Papers

As networked dynamical systems grow in scale, distributed controller architecture design has become a critical issue. To address this, prior studies have incorporated the regularization for design (RFD) framework into system-level synthesis (SLS), focusing primarily on actuator and sensor placement. However, communication architectures also fundamentally impact the performance of distributed control, and scalable explicit co-design of the underlying communication topology within SLS remains challenging. This paper proposes a scalable convex framework for the co-design of communication architectures and distributed controllers within the SLS paradigm. We explicitly characterize a communication topology-induced feasible subspace of system responses, parameterized by the communication adjacency matrix and separate from the physical plant topology. By deriving a communication link norm from this characterized subspace, we formulate a convex SLS problem for communication architecture co-design. A proximal ADMM scheme is employed to appropriately decompose the optimization problem in a manner that preserves scalability to large networks. Numerical experiments validate the efficacy of the proposed framework in optimizing the trade-off between closed-loop performance and communication architecture complexity, while also confirming its scalability.

This work presents a fully analog memristive synaptic circuit for online spike-timing-dependent plasticity (STDP) learning in spiking neural networks (SNNs). The proposed synapse integrates a local STDP circuit generating gradual timing-dependent conductance updates directly from pre- and post-synaptic spikes. Learning occurs during normal network operation without requiring external digital control or explicit STDP waveform synthesis. Post-layout simulations of the memristive synapse implemented in a 130 nm CMOS technology show spike-timing-dependent conductance adaptation during SNN operation. A 2x2 SNN simulation further illustrates online neuron specialization through unsupervised learning.

Large Language Models (LLMs) primarily perform inference at the token level, resulting in substantial memory overhead and compromised computational efficiency. In this paper, we propose a Dynamic Semantic Extraction and Inference (DSEI) framework, which achieves segment-level inference within the latent space through a two-stage training strategy. First, we construct a Dynamic Semantic Autoencoder (DSAE) via self-supervised learning. DSAE dynamically extracts segment-level semantics and compresses them into compact latent representations via adaptive semantic weighting and gated fusion. Subsequently, we integrate the DSAE into the LLM architecture and train the model to infer over dense latent space. DSEI substantially reduces both input and generation sequences and significantly enhances inference efficiency. Extensive experiments conducted on the Wanjuan dataset demonstrate that DSEI reduces perplexity by 48% compared to static sentence-level latent inference baseline. Furthermore, compared to standard LLMs using token-level inference, DSEI accelerates inference speed by 2.5$\times$ and reduces memory overhead by 90%.

Multimodal retrieval integrates video, audio, subtitles, and text; however, recent geometric aggregators, such as Gramian volumes, hyperbolic volumes, and spectral objectives, treat all modalities symmetrically. Under a unified evaluation protocol, their joint scores frequently lag behind the strongest single-modality pathway by 1.9 to 27.6 R@1. Controlled analyses attribute this outcome to uniform modality influence. This work introduces Spherical Centroid Aggregation with Learned Adaptive Relevance (SCALAR), a query-conditioned aggregator that assigns relevance-based weights to each available modality before computing a spherical centroid. SCALAR accommodates arbitrary modality subsets and is trained on masked, reduced-arity views using rank-8 LoRA adapters. Across five benchmarks, SCALAR achieves positive aggregation gain on four, reaching +4.0 R@1, while none of the evaluated prior aggregators is positive on more than one. A uniform-weight ablation reproduces the degradation observed with symmetric aggregation. With only 4.8 million trainable parameters, SCALAR attains the highest text-to-video R@1 on three and performs within seed variation of the best result on a fourth. Under test-time modality dropout, SCALAR's representation-stage score surpasses the released GRAM checkpoint at every evaluated masking rate and benchmark by 3.2 to 10.9 R@1. Finally, as modalities are removed, rerankers trained exclusively on complete modality sets increasingly converge toward their video-only pathways, diminishing these representation-level gains and underscoring a limitation of standard two-stage retrieval pipelines.

