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Zirah is a hardware signer built around an STM32F407 microcontroller, and its purpose is to find out, on inexpensive hardware, where a post-quantum signing key is exposed and what actually protects it. The device draws every random bit from a reverse-biased 2N3904 junction in avalanche breakdown, amplified by an LM358 and screened by SP 800-90B health tests, computes ML-DSA-65 (FIPS 204, hedged) on the STM32 with two-share arithmetic masking of the secret-key multiplications, and adds ECDSA P-256 from an ATECC608 secure element over the same digest, once a person has matched an eight-digit digest prefix on its OLED with the PC and pressed a button. A desktop application and a command-line tool drive the board and verify its output, and because only a 32-byte manifest digest reaches the device, it signs files of any type and size, returning signed copies for PDF, Office Open XML, ZIP, PNG and JPEG files and detached records for every other format. NIST's SP 800-90B tool rejected the IID assumption for 1,000,000 raw samples and assessed 6.898 bits of min-entropy per byte on the non-IID track, against the 1 bit the firmware credits, while spectral lines near 116 Hz that hold about 5 % of the variance remain unexplained. At 168 MHz the masked signature took a median of 157 ms over 20 runs and a complete signing operation under 0.8 s, and the signer matched the pq-crystals reference in 1,976 checks natively and on an emulated Cortex-M4. The ATECC608 can neither store the 4,032-byte ML-DSA-65 key nor compute with it, so that key sits in ordinary flash behind readout protection, and on an earlier board, before that protection was enabled, a debugger copied it out and the copy produced a valid ML-DSA-65 signature without the device, although the leakage results come from an instruction-level emulator and nothing here is certified.

sEMG Foundation Models aim to learn general purpose representations over diverse subjects and recording conditions that boost performance on a variety of downstream tasks. However, existing evaluations make it difficult to discern whether pretraining alone is sufficient to combat the cross-subject overfitting which makes machine learning on sEMG so challenging. We conduct a systematic evaluation of three sEMG foundation models across three gesture classification datasets under both intra-session and inter-subject splits, using three fine-tuning strategies designed to isolate the contribution of pretraining. We find that pretraining boosts performance when train and test samples are drawn from the same recording session, but this benefit largely disappears under inter-subject evaluation. In low subject count datasets, pretraining provides little to no benefit and classical ML baselines match or exceed foundation model performance.

Text-to-image (T2I) systems serve users across languages and cultural contexts. However, evaluations of cultural representation focus mainly on recognizable elements such as landmarks, clothing, and activities, overlooking the cultural values that generated images convey. To bridge this gap, we introduce VisionValueBench, a multilingual benchmark that operationalizes six of Hofstede's cultural value dimensions (e.g., individualism versus collectivism) to investigate how T2I systems frame neutral social situations through a particular cultural orientation. We find that value-neutral prompts, which admit diverse cultural interpretations, nonetheless yield images that favor particular value orientations, a phenomenon we call visual value leakage. We evaluate prompts varying in language and geographic cues across 960 social scenarios and six T2I configurations. Generated images consistently favor the same value orientations across all six dimensions, for example, equality over hierarchy (low power distance), individual autonomy over group obligation (individualism), and enjoyment over restraint (indulgence). Prompt language has limited influence on these orientations, whereas geographic cues shift some dimensions toward the associated cultural values while largely preserving the prevailing orientations. These findings reveal substantial homogeneity in the cultural values conveyed by T2I systems worldwide.

Streaming video understanding requires models not only to process temporally incoming frames, but also to anticipate user intent for realistic applications such as Augmented Reality (AR) glasses. While prior streaming benchmarks evaluate temporal reasoning, none measure whether Multimodal Large Language Models (MLLMs) can interpret or leverage human gaze signals within a streaming setting. To fill this gap, we introduce StreamGaze, the first benchmark designed to evaluate how effectively MLLMs utilize gaze for temporal and proactive reasoning in streaming videos. StreamGaze introduces gaze-guided past, present, and proactive tasks that comprehensively assess streaming video understanding. Past and present tasks require immediate responses based on observations available at query time, whereas proactive tasks require models to continuously process incoming frames and respond at the appropriate future moment. To build StreamGaze, we develop a gaze-video Question Answering (QA) generation pipeline that aligns egocentric videos with raw gaze trajectories through fixation extraction, region-specific visual prompting, and scanpath construction. This pipeline produces spatio-temporally grounded QA pairs that reflect human perceptual dynamics. Across all StreamGaze tasks, we observe substantial performance gaps between state-of-the-art MLLMs and human performance, highlighting key limitations in gaze-based temporal reasoning, intent modeling, and proactive prediction. We further provide detailed analyses of gaze prompting strategies, reasoning behaviors, and task-specific failure modes, offering insights into current limitations and directions for future research. All data and code are publicly available to support research in gaze-guided streaming video understanding.

