, while larger deviations are observed for nominally forbidden transitions. Our results suggest that transition dipole operators can be quantitatively inferred from 2D IR spectra, highlighting the potential of physics-informed deep learning for extracting microscopic quantum parameters from multidimensional spectroscopic data.

Automated jailbreak attacks rely on evaluation feedback to optimize adversarial prompts, but existing methods often lack fine-grained diagnostic information. We propose Jev-Guided Strategy Bandit (JSB), a query-based jailbreak framework that leverages multi-dimensional probabilistic feedback to guide prompt optimization. JSB combines continuous jailbreak scoring with targeted refinement, strategy switching, and best-state reseeding to balance exploration and refinement. We evaluate JSB on two harmful request datasets across five open-source and three closed-source LLMs. Under a budget of only 10 target-model queries, JSB achieves an average HarmBench attack success rate of 89.8% across ten open-source settings, consistently outperforming existing automated jailbreak attacks. Further analyses demonstrate its effectiveness under varying query budgets and attacker models. Defense experiments also reveal limitations in existing filtering mechanisms and highlight the potential of Jev-based output filtering.

Repository-level code comprehension question answering (QA) supports developer reasoning over functionality and usage distributed across codebases. However, repository-specialized large language models (LLMs) can become misaligned as code evolves. We study this challenge as temporal repository adaptation: acquiring new knowledge, suppressing obsolete, retaining still-valid, and preserving semantically neighboring knowledge. Existing retrieval, fine-tuning, and model-editing methods address only parts of this problem. We propose Temporal Adaptive Fine-Tuning (TAFT), a novel adaptation approach that treats repository transitions as supervision. TAFT derives temporally grounded QA data from repository transitions, pairs newly valid with obsolete knowledge through preference optimization, and replays transition-conditioned retention examples to preserve still-valid knowledge. We evaluate TAFT on an augmented temporal SWE-bench dataset comprising 255,295 QA entries across ten temporal slices, comparing deferred (Baseline), per-slice retrained (Baseline-Batched), and variants with knowledge anchors along four dimensions: updated knowledge, obsolete-answer suppression, retention, and neighbor stability. TAFT consistently outperforms both the deferred and batched baselines, with an average relative improvement of 18% in updated/suppressed knowledge accuracy, doubled retention accuracy, and roughly 1.5 times the neighbor accuracy. With directly supplied knowledge anchors, TAFT-KANT further improves mean updated/suppressed, retention, and neighbor accuracy over TAFT by 3.55%, 8.35%, and 13.00%, respectively. Overall, TAFT demonstrates its effectiveness across all evaluated areas, effectively enabling code comprehension QA alignment with repository evolution.

Motion capture is increasingly important in healthcare, rehabilitation, and sports applications. However, conventional vision-based systems require camera infrastructure and line-of-sight conditions, limiting their use in daily environments. This paper proposes a location-independent platform for motion capture, based on an array of IMU (inertial measurement unit) sensor nodes without individual wiring or onboard batteries, enabled by two-dimensional communication and power delivery over conductive fabric. Pipeline processing in each sensor node, combined with a token-passing protocol, enables collision-free and stable data acquisition at 50 Hz. Real-time three-dimensional reconstruction of flexible objects is further demonstrated by applying Hermite spline interpolation to orientation data from grid-aligned IMUs. Against a cylinder of known radius, the reconstructed surface deviates by 2.60 mm RMS over the 225 mm span of the array. The reconstruction is formulated for the quasi-static regime, and this letter empirically validates it in that regime. The hardware platform and communication protocol implemented in this work enable further investigation toward dynamic motion capture textiles.