Medical imaging modalities such as ultrasound and X-ray are widely used in clinical practice, where diagnosis follows a structured, evidence-driven workflow aligned with standardized criteria. While multimodal large language models (MLLMs) show promise for automated medical report generation, most existing systems rely on end-to-end multimodal fusion without modeling clinically defined intermediate attributes, leading to limited grounding and interpretability. To address this issue, we propose CORAL (COncept-grounded ReAsoning with Localization), a multimodal framework that integrates spatial grounding and concept-level supervision into a unified reasoning process. CORAL employs a prompt-driven medical segmentation model to localize lesions and predicts multi-class clinical attributes through a Concept Bottleneck module. The resulting textual concept tokens are combined with mask-modulated visual features within an MLLM to enable structured report generation and diagnostic prediction. Experiments on BUS-CoT and IU X-ray datasets demonstrate consistent improvements in diagnostic accuracy, concept consistency, and report quality over strong general-purpose and medical MLLMs, indicating that concept-grounded reasoning better aligns generation with clinical decision processes.

Complementary FETs (CFETs) extend nanosheet FET (NSFET) scaling by vertically stacking n- and p-type gate-all-around (GAA) devices, thereby shrinking standard-cell area. The performance gain, however, cannot be assessed from device metrics alone, as CFET layouts also introduce larger cell-level parasitic resistance and capacitance (RC). In this work, we present a physics-based thermal- and aging-aware system-technology co-evaluation (STCO) flow to assess parasitic RCs in A7 CFET and A10 NSFET technology nodes. Our flow links calibrated device models, optimized standard-cell generation, automated GDS-to-TCAD conversion enabling accurate 3D parasitic RC extraction, full RTL-to-GDS implementation for an AI accelerator, multiphysics thermal analysis, and physics-based bias temperature instability (BTI) aging evaluation. Using the same device model for both technologies, we can isolate the impact of parasitic RCs and design at different levels of the design flow. The results of the AI accelerator design demonstrate that the A7 CFET reduces the chip area by 24.7% and the total wire length by 12%, improving the area efficiency TOPS/mm^2 by 74% relative to the baseline of the A10 NSFET. Under iso-frequency operation, results reveal that CFET voltage scaling reduces power by 68% and lowers power density from 148 W/cm^2 to 55 W/cm^2, which reduces the chip's temperature from 125 degrees C down to merely 62 degrees C. The resulting reduction in stress temperature suppresses 10-year BTI-induced degradation by 39%, reducing the required aging timing guardband by 53%.

Pretrained driving vision-language models (VLMs) integrate visual, route, language, and driving context into rich driving priors, yet their representation objectives remain separated from continuous driving planning. Existing methods typically begin trajectory generation only after the VLM has formed a final condition, leaving depth-wise condition computation outside the stepwise formation of trajectory state. We introduce DiffAdapterVLA, which realizes Planning in the Backbone: it injects explicit trajectory tokens into selected VLM late layers, bringing trajectory state into backbone forward computation, where it co-evolves with driving conditions at different depths. Lightweight layer-wise DiffAdapters organize this computation into recursive trajectory refinement, while asymmetric joint attention preserves directed guidance from the condition stream to trajectory planning. By placing planning within existing backbone computation rather than relying on an independent trajectory planner, DiffAdapterVLA adapts only lightweight trajectory modules to turn existing driving priors into efficient continuous planning capability. NAVSIM results show that it achieves high-quality closed-loop planning with low end-to-end latency using few trainable parameters, and demonstrate that jointly evolving trajectory state and depth-wise driving conditions in VLM late-layer computation effectively realizes continuous trajectory planning.