Smooth sequences over an alphabet of positive integers $\{a,b\}$ are sequences that are infinitely derivable, the emblematic example being the Oldenburger-Kolakoski sequence $κ$ over $\{1,2\}$. The main way to study their language is to consider a finite version of smooth sequences called smooth words. In this paper we prove that the smooth words are exactly the factors of smooth sequences and we make progress towards the conjecture that the complexity of smooth words over $\{a,b\}$ grows like $Θ\left(n^{\log(a+b)/\log((a+b)/2)}\right)$: we prove the lower bound over any alphabet and the upper bound over even alphabets, and we improve the known upper bound over odd and mixed alphabets. We also provide a dichotomy that links the language, the morphicity and the factor complexity of $κ$.

The use of algorithmic predictions in decision-making leads to a feedback loop where the models we deploy actively influence the data distributions we see, and later use to retrain on. This dynamic was formalized by Perdomo et al. 2020 in their work on performative prediction. Our main result is an unconditional reduction showing that any no-regret algorithm deployed in performative settings converges to a (mixed) performatively stable equilibrium: a solution in which models actively shape data distributions in ways that their own predictions look optimal in hindsight. Prior to our work, all positive results in this area imposed strong restrictions on how models influenced distributions. By using a martingale argument and allowing randomization, we avoid any assumption on how populations respond to predictions and sidestep recent hardness results showing that deterministic stable models are in general PPAD-hard to compute. Lastly, on a more conceptual note, our connection sheds light on why common algorithms, like gradient descent, are naturally stabilizing and prevent runaway feedback loops. We hope our work enables future technical transfer of ideas between online optimization and performativity.

In practice, auction data are often endogenously censored and anonymous, revealing only limited outcome statistics rather than full bid profiles. We study robust auction design when the seller observes only the distribution of a single anonymous order statistic of the bidders' values and seeks to maximize worst-case expected revenue over all product distributions consistent with the observed statistic. We show that simple and widely used mechanisms are robustly optimal. Specifically, posted pricing is robustly optimal given the distribution of the highest value; the Myerson auction designed for the unique consistent i.i.d. distribution, with uniformly random tie-breaking, is robustly optimal given the lowest value distribution; and the second-price auction with an optimal reserve is robustly optimal when an intermediate order statistic is observed and the implied i.i.d. distribution is regular above its reserve. Without any regularity assumption, when the second-highest value is observed, the best worst-case revenue of a second-price auction with a reserve is still at least a $2-\sqrt{2}\approx 0.586$ fraction of the optimal worst-case revenue. More generally, for a broad class of monotone symmetric mechanisms depending only on the top $k$ order statistics, including multi-unit and position auctions, the worst-case revenue is attained under the i.i.d. distribution consistent with the observed $k$-th order statistic. Our results provide a tractable foundation for non-discriminatory auction design, where fairness and privacy are intrinsic consequences of the information structure rather than imposed constraints.

World action models increasingly rely on pretrained diffusion/flow-based video generators assumed to capture physical dynamics for prediction, planning, and action generation. Existing evaluations assess plausibility, probe representations, or measure predictive surprise, yet physical consistency is history-dependent: preceding events constrain what can physically occur later. We introduce PhysTrace, a training-free framework that uses MLLMs to formulate history-conditioned physical expectations and tracks their agreement with observed video windows through temporal video--language alignment, rather than relying on direct plausibility judgments or task-specific probes. On IntPhys2, PhysTrace achieves 67.2% possible--impossible discrimination accuracy, outperforming the evaluated direct MLLM baselines. We further introduce reference-guided masked denoising for controlled reconstruction from mixed possible--impossible video latents. To support these reconstructions and evaluate temporal localization as an additional capability, we introduce IntPhys2-Timing, adding violation intervals to IntPhys2, with PhysTrace achieving a Hit Rate of up to 77.4%. On these reconstructions, human evaluations reveal model-dependent differences in physical consistency and fewer physically impossible outcomes at higher initial noise levels, trends broadly captured by PhysTrace.