Federated fine-tuning enables large language models (LLMs) to learn collaboratively from distributed client data, but malicious client updates can compromise global model safety. As federated tasks evolve, changing malicious update patterns challenge the ability of existing defenses to maintain reliable risk detection over time. To address this challenge, we propose Safe-FCL, a framework integrating continual risk awareness with fine-grained safety aggregation for federated continual learning of LLMs. Specifically, the Continual Risk Awareness (CRA) mechanism learns emerging risk patterns across sequential tasks and constrains detector updates using a protective subspace derived from historical features, mitigating forgetting of previously learned malicious patterns while adapting to new risks. To translate risk awareness into aggregation-level safety control, the Fine-Grained Safety Aggregation (FGSA) mechanism combines client-level risk assessments from CRA with module-level deviations from historical update behavior to adaptively regulate aggregation contributions, suppressing potentially malicious updates while minimizing unnecessary restrictions on benign updates. Extensive experiments demonstrate that Safe-FCL outperforms current SOTA methods, improving global-model Rule and MD-Judge scores in federated continual learning by 0.41% and 0.64%, respectively, while increasing average risk recognition accuracy by 2.01%.

Nuclear quantum effects are essential for an accurate description of the hydrogen-bonded structure of liquid water, yet their spectroscopic signatures can be subtle and difficult to measure. Moreover, probing these effects in solution on femtosecond timescales (or below) is an open challenge that is pivotal for optical control of hydrogen bonds and ultrafast spectroscopy of proton transfer. Here, we combine path-integral molecular dynamics with real-time time-dependent density-functional theory to explore high-harmonic generation (HHG) in liquid water from first principles, rigorously accounting for quantum nuclear delocalisation. Relative to classical-nuclei simulations, quantum sampling suppresses the harmonic yield around certain harmonics by up to an order of magnitude, inducing local structural minima. By analysing the ab initio simulations and reproducing the key effects with a simplified model Hamiltonian, we trace the physical origins of the interference minima to the broadening of valence-band states induced by hydrogen-bond fluctuations, a mechanism expected to generalise to other hydrogen-bonded structures. Our work shows that nuclear quantum effects are indispensable for capturing ultrafast electronic dynamics in liquids, and demonstrates the power of liquid HHG spectroscopy for attosecond probing of nuclear fluctuations.

The number of attention heads in a transformer is usually set by convention or grid search. We test a simple heuristic for setting it in advance: estimate the intrinsic dimension of token representations without labels, and use roughly that many heads. We estimate intrinsic dimension with a nested-dropout VAE trained on DistilBERT embeddings of WikiText-2, choosing the KL weight at the knee of the VAE's rate-distortion curve rather than by hand. This gives $k^*=9.2$ (95% CI [8.6, 9.8]). In a small 4-layer transformer trained from scratch, 10 heads and 32 heads are statistically equivalent on SST-2 and on MRPC (paired TOST over 10 seeds, $\pm1$ point margin), with 69% fewer attention parameters for the 10-head model. Training 10 heads from the start also slightly outperforms training 32 heads and pruning to 10 (0.6 points, $p=0.008$). The evidence is narrow: two classification tasks, one small architecture, no pretrained models, and no formal link between intrinsic dimension and head count. We present the result as a practical heuristic worth testing at larger scale, not as a general principle.

For integers $r\ge1$ and $n\ge2$, let $s_r(n)$ be the least $N$ such that every sequence of $N$ vectors in $\Z^r$, each nonzero modulo $n$, contains $n$ terms whose sum is zero modulo $n$ but nonzero modulo $n^2$. Let $w_r(n)$ be the corresponding least $N$ when any nonempty subsequence is allowed. These constants were introduced as zero-sum problems of new types by Z.-W. Sun. We prove $s_r(n)\ge(2^{r+1}-2)(n-1)+1$ by constructing an explicit sequence from a lattice polytope, disproving his conjecture $s_2(n)=4n+1$ for $n\ge4$. We obtain $w_r(2)=2r+1$ by classifying all sequences avoiding such nonempty subsequences modulo $4$. We also prove Sun's conjecture $w_2(n)=4n-3$ for $n=2^k3^\ell p$, where $p$ is a prime and $k,\ell\ge0$ are integers, by classifying the extremal sequences of length $4p-4$ modulo $p^2$ when $n=p$. For every fixed $n\ge2$, we prove $w_r(n)/s(\Z_n^r)=O_n(r^2/2^r)\to0$ as $r\to\infty$, where $s(\Z_n^r)$ is the classical Erdős-Ginzburg-Ziv constant, with an explicit threshold on $r$ for strict inequality. Thus, for every fixed modulus $n\ge2$, Sun's proposed equality fails for sufficiently large $r$.