Volume-based multimodal retrieval jointly scores a text query with a candidate's video, audio, and subtitle embeddings. While this approach captures higher-order within-candidate alignment, the score remains candidate-local, and semantically related training samples primarily serve as contrastive negatives. This work introduces Hypergraph-Regularized Gramian Volumes (HyVol), a training-time module that incorporates these semantic relations prior to evaluating the original volume loss. Document hyperedges connect the observed modalities of each candidate, whereas semantic hyperedges link candidates whose detached captions are mutual top-k neighbors. A shallow gated hyper-graph network applies residual corrections to the modality embeddings. Presence masks exclude unavailable streams from message passing, and identity padding preserves the determinant of the observed Gram submatrix without feature imputation. As refinement operates on embeddings rather than scores, the same construction applies to both Gram and HyperGram. We remove the hypergraph after training, leaving the backbone-only architecture, original scoring function, and retrieval cost unchanged. We train both backbones on a 150K-clip subset of VAST-27M and evaluate zero-shot performance on six benchmarks. Under the paired protocol, HyVol improves R@1 across all five retrieval benchmarks, with video-to-text gains reaching +8.3 on MSR-VTT and +7.6 on VATEX. Under missing-modality masking, the V2T margin remains positive in all experimental settings, although the T2V margin becomes slightly negative in four.

Frontier models score well on shallow document/chart reading tasks. In a controlled data-room audit, moving evidence into buried conditions reduced accuracy, increased forced declarations, increased tool calls, and increased cost per correct answer. Confidence and benchmark calibration did not fully capture wrong answers; a documented production incident shows fabricated structural claims can be mixed with accurate numeric tables. Agentic evaluations need claim-level receipts (statement-level provenance, not answer-level scores), condition-aware scoring, and human-adversarial verification - an auditing discipline, not a leaderboard. The setting we measure is financial due diligence; the setting we are building toward next is defense staff work, where the same buried-evidence shape appears. In both, the model is not a party to the consequences; the person who signs is. In plain terms: in the documented cases we examine, agents can pair accurate numbers with confident fabricated explanations, and the burden of proof must therefore move from the model to the evidence trail.

Recently, the use of Large Language Models (LLMs) for different tasks in the Electronic Design Automation (EDA) life-cycle has been studied extensively, but an integrated view is lacking. Specifications are the foundation of this life-cycle, but they suffer from ambiguity when written in natural language, which especially affects the quality of LLM output. Formal specifications mitigate these ambiguities, but they come with their own challenges. On the other hand, Controlled Natural Language (CNL) specifications can serve as a middle-ground, reducing ambiguity while retaining interpretability. In this work, we propose an integrated view on the use of LLMs for EDA and establish an LLM-enabled behavior driven hardware development workflow. We introduce and define Formal Verification Gherkin Scenarios (FV Gherkin Scenarios), unlocking CNL specifications as the foundation for formally verified hardware designs via Formal Property Verification (FPV). Experimental evaluation shows that our workflow is able to outperform other established LLM-based methods by 2.48x in functional correctness of generated Register Transfer Level (RTL) designs and by 2.54x in formal coverage of generated assertions for FPV.

Safe reinforcement learning (RL) is commonly formalized as a Constrained Markov Decision Process (CMDP), in which an agent maximizes expected reward while keeping its expected cumulative cost below a specified safety bound. Existing safe RL benchmarks predominantly report whether an algorithm is safe on average, following this expectation-based guarantee. We argue that this convention is insufficient to reliably characterize an algorithm's true safety: it fails to capture how often and how severely the safety bound is violated, whether this holds consistently across tasks and safety bounds, and whether training-time behavior is representative of behavior of the final converged policy. Therefore, we introduce (i) evaluation metrics for safe RL that address each of these concerns and in addition allow for aggregation across tasks and safety bounds. We furthermore define (ii) a safety tier system to systematically categorize and compare algorithms in terms of safety and reliability at both training and for a final policy. Using this framework, we provide (iii) an empirical safety evaluation across multiple safety navigation tasks. Our results show that aggregate metrics, distributional reporting, and task- and safety bound-specific results each reveal information the other metrics cannot. We therefore recommend reporting all three jointly, rather than compressing this information into a single value, as is common practice. We provide SafeRLEval, an open-source evaluation suite to support the reliable characterization of safety in future safe RL research.