Streaming video models should respond at the moment an event unfolds, not after the moment has passed. Yet existing online VideoQA benchmarks remain largely retrospective. They pause the video at fixed timestamps, pose questions about current or past events, and score models only at those moments. This protocol leaves streaming outputs untested. To close this gap, we introduce SPOT-Bench, featuring multi-turn proactive queries that evaluate general streaming perception required by an always-on, real-time assistant. SPOT-Bench comes with Timeliness-F1, a consolidated metric that measures streaming outputs by their temporal precision and balanced coverage across the entire video. Our benchmark reveals that during streaming inference: (i) MLLMs detect events reliably in a stream but spam predictions unprompted; (ii) post-training MLLMs for silence reduces spamming but induces unresponsiveness; (iii) half of the streaming video expects no response, which we term dead-time - compute spent here does not affect response latency. These findings motivate Ctrl-SPOT, a training-free streaming controller for MLLMs, that retains their event perception while controlling their streaming outputs for balanced coverage. This establishes a strong baseline on SPOT-Bench.

Person identification from millimeter-wave (mmWave) radar point clouds has primarily focused on gait. However, since indoor walking is typically brief and fragmented, gait-based identification is largely constrained to designated passages that support continuous walking. Meanwhile, non-gait activities of daily living (ADLs) are pervasive and also encode discriminative personal signatures. In this study, we evaluate the feasibility of ADL-based identification from sparse mmWave point clouds using mm-ADL, a dataset comprising seven core ADLs collected from 11 subjects under controlled protocols. Moving beyond uniform gait introduces significant activity-dependent variations that confound identity representations. To address this challenge, we systematically benchmark three activity-identity learning paradigms: monolithic learning, joint multi-task learning, and two-stage activity-conditioned routing, under both closed-set identification (ID) and subject-disjoint re-identification (ReID) biometric settings. In parallel, we propose Dual-Stream Static-Dynamic PointNet (DS-SDPNet), an architecture tailored to radar point clouds that captures complementary spatial morphology and motion dynamics. Across seven ADLs, DS-SDPNet achieves 70.2% mean closed-set identification accuracy and outperforms existing baselines on both mm-ADL and mmGait. Moreover, benchmarking the three paradigms without ground-truth activity labels during inference yields up to 68.0% closed-set accuracy and 75.4% ReID mAP, providing a systematic baseline and confirming the feasibility of point-cloud-based biometric identification across diverse daily activities.

Medical 3D scans and reports are inherently hierarchical, with diagnostic cues concentrated in specific anatomical regions across multiple levels of organization. Yet, most medical vision-language models ignore this structure and fail to focus on clinically relevant anatomy. We introduce MedHiVE, which combines hierarchical vision-language Soft Mixture-of-Experts (SMoE) with contrastive learning to jointly model fine-grained anatomy and global scan context. To our knowledge, MedHiVE is the first framework to route both vision and text tokens through a two-level SMoE hierarchy organized by anatomical scale, coupling this with report-derived anatomy-level contrastive alignment for 3D medical imaging. This replaces the direct region-text alignment of statically pooled features and vision-only hierarchical routing of prior work with dynamic, slot-based cross-modal information flow across anatomical scales. MedHiVE operates via a two-level, learnable token-routing mechanism, where local image and text features are first routed through a local SMoE and then fused by a global SMoE into unified multimodal representations. Contrastive learning aligns both anatomy-level and global vision-language representations in a unified space. Pre-trained on 25,000+ CT scans with anatomical supervision, MedHiVE consistently surpasses 11 state-of-the-art methods across 6 datasets on 3 tasks: segmentation, classification, and detection, demonstrating the importance of hierarchical modeling. The code for MedHiVE is at github.com/szczurek-lab/MedHiVE.