Preserving the underlying statistical properties of light during frequency transduction is essential for interfacing spectrally disparate quantum systems. To do this successfully, the process needs to be highly efficient, broadband and noiseless. Despite significant progress in this field, satisfying all these conditions remains challenging. Recently, molecular modulation-based transduction in hollow-core fibers has emerged as a promising approach, where biphoton correlations were proven to be preserved during frequency up-conversion. However, beyond this previous demonstration of correlation-maintaining conversion, whether molecular modulation can preserve more general statistical properties of light remains experimentally unexplored. Here, we demonstrate the conservation of photon-number statistics during selective frequency transduction by Raman molecular modulation in a hydrogen-filled hollow-core fiber. As a proof of concept, weak 585-nm signals are selectively converted to 773 nm in the near-infrared and to 471 nm in the blue spectral region with near-unity efficiencies. Phase matching between the generated coherence waves and the transitions of interest is achieved through the effective dispersion of the system, enabling independent selection of the frequency up- and down-conversion processes. The preservation of the photon-number statistics of the shifted signals, along with the large frequency shifts, broad tunability and compatibility with quantum-optical fields, provides a versatile fiber-based platform for quantum frequency transduction. In particular, the demonstrated interfacing between visible and near-infrared wavelengths using low pump energies and low gas pressures offers a route towards connecting spectrally distinct quantum systems, including quantum emitters, sensors and atomic quantum memories, within hybrid quantum networks.

We study the linear energetic stability of non-Abelian vortices in an $SO(3)$ gauge-Higgs theory with residual gauge group $A_4$. In our previous work, we identified two families of such vortices associated with order-two and order-three elements of $A_4$, and found Bogomol'nyi–Prasad–Sommerfield-like behavior at special ratios of the Higgs and gauge-boson mass scales. Here, we investigate their stability against $SO(3)$ gauge and Higgs perturbations by analyzing the second order variation of the vortex tension using analytical and numerical methods. In particular, when all relevant mass scales are equal, we prove linear stability for all vortices in the order-three family. By contrast, at the same mass point, we prove that a vortex in the order-two family is unstable. Thus, although both vortex families exhibit Bogomol'nyi–Prasad–Sommerfield-like behavior in their reduced equations at this mass point, their stability properties in the full $SO(3)$ theory are qualitatively different.

The graph isomorphism problem asks whether two graphs are equivalent up to a permutation of their vertices. Its precise computational complexity remains unresolved, and it is still unknown whether a polynomial-time algorithm exists. We investigate whether simple graph-dependent Instantaneous Quantum Polynomial-time (IQP) and Quantum Approximate Optimisation Algorithm (QAOA) circuits can distinguish non-isomorphic graphs. We first show that suitable IQP and QAOA constructions allow the underlying graph to be reconstructed using a polynomial number of samples. Building on previous work using the QAOA energy, we show that Hamming weight distributions can distinguish graph pairs at circuit depths for which the numerically computed energy gap is zero. We then apply graph invariants to the matrix of ZZ correlators on the output distribution. For the specific case of the graph spectrum, at QAOA depth $p=2$, this invariant numerically distinguishes all $10{,}486$ cospectral regular graph pairs tested on up to 18 vertices. For IQP circuits, we introduce a finer invariant based on probability multiplicities within Hamming weight sectors, which distinguishes every non-isomorphic graph pair tested numerically. Finally, we derive exact graph-theoretic characterisations of the IQP output distribution at $\theta=\pi/2$ and $\theta=\pi/4$. These results show that simple graph-dependent quantum circuits encode substantial structural information, while leaving open whether this information can be extracted efficiently for general graph isomorphism.