We introduce the Universe of Universes (UoU) framework, which treats the full ecosystem of major large language models (LLMs) as a structured retrieval corpus and proposes a compositional Automated Reasoning (AR) and Machine Learning (ML) architecture for cross-model retrieval-augmented generation. The central contribution is the formal characterization of the Benefit Yield Function (BYF), the marginal performance gain per additional model added to an ensemble, and the identification of the implosion threshold {\theta}*: the ensemble size at which BYF crosses zero and aggregate performance begins to degrade. Existing LLM ensemble and mixture-of-agents systems treat models as responders and aggregate outputs, but do not study performance as a function of ensemble size N across the full model universe. Benchmark research confirms performance plateaus at the individual model level; model collapse literature establishes that iterative training on AI-generated outputs degrades individual model distributions. Neither body of work formalizes the ensemble-level implosion threshold, models Epistemic Hereditary Drift (EHD) at the ecosystem level, or treats AI manufacturing velocity as a co-variable of {\theta}*. The framework has direct implications for DoD multi-model AI acquisition policy and the emerging science of testing AI-enabled systems.

Autoregressive generation of interleaved text and acoustic tokens is a common approach to spoken-response generation in speech large language models. Although this design enables streaming generation with explicit textual guidance, generated acoustic tokens become part of the context for subsequent text predictions. Given identical speech inputs, we observe markedly lower answer accuracy for the internal text generated in speech-to-text-and-speech (S2TS) mode than for speech-to-text (S2T) responses. We term this discrepancy the output-mode gap (OMG). To reduce OMG, we propose Joint-Output On-Policy Distillation (JO-OPD), which distills the model's stronger S2T policy into joint generation using student-generated S2TS trajectories. At each text position, the S2T teacher provides soft targets from a text-only projection of the student's preceding outputs, while the student predicts from the corresponding full interleaved history. A preservation objective further regularizes native non-text predictions. Experiments on Step-Audio-2-mini and Baichuan-Audio-Instruct reveal OMG across two interleaved generation architectures. On Step-Audio-2-mini, JO-OPD reduces OMG from 42.87 to 16.26 percentage points on Spoken-MQA and from 29.72 to 13.04 points on speech-rendered GSM8K, with little change in S2T accuracy and substantially larger reductions than matched SFT baselines. ASR-based evaluation further shows a 7.49-point improvement in spoken-answer accuracy on Spoken-MQA.

Katz et al. (CANS'17) introduced Subset Predicate Encryption (SPE). This scheme is a generalization of broadcast encryption as it emulates the subset containment predicate in the encrypted domain. They proposed two selectively IND-CPA secure SPE constructions in the small universe setting. They also showed some black-box transformations of SPE to well-known primitives like WIBE and ABE to establish the richness of the SPE structure. Chatterjee and Mukherjee (RSA'19) proposed two SPE constructions in the large-universe setting. Their first construction achieved constant-size ciphertexts and secret keys, but it is proven secure in a restricted version of selective security. Although the second construction achieves adaptive security, the ciphertext size depends on the size of the data-attribute set. Furthermore, neither of these two constructions achieves CCA security. In this work, we propose the first large-universe CCA-secure subset predicate encryption with constant-size ciphertext and secret keys. We prove this construction achieves standard selective security under the standard subgroup decision problems. Finally, we transform our extremely efficient SPE into the first CCA-secure WIBE, WKD-IBE, etc., with constant-size ciphertexts and secret keys via black-box transformations.