We identify an intriguing phenomenon when linearly interpolating between permutation-aligned neural networks: test accuracy briefly improves near the interpolation endpoints before dropping toward the midpoint, which we term BUMP (Brief Unexpected Mid-interpolation Peak). We observe that BUMP appears consistently across datasets, architectures, training regimes, and remains robust under substantial perturbations such as early checkpoints and extreme pruning. Moreover, controlled ablations suggest that it cannot be attributed to trivial regularization effects. While similar near-endpoint gains are visible in prior interpolation plots, they have not been explicitly documented or systematically and thoroughly analyzed. Leveraging this effect, we propose a simple, novel ensembling scheme: weight-prediction mixed ensembling that combines weight mixing with prediction-space mixing. Across our experiments, the resulting ensembling method consistently outperforms standard logit ensembling in test accuracy and yields improved calibration trade-off, highlighting complementary benefits of weight- and prediction-space mixing.

Exploration has been a focus of reinforcement learning research for a long time. Recently, there has been growing evidence that it is also an important ingredient in LLM reinforcement learning recipes that can significantly impact downstream performance. Many existing methods control exploration in the action-space, for example, using temperature scaling. However, these methods cannot reorder tokens but only influence the variance in the output distribution. This limits exploration and can lead to divergence or stalled training. Here, we investigate parameter-space exploration, where rollouts are generated by sampling different policies from a posterior that may each explore different rollouts. Sampling less or more diverse policies is then a complementary control lever over exploration. We introduce a family of methods called Perturbed Parameter Policy Optimization (3PO) which use different sampling strategies and different rollout grouping for reward estimation. Experiments on Olmo-3-1025-7B and Qwen2.5-Math-7B across mathematical reasoning and code generation tasks show that these approaches can improve the average downstream performance over standard GRPO at a near-identical FLOPs cost. Moreover, using multiple parameter samples generally produces fewer zero-advantage groups and malformed or incorrect rollouts during training than GRPO and action-space baselines. Overall, our work presents evidence that parameter-space exploration can improve reinforcement learning for LLMs.

The Rectified Power Unit (RePU) activation function, a differentiable generalization of the Rectified Linear Unit (ReLU), has shown promise in constructing neural networks due to its smoothness properties. However, deep RePU networks often suffer from critical issues such as vanishing or exploding values during training, rendering them unstable regardless of hyperparameter initialization. Leveraging the perspective of effective field theory, we identify the root causes of these failures and propose the Modified Rectified Power Unit (MRePU) activation function. MRePU addresses RePU's limitations while preserving its advantages, such as differentiability and universal approximation properties. Theoretical analysis demonstrates that MRePU satisfies the criticality conditions in the limit of a small kernel, and a finite-kernel analysis yields an initialization rule for deep MRePU networks. Experiments on polynomial regression, physics-informed neural networks (PINNs) and real-world vision tasks show that MRePU networks initialized by this rule remain trainable at depths at which RePU networks fail, while their accuracy relative to standard activations depends on the task.

The Segment Anything Model (SAM) has revolutionized interactive segmentation through spatial prompting. While existing work primarily focuses on automating prompts in various settings, real-world annotation workflows involve iterative refinement where annotators observe model outputs and strategically place prompts to resolve ambiguities. Current pipelines typically rely on the annotator's visual assessment of the predicted mask quality. We postulate that a principled approach for automated interactive prompting is to use a model-derived criterion to identify the most informative region for the next prompt. In this work, we establish active prompting: a spatial active learning approach where locations within images constitute an unlabeled pool and prompts serve as queries to prioritize information-rich regions, increasing the utility of each interaction. We further present BALD-SAM: a principled framework adapting Bayesian Active Learning by Disagreement (BALD) to spatial prompt selection by quantifying epistemic uncertainty. To do so, we freeze the entire model and apply Bayesian uncertainty modeling only to a small learned prediction head, making intractable uncertainty estimation practical for large multi-million parameter foundation models. Across 16 datasets spanning natural, medical, underwater, and seismic domains, BALD-SAM demonstrates strong cross-domain performance, ranking first or second on 14 of 16 benchmarks. We validate these gains through a comprehensive ablation suite covering 3 SAM backbones and 35 Laplace posterior configurations, amounting to 38 distinct ablation settings. Beyond strong average performance, BALD-SAM surpasses human prompting and, in several categories, even oracle prompting, while consistently outperforming one-shot baselines in final segmentation quality, particularly on thin and structurally complex objects.