Online Software Engineering (SE) communities such as Stack Overflow have become unwelcoming and hostile spaces, as evidenced by the presence of rude and offensive comments that are detrimental to the emotional wellbeing of participants. The main objective of this work is to investigate the prevalence and nature of offensive language in online SE communities, and develop approaches to classify them with the ultimate goal of reducing offensive language by proposing an Offensive Language Reduction System (OLRSSE) that has the ability to detect, classify, and explain to the poster why a comment is offensive and also propose non-offensive alternative suggestions. Using data from 130,000 user comments on discussions held in four prominent SE platforms: Stack Overflow, GitHub, Gitter and Slack, we developed six sets of twelve (72 in total) different machine learning models (both traditional and deep learning). The F1-Score of the best performing models in the system ranges from 0.56 to 0.94, with an average F1-Score of 0.85, predominantly using BERT as the primary model for various classification tasks. Also, two language-based models were developed for paraphrasing offensive to non-offensive comments. The overall utility of the OLRS-SE was evaluated using user studies with 30 participants, which showed that the developed system is easy to use and also effective in reducing offensive language. Investigating the capabilities of different large language models for offensive language reduction is a promising avenue for future research.

Let $A_q(n,d)$ denote the largest size of a code of length $n$ and minimum Hamming distance $d$ over an alphabet of $q$ symbols. For fixed $q\ge2$ and $d\ge4$ we construct codes with redundancy $n-\log_q A_q(n,d)\le(d-3)\log_q n+O(\sqrt{\log n})$ for all large $n$. No algebraic structure is imposed on the alphabet, and the codes are not linear. For $d=4$ and $d=5$ the coefficient of $\log_q n$ matches the Hamming bound, so the redundancy is determined up to lower-order terms. At distance four the codes are provably better than every linear code: by the polynomial-method bound for cap sets, $\mathbb{F}_q$-linear codes with $q>2$ require a strictly larger coefficient in front of $\log_q n$. The construction imposes moment checksums over an auxiliary finite field, as BCH codes do, but one fewer than the distance would normally require. The affine-line theorem from prior work describes the dependencies left by these checks. We exclude them by placing the code positions inside a specially structured subset of the field, built from Behrend's sphere construction with the help of algebraic number theory.

This special issue brings together a collection of original research articles and review papers addressing topics directly related to the MoEDAL-MAPP experiment at the Large Hadron Collider (LHC). The experiment is designed to search for (meta-)stable, anomalously ionising particles predicted by theoretical extensions of the Standard Model. Several contributions explore the theoretical and phenomenological aspects of models of particular relevance to the experiment, including scenarios involving magnetic monopoles, highly electrically charged particles, and millicharged particles. Other contributions focus on experimental developments, highlighting novel detection techniques and technological advances aimed at identifying these unconventional signatures and probing new phenomena beyond the Standard Model.

This paper presents a preliminary study on the efficacy of network device configuration produced by Large Language Models (LLMs). Currently, the study focuses on routing protocol configurations in a predefined small internetwork with Cisco-based routing devices. The capability of three freely available LLMs with standard capabilities (i.e., with no enhanced features) to produce effective setups is investigated. Prompt engineering methods are excluded in order to assess the "first-response" configurations of the models under consideration. The assessment method is based on the contents of the resulting routing table, aiming at measuring the device functional correctness. For that purpose, the Jaccard index is used to indicate the percentage of correct network prefixes contained in the routing table constructed by the model-based configuration commands. The work provides insights on the maturity and limitations of modern LLMs on aiding network administrators with network device configurations in real deployments.

World action models (WAMs) jointly predict future visual states and robot actions, but processing dense future-frame tokens incurs substantial inference latency. We propose CF-Prune, a training-free framework for pruning future-frame tokens in pretrained WAMs. Our key insight is that future visual predictions support action generation and therefore need not preserve every visual detail required for high-fidelity video synthesis. CF-Prune combines instruction and action attention to identify task-relevant tokens during the initial denoising forward pass, even when future-frame and action representations remain highly noisy. An entropy-based phase identification mechanism further retains dense computation during precision phases to mitigate pruning-induced performance degradation. Experiments on RoboLab, RoboCasa, and real-world manipulation tasks demonstrate consistent inference speedups. At a 35% pruning ratio, CF-Prune achieves average speedups of 1.19-1.27x while improving task success rates. At a 50% pruning ratio, it achieves 1.29-1.33x average speedups on both simulation benchmarks, with overall success rates within 1.0 percentage point of the baseline.

In this paper, we evaluate two companion $q$-series recently suggested for investigation by Andrews and El Bachraoui in the concluding remarks of their work. From these evaluations, we derive the corresponding partition identities and give combinatorial proofs.