As AI becomes increasingly ubiquitous, modern AI systems are shaped by a tight software-hardware co-design loop. Later GPUs expose features such as asynchronous data movement, tensor core pipelines, and fine-grained synchronization that high-performance kernels aggressively exploit, while emerging application behaviors increasingly influence the next generation of hardware design. Unfortunately, the latest open-source simulators for NVIDIA GPUs focus on architectures and software stacks from roughly six years ago. Therefore, they cannot support many state-of-the-art AI kernels generated by modern compiler stacks, e.g. Triton, or accurately model the hardware features they depend on. As a result, architects lack a credible platform for analyzing bottlenecks in this flywheel or evaluating design trade-offs for future AI systems. To bridge this gap, we present FlashGPU-sim, an open-source, execution-driven, cycle-accurate GPU simulator for modern AI workloads. FlashGPU-sim faithfully models modern hardware features such as asynchronous data movement, fine-grained synchronization, tensor-core execution, and distributed shared memory. A Triton extraction front-end allows direct simulation of optimized AI operators without manual porting, while multi-threaded execution makes large-scale software-hardware co-design practical. Across 131 workload configurations on RTX 5090, H100, and B200, FlashGPU-sim achieves a cycle-level MAPE of 5.24%, while multi-threaded simulation reaches a 7.86x speedup with 16 host threads. An H100 case study further demonstrates its utility for microarchitectural design exploration.

Large language model (LLM) agents allocate test-time compute adaptively as they revise solutions, use tools, explore alternatives, and decide when to stop. This test-time strategy makes it difficult to measure how agent performance scales. We study open-ended tasks that provide continuous scores for intermediate submissions, making progress observable throughout long trajectories. We propose Elo-per-token analysis, which tracks the best solution found at each token budget and uses a Bradley-Terry model to aggregate within-task orderings into Elo ratings across tasks with different score scales. We apply it to four general-purpose agents on four open-ended benchmarks, with sessions of up to 100M tokens, and to three feedback-driven LLM optimization harnesses in controlled single-task interventions. Independent sampling provides a theoretically characterized reference, for which Elo grows linearly with log compute. Against this reference, agents can initially convert tokens into Elo faster than independent sampling, but their marginal gains diminish and eventually fall below the reference. In contrast, the strongest historical human contestants improve superlinearly over contest time on shared AtCoder Heuristic Contest tasks, providing evidence of continual learning and substantial headroom after agents slow down. We define the scaling inflection point as the per-session budget where marginal Elo gains match the independent-sampling reference. Using this point as the per-session budget, we split 100M tokens across parallel sessions on FrontierCS Polyomino Packing, gaining +264 Elo over one long session and +355 over ten short sessions.

We present a deterministic machine-learning method for denoising candidate signals from all-sky searches for continuous gravitational waves from rotating neutron stars. Using the time-domain $F$-statistic search pipeline, we post-process the resulting $F(f,\dot{f})$ candidate patterns with iterative $\alpha$-(de)blending, a deterministic diffusion-type generative model implemented as a U-Net, well suited to the non-Gaussian, correlated noise of the $F$-statistic output. Two models, trained on data based on simulated 6- and 12-day time-domain segments with software-injected signals similar to the LVK hardware injections, are tested by comparing deblended images to the library of expected signal patterns via the Structural Similarity Index Measure. In general the method recovers the correct sky-position-dependent pattern for signal-to-noise ratios $\rho \gtrsim 4$, moderately below typical all-sky detection thresholds, with recovery depending strongly on pattern morphology, demonstrating that deterministic diffusion-based denoising may serve as a consistency/veto tool ahead of the semi-coherent coincidence stage. We also discuss limitations and possible improvements of the method.

Graphical User Interface (GUI) grounding is essential for autonomous agents to map natural language instructions to precise screen coordinates. However, existing supervised fine-tuning and reinforcement learning methods are constrained by the high cost of annotation, creating a scalability bottleneck. In this paper, we introduce a label-free test-time training paradigm driven by two key insights: (1) confidence patterns in coordinate tokens are a better indicator than full-sequence confidence, and (2) in sparse GUI coordinate spaces, negative samples offer more reliable learning signals than potentially noisy positive ones. We first propose Confidence-Anchored Learning (CAL), which utilizes coordinate-token confidence to filter pseudo-labels and assign distance-based binary rewards. Building on this, we develop Confidence-Anchored Negative Learning (CANL), which exclusively optimizes the model using negative samples to bypass the risks of incorrect positive samples. Experimental results demonstrate that CANL-7B achieves 92.1% on ScreenSpot-V2. On more challenging ScreenSpot-Pro, CANL-7B reaches 33.8%, an 8.9% absolute improvement over the base model. Our findings establish coordinate-token confidence as a powerful alternative to manual annotations for scalable GUI agent development.