Quadratic ball discrepancy measures how uniformly a code meets Hamming balls over all centers and radii. Perfect codes minimize this quantity among codes of the same cardinality. We prove a quantitative refinement: at the parameters of every perfect code other than a one-word code or the full space, the discrepancy excess over the minimum is at least an explicit positive multiple of the discrepancy at the packing radius. The latter equals the tiling defect divided by the square of the code cardinality. This defect is the total squared deviation of the covering multiplicity from one. The comparison applies to all codes of that cardinality. For one-error perfect codes, the coefficient is at least one, and no larger constant holds for all such codes; explicit coefficients depending on the parameters can be much larger. The tiling defect also measures the failure of uniform ball noise to smooth a code distribution. Consequently, the same discrepancy excess gives explicit bounds on holes, overlaps, and divergence from the uniform distribution.

Several landmark oracle results (FOCS 2000, FOCS 2025, STOC 2026) establish strict separations along the chain $\mathsf{MA} \subseteq \mathsf{QCMA} \subseteq \mathsf{QMA}$, showing that quantum verification and quantum witnesses can each provide additional power over classical proof systems. These separations, however, use substantial coherent quantum computation, often through the quantum Fourier transform. We prove that a minimal quantum resource already suffices to outperform every classical verifier. Namely, we show the separation $$\mathsf{MA} \subsetneq \mathsf{StoqMA}$$ relative to a classical oracle. The class $\mathsf{StoqMA}$, introduced by Bravyi, Bessen, and Terhal (arXiv 2006), restricts the verifier to classical reversible computation, followed by a single Hadamard-basis measurement. Its power is closely tied to the complexity of stoquastic Hamiltonians, a sign-problem-free and seemingly more tractable class of quantum Hamiltonians. Our separating problem is to determine whether a sparse high-girth graph, given via an adjacency-list oracle, has a large or small Perron--Frobenius eigenvalue. This amounts to a ground-energy estimation task for a related stoquastic Hamiltonian. Our construction builds on a line of work on graph exploration problems with exponential quantum speedups, from welded trees (STOC 2003) to recent constructions (STOC 2021, arXiv 2026).

On-Policy Self-Distillation (OPSD) improves reasoning by training a student on its own reasoning, using the same model conditioned on reference solutions as a teacher. Applying OPSD to multilingual reasoning requires the teacher to provide useful feedback across languages, even when the student makes mistakes in intermediate steps. We observe a phenomenon we call Teacher Drift: as these mistakes accumulate, the teacher may follow the student's incorrect steps instead of correcting them. Our analysis shows that this shift tends to occur earlier in lower-resource languages. To account for these differences across languages, we propose Teachable On-Policy Self-Distillation (TOPSD), which determines where and whether teacher supervision should be applied to each reasoning trajectory. TOPSD uses teacher-student likelihood to estimate where drift begins and select a prefix for supervision. It then verifies whether the teacher can recover the correct answer from that prefix, applying distillation only to prefixes that pass verification. Experiments on multilingual mathematical reasoning across ten languages and three model scales show that TOPSD consistently outperforms conventional OPSD, particularly in low- and medium-resource languages.

This paper investigates a non-orthogonal multiple access assisted coordinated beam hopping (NOMA-CBH) scheme in multidimensional very low Earth orbit (VLEO) satellite communication systems, where multiple satellites employ CBH and coordinated beams jointly serve ground users and a dedicated ground station (GS). To characterize the VLEO-specific propagation environment, we develop a channel model that incorporates atmospheric attenuation, Doppler effects, and pointing perturbations. Building upon this architecture and channel model, a low-complexity decoupled (LCD) algorithm is designed to optimize beam scheduling and power allocation. We further derive closed-form outage probability expressions for the ground users and the GS, perform asymptotic analysis to characterize their diversity orders, and evaluate the delay-limited throughput. Simulation results demonstrate that: i) The NOMA-CBH with LCD algorithm achieves an enhanced system sum rate relative to orthogonal multiple access with coordinated beam hopping (OMA-CBH); ii) Across the considered heterogeneous traffic-demand operating points, the NOMA-CBH scheme achieves higher aggregate delivered traffic than the benchmark schemes; and iii) The outage performance of NOMA-CBH is better than that of OMA-CBH.