World models aim to learn compact representations of an environment from observations, enabling agents to predict future states and plan their behaviour. However, most existing approaches learn black-box representations, with limited ability to incorporate prior knowledge about the world. We introduce Concept-Grounded World Models (CGWMs), a neurosymbolic world model design that instead learns interpretable concept representations. We learn these concepts from observations using explicit and complete knowledge, expressed in temporal logic, that specifies the valid world states and the temporal relations governing their dynamics. Furthermore, we directly use this knowledge by formulating planning as differentiable reasoning, optimising the agent's actions by gradient ascent to satisfy a goal. We experimentally compare CGWM with a purely neural baseline and a neurosymbolic baseline on two game environments. We find that CGWMs ground concepts much more accurately, even over long horizons, resulting in significantly more robust planning both in and out of distribution.

We investigate the existence of (metrically) expansive operators on Fréchet spaces without continuous norm. We first solve a problem posed by Bernardes, Caraballo, Darji, Fávaro, and Peris in 2025, by showing that there is no expansive operator on the Fréchet space $\omega$ of all sequences. We prove this fact by investigating the existence of orbits remaining cofinitely inside some fixed closed subspace of finite codimension. We then give examples of expansive operators on some other Fréchet spaces without continuous norm.

We study the discrete Huygens phase map on the ring $C_n$, the simplest oscillator network in which the coupling can be frustrated. Reciprocal coupling favours phase opposition between neighbours, while the edge phase differences must sum to zero modulo $2\pi$ around the cycle; for odd $n$ these two requirements are incompatible. The parity of $n$ determines the absolute minima of the potential. When $4\mid n$, the critical set also contains circles of critical points, all of which meet at two completely degenerate configurations. After quotienting by the common phase, the map is a gradient step for an intrinsic potential on an $(n-1)$-torus, and the cycle spectrum gives an explicit interval of interaction strengths on which every orbit converges to a critical point. Our main result is that, on this whole interval and for every $n\ge3$, almost every orbit converges to a uniform twisted minimum, including at interaction strengths for which the map is not invertible. When $4\mid n$, the non-minimal points of the critical circles are treated by a centre-stable manifold argument. At the two degenerate intersections, a local blow-up reduces the problem to the cubic leading term of the potential and its restriction to the unit sphere. Orbits approaching along directions where this restriction is positive form a null set, because the cubic is harmonic in the intrinsic metric. No orbit approaches along its zero level, where the critical points are non-degenerate saddles on invariant rays. Hence the degenerate equilibria also have basins of zero measure.

Compactness is widely used to identify candidate relic galaxies, the largely untouched survivors of the first compact massive galaxies. Yet relicness is an evolutionary rather than structural property. Using the COLIBRE cosmological hydrodynamical simulations, we test whether present-day structure traces galaxy formation and assembly histories. Six complementary tracers (stellar age, metallicity, [Mg/Fe], sSFR, velocity dispersion and ex-situ mass fraction) vary coherently across the stellar mass-size plane and independently identify a characteristic compactness scale of $\log_{10}(\Sigma_{1.5,\mathrm{crit}}/(\mathrm{M}_\odot\mathrm{kpc}^{-1.5}))=9.75\pm0.10$. We term this mapping between present-day structure and assembly history morpholography. Combining this threshold with the Degree of Relicness ($\mathrm{DoR}>0.6$), which quantifies early and rapid star formation, we distinguish compact from ancient galaxies and identify 267 relic candidates at their intersection. Ancient galaxies span nearly the full ex-situ-fraction range, from predominantly in-situ formation to substantial merger-driven growth. Relic candidates are concentrated at stellar masses of $\approx 10^{10}$-$10^{11}$ solar masses, host black holes that lie $\approx 0.25$-$2.5$ dex above the median black-hole-stellar-mass relation, and are predominantly satellites (76%), preferentially in cluster environments. Only $\approx 3$% show evidence of strong tidal stripping, suggesting that environment primarily preserves rather than creates relic-like systems. Approximately one third (87/267) are direct descendants of the $z=2$ massive quiescent galaxies identified in COLIBRE. Present-day structure thus retains a statistical fossil record of assembly history, supporting morpholography as a link between nearby galaxies and the early Universe.