Urban region representation learning commonly combines heterogeneous data sources, such as mobility flows, points of interest, and land-use information, to support tasks including mobility analysis, public safety forecasting, and service demand estimation. Existing multi-view methods typically improve region embeddings by strengthening interactions across views. However, such methods often overlook view-specific regional structures and may propagate correlations induced by shared latent factors, which can reduce the stability of downstream predictions. To overcome this major limitation, we propose CURE, a confounder-aware framework for multi-view urban region representation learning. CURE first encodes each view with its regional graph structure, estimates a shared latent component, and then reduces its projected influence before cross-view interaction. A hierarchical graph-aware fusion module subsequently aggregates the residual view representations using local and global regional contexts Experiments on three real-world cities show that CURE improves predictive performance, remains robust under missing and noisy input views, and provides reliable cross-view integration through shared component separation and context-dependent view weighting.

In order to make Reinforcement Learning algorithms applicable in real world scenarios, safety must be ensured even under adverse operating conditions. In this work, we consider the challenge of adversarial feature missingness: a scenario in which an adversary occludes features from the agent's observation in order to reduce performance as much as possible. We formally define adversarial missingness for Reinforcement Learning and compare it to the related concepts of $\ell_\infty$-norm bounded adversarial perturbations and learning with missing data. We develop an adversarial training algorithm and show its effectiveness in increasing robustness against adversarial missingness on three MuJoCo benchmark environments. Compared to a baseline trained with random uniform missingness, our method achieves better robustness on all three tasks.

Universal multimodal embedding (UME) maps multimodal inputs into a shared embedding space for diverse retrieval tasks. Recent methods improve embeddings through Chain-of-Thought (CoT) reasoning optimized with GRPO using retrieval rewards. However, existing methods overlook the mismatch bettween candidate-aware retrieval supervision and input-only CoT generation: (1)trajectory-level rewards convey retrieval outcomes without explicitly identifying the input-supported evidence that distinguishes the positive from hard negatives; (2) input-only generation cannot directly assess whether further reasoning improves retrieval, potentially producing redundant CoTs with substantial latency. To bridge this gap, we propose Reason What Matters (ReWAM), a retrieval-grounded framework that aligns candidate-aware supervision with input-only generation. Specifically, we introduce Retrieval-Aware Self-Distillation (RASD), which extracts privileged guidance from input-supported facts and evidence distinguishing the positive from hard negatives. Conditioned on this guidance, an on-policy self-teacher provides token-level feedback to refine credit assignment, directing policy updates toward retrieval-relevant reasoning grounded in the input. We further propose Retrieval-Adaptive Inference (RAI), which learns a retrieval-aware stopping criterion from prefix-level retrieval feedback. It stops redundant reasoning without candidate access and uses speculative decoding to further reduce CoT latency. Extensive experiments on MMEB-V2 and MRMR demonstrate that ReWAM achieves state-of-the-art retrieval performance while delivering up to 5x the inference throughput of competitive explicit-CoT UME methods. ReWAM thus enables high-quality retrieval through efficient input-only reasoning, making explicit CoT practical for corpus-scale multimodal retrieval. The code will be publicly available.