Wi-Fi human pose estimation requires high-rate channel state information (CSI), making communication a bottleneck when sensing is offloaded from resource-constrained devices. Effective compression must therefore preserve pose information while accommodating different communication budgets. We present TinySense+, an efficient compression framework for scalable Wi-Fi-based human sensing with entropy-aware transmission and test-time rate adjustment. The framework uses a vector-quantized generative adversarial network to encode CSI into discrete latent indices shared between an edge device and a server. A causal Transformer predicts conditional index probabilities for arithmetic coding, while a differentiable rate-distortion objective balances expected code length, CSI reconstruction, and pose accuracy. Prefix-conditioned latent completion reuses the entropy model to infer an omitted suffix, allowing the transmitted prefix length to change without retraining the encoder. We evaluate the framework on MM-Fi and WiPose datasets and prototype it on Raspberry Pi and Jetson Nano devices connected to an RTX 8000 server. On MM-Fi, entropy coding reduces the baseline cost from 8.00 to 4.82 bits per index without changing pose accuracy. Rate-aware training further reduces this cost to 3.21 bits per index and improves PCK20 from 41.21% to 44.01%. Results also show that transmitting half of the latent sequence retains a PCK20 of 40.36%. The evaluated operating range reaches a compression ratio of 5840 with PCK20 = 37.92%. These results show that optimizing latent predictability alongside sensing fidelity provides a useful communication-accuracy trade-off for edge-server Wi-Fi sensing.

Bilateral trade models the task of intermediating between two strategic agents, a seller and a buyer, willing to trade a good for which they hold private valuations. We study this problem from the perspective of a profit-maximizing broker in a regret minimization framework. At each time step, a new seller and buyer arrive and the broker proposes a trading price to each agent. The trade happens if both agents accept, and the profit of the broker is the difference between the price received from the buyer and the one paid to the seller. At the end of each interaction, the learner only observes whether the trade occurred, and its goal is to achieve sublinear regret relative to the best fixed pair of prices in hindsight. We start by investigating the adversarial version of the problem, where buyer and seller valuations are generated by an adversary. In this setting, we construct a polynomial-time learning algorithm with a $\tilde O(T^{\frac 23})$ regret rate, which is nearly tight even if the valuations are drawn i.i.d. from independent distributions, thus matching the rate for one-sided pricing. Our adversarial algorithm combines a localized estimation procedure with an information-based minimax construction. We then consider valuations drawn i.i.d. from independent distributions satisfying the monotone-hazard-rate (MHR) property and provide a learning algorithm with nearly tight $\tilde{O}(\sqrt{T})$ regret. The algorithm combines localized estimation with a stochastic convex bandit routine applied to the negative logarithm of expected profit. Finally, we complement this result by showing a separation between MHR and regular distributions, proving that the minimax regret rate in the latter setting is $\tilde Θ(T^{\frac 35})$. This last result contrasts with the $\tilde{O}(\sqrt{T})$ regret bound that can be obtained for one-sided pricing with regular distributions.

A collection of classical codes $C_1,\dots,C_m$ has product expansion if every low-weight word in the sum of their extensions to the product space can be written as a sum of words supported on few lines, each line being a codeword of the corresponding $C_i$. For $m=2$ product expansion is equivalent to robust testability of the tensor code, while for $m\ge 3$ it is strictly stronger; it is the hypothesis on the local codes behind recent constructions of good quantum LDPC codes, good quantum locally testable codes, and quantum codes with transversal non-Clifford gates. No explicit family over a fixed field was previously known to achieve constant rate, linear distance for both the code and its dual, and 3-fold product expansion at growing length. We prove that for the one-point evaluation codes $C_i$ of length $N_i=728\cdot27^{\,i-1}$ and pole order $\lfloor N_i/5\rfloor$ on the Garcia--Stichtenoth tower over $\mathbb{F}_{729}$, the triple $(C_i,C_i,C_i)$ has product expansion with a constant independent of $i$. The dual codes $C_i^\perp$ then form an explicit fixed-field family of rate tending to $109/130$ and relative distance at least $8/65$. The proof is geometric: we view the words of the sum code as arrays on the product of three copies of the $i$-th curve of the tower, where the parity checks are sections of a line bundle. An exact generation theorem describes the sum-code words supported on the grid footprint of a suitable divisor. A support-localisation argument then shows that every low-weight array lies on such a divisor, after deleting a small number of coordinates. We also give a sufficient criterion for three-fold product expansion in terms of degree and genus ratios, yielding explicit families over every non-prime finite field of order at least $512$. The principal conclusions have been formally verified in Lean 4.

Scammers have increasingly adopted AI-driven capabilities, evolving from automated message generation to fully agentic conversational systems that scale operations and maximize the exploitation of fraudulent resources before detection and takedown. In parallel, agentic scambaiting has emerged as a defensive approach in which autonomous agents impersonate potential victims and engage scammers in sustained interactions to extract actionable threat intelligence, such as mule bank accounts and cryptocurrency wallet addresses, that can be reported to disrupt fraudulent infrastructures. Together, these developments transform online fraud into an adversarial socio-technical ecosystem in which autonomous scamming and scambaiting agents engage in deceptive interactions while competing over the discovery, preservation, and exploitation of one another's resources. A fundamental and largely unexplored question is how defensive scambaiting can remain effective in an agent-to-agent environment, and under what conditions either side gains a strategic advantage. In this paper, we present a formal model of agent-to-agent fraud interactions that captures the strategic decision spaces available to both attackers and defenders. Using this framework, we analyze the dynamics of engagement, resource consumption, belief adaptation, and disruption outcomes. We find that scammer profitability turns negative once baiting-agent prevalence exceeds certain thresholds, and that when both sides improve at the same pace, defender investment in mimicry quality outpaces equivalent gains in scammer detection capability, so the arms race favors the defender under our baseline parameters. Our model and findings provide insights into the stability, scalability, and long-term effectiveness of autonomous defensive agents in an evolving AI-mediated fraud landscape.

Wireless links deployed in orchards often exhibit significant variability in the strength of the received signal that is not adequately captured by classical distance-based propagation models. In row-structured olive groves, signal attenuation differs markedly between along-row and cross-row propagation directions, leading to discrepancies when using omnidirectional propagation assumptions such as those adopted in the Free Space Path Loss (FSPL) model or ITU-R vegetation loss formulations. This paper proposes a topology-based propagation model that explicitly accounts for orchard layout and the relative positions of radio devices within the plantation structure. Experimental validation was conducted using LoRa technology operating at 868 MHz, and the results were compared with established models from the literature and with the proposed two-dimensional model. The proposed approach achieves a closer fit to measured RSSI data than conventional models, providing a more reliable basis for link budgeting and network planning in structured agricultural environments.

Despite the numerous applications of convex constraints in Robotics, enforcing them within learning-based frameworks remains an open challenge. Existing techniques either fail to guarantee satisfaction at all times, or incur prohibitive computational costs. This paper presents RAYEN, a framework for imposing hard convex constraints on the output or latent variables of a neural network. RAYEN guarantees constraint satisfaction during both training and testing, for any input and any network weights. Unlike prior approaches, RAYEN avoids computationally expensive orthogonal projections, soft constraints, conservative approximations of the feasible set, and slow iterative corrections. RAYEN supports any combination of linear, convex quadratic, second-order cone (SOC), and linear matrix inequality (LMI) constraints, with negligible overhead compared to unconstrained networks. For instance, it imposes 1K quadratic constraints on a 1K-dimensional variable with only 8 ms of overhead compared to a network that does not enforce these constraints. An LMI constraint with 300x300 dense matrices on a 10K-dimensional variable can be guaranteed with only 12 ms additional overhead. When used in neural networks that approximate the solution of constrained trajectory optimization problems, RAYEN runs 20 to 7468 times faster than state-of-the-art algorithms, while guaranteeing constraint satisfaction at all times and achieving a near-optimal cost. Finally, we demonstrate RAYEN's ability to enforce actuator constraints on a learned locomotion policy by validating constraint satisfaction in both simulation and real-world experiments on a quadruped robot. The code is available at https://github.com/leggedrobotics/rayen

Brain foundation models have transformed medical artificial intelligence and computational neuroscience by reducing the reliance on task-specific data through large-scale pretraining. While they have been successful with non-invasive neuroimaging data, their adoption in functional near-infrared spectroscopy (fNIRS) has lagged due to the limited size and heterogeneity of public datasets, which are collected under varying protocols, devices, and sensor configurations. In addition, no single fNIRS dataset is comparable in size to the largest datasets in functional magnetic resonance imaging (fMRI), electroencephalography (EEG), or magnetoencephalography (MEG). The fNIRS datasets are also spread across different platforms and often have insufficient information, or lack the protocols that would make them easier to use. Given the advances in EEG foundation models that enable flexible modeling across diverse EEG montages, we curated 1,955 hours of fNIRS data from 67 public datasets spanning 2,798 participants, representing the largest fNIRS curation effort to date. The curated data include oxygenated (HbO) and deoxygenated (HbR) hemoglobin signals along with the three-dimensional position of every channel in the standard space of the Montreal Neurological Institute (MNI), which makes positions comparable across datasets. We release dataloaders that handle each dataset automatically, along with the minimal preprocessing pipeline used to prepare the data, at https://github.com/sposso/fnirs-datasets. This work aims to facilitate the future development of foundation models for fNIRS.

Large language models can reason over biological knowledge, but they are not naturally equipped to work with quantitative omics measurements. Existing approaches either convert expression profiles into long textual representations, often losing quantitative information, or connect omics encoders to language models for narrow tasks. We introduce Thalamus-Reasoning, a 9B multimodal language model that represents each bulk or single-cell transcriptome as a compact continuous embedding that can be interleaved with natural-language instructions and with other samples in the same context. A key contribution is a training corpus that connects experimental measurements with biological knowledge and task supervision. We combine templates linking transcriptomic profiles to annotations and experimental outcomes, reasoning examples connecting evidence across sources, and LLM-generated supervision with task-specific quality checks. The instruction-tuning corpus spans 157 biological and general-purpose task groups. Training includes continued pretraining on 20 billion tokens and supervised fine-tuning on 5.21 million conversations. We further introduce GEO-OmicsQA, a publication-disjoint benchmark of 3,000 questions requiring models to interpret and compare expression profiles from real GEO studies. Thalamus-Reasoning achieves the best results among the evaluated models on three of four held-out annotation tasks and on all six GEO-OmicsQA variants, and the best average performance among compared methods on PerturbQA perturbation-response prediction. Ablations show a clear advantage for continuous omics representations over a text-only gene-list representation. These results show that quantitative transcriptomic measurements and biological language can be integrated within a general conversational model, enabling both predictive tasks and language-guided interpretation of experimental samples.

Total quadratic ball discrepancy measures the deviation of codeword counts from uniformity over all Hamming balls. We prove that, whenever a Hamming space and cardinality admit a perfect code, the discrepancy minimizers among all subsets of that cardinality are precisely the perfect codes. This extends Barg's binary minimizing result and characterizes equality over arbitrary finite alphabets. At parameter sets that satisfy the sphere-packing condition and Lloyd's integral-root condition for correcting one or two errors, we give an explicit lower bound whose attainment is equivalent to perfect tiling: the discrepancy that a perfect code with these parameters would have. For one error, these include parameters at which the existence of a perfect code is open. For alphabets of size at least four, the discrepancy is an affine function of an energy with a strictly completely monotonic potential; for these alphabets, known universal energy bounds also give these lower bounds, and, when a perfect code exists, known universal optimality results also give the characterization of the minimizers. Over the ternary alphabet, complete monotonicity fails, and we prove the ternary bounds directly at all Hamming parameters and at the Golay parameters, the only nontrivial ternary cases.

Attention-based time series forecasters commonly group consecutive observations into patches. Patch length is known to have a substantial impact on forecasting performance, yet its selection remains largely empirical. We develop a theoretical framework that explains why patch length matters for forecasting accuracy and provides a principled basis for its selection. For linear state-space models, we derive an exact factorization of the forecasting coefficient matrix that separates forecast dynamics from filtering dynamics. We show that dominance of a single forecast component at long horizons does not generally imply a rank-one representation. This explains why longer horizons alone need not reduce representational complexity. We combine the factorization with estimation bounds to develop a patch-selection criterion that balances representation and estimation errors under temporal dependence. Our analysis establishes conditions under which balanced patching is justified and clarifies how predictive structure, head count, training sample size, and long-run dependence enter the selection criterion.