Binding the audit flag in Reflexion-style agents — without changing the auditor — reduces attack success rate substantially, reaching near zero on models whose flags parse cleanly. This single control-flow change exposes the enforcement gap: the controller receives a safety flag and executes anyway. Separating detection probability $p_d$ from enforcement probability $p_e$ establishes that $p_e \approx 0$ by default across every framework we tested, making detection quality formally irrelevant to security when enforcement is absent — a finding consistent with the spontaneous collapses recorded in unsupervised frontier-agent deployments~\citep{emergence2026}. Residual attack success concentrates where flags are unparseable or auditors leak; an RL-trained enforcement controller handles hedged and malformed verdicts that rule-based parsing cannot, cutting ambiguous-critique failure to a fraction of the rule-based baseline. Concurrent filtering and information-flow defenses address detection, not enforcement, leaving the binding constraint untouched. The Audit Enforcement Specification (AES) packages three concrete requirements that close each residue independently; each primitive is adoptable without redesigning the host framework, and no deployed framework currently implements any of them.

Automatic Item Generation (AIG) is pivotal for personalized education, yet guaranteeing the pedagogical value of generated items remains a bottleneck. Existing Item Quality Assessment (IQA) methods typically rely on unscalable manual reviews or shallow stem-based metrics, failing to capture the reasoning process required for mathematical problem-solving. To bridge this gap, this paper proposes Process-based Item Quality Assessment (ProIQA), a process-aware framework for fine-grained quality assessment of math items. We first formulate IQA across three heterogeneous dimensions, including knowledge concepts, difficulty, and disciplinary competencies, under a unified process-aware perspective. Based on this formulation, we construct a process-enhanced IQA resource by augmenting original item data with structured reasoning trees derived from raw solutions. Technically, ProIQA leverages Large Language Modelsto construct hierarchical reasoning trees and employs Graph Neural Networks (GNN) to encode their topological dependencies and procedural semantics. The resulting solving representation is fused with stem semantics through a dual-view (“Stem + Solving”) architecture, enabling comprehensive assessment across learning objectives. Extensive experiments on K12 mathematical datasets show that ProIQA effectively captures process-oriented features, offering a scalable data-driven solution for evaluating AIG outputs in intelligent education systems.

Artificial intelligence threatens to outrun human understanding and control. New mathematics is needed to design AI that is legible, steerable, and cooperative with humanity. I organize this invitation by mathematical field, so you can turn straight to your own: logic and game theory for cooperation; probability for agency and world-models; algebra and representation theory for learned features; analysis and geometry for generalization and training dynamics. Each section ends with an open problem that is accessible to a working mathematician with no prior experience in AI safety.

Amyotrophic lateral sclerosis (ALS) is a progressive neurodegenerative disease in which early assessment remains challenging, particularly in low-resource settings where MRI is often unavailable. High-resolution ultrasound (HRUS) of the tongue offers a portable and low-cost alternative for evaluating bulbar involvement, but learning reliable diagnostic models is limited by small datasets and the difficulty of extracting robust representations from ultrasound alone. We propose AlignUS, a cross-modal knowledge distillation framework that transfers anatomical knowledge from MRI to a HRUS-based classifier while requiring only HRUS at inference time. The model combines classification loss, supervised contrastive learning, and feature-level distillation to align HRUS representations with MRI embeddings. AlignUS achieves a patient-level balanced accuracy of 0.958, macro-F1 of 0.963, and ROC-AUC of 0.990, aggregated across four patient-level cross-validation folds, with consistent improvements over HRUS baselines and cross-modal alternatives. These results demonstrate that MRI-derived supervision can substantially improve ultrasound-based ALS assessment while preserving low-cost, inference-time independence from MRI.

Missing values are ubiquitous in heterogeneous data mining, where numerical, categorical, and binary variables often coexist. Many imputation methods, especially diffusion-based ones, treat discrete variables through continuous surrogates such as one-hot relaxations rather than modeling them natively. This creates a mismatch between the model state space and the mixed discrete and continuous structure of the data. We propose Impute-EM, an Expectation Maximization style framework that alternates between imputing missing entries with the current model and refitting a diffusion backbone on completed data. We instantiate Impute-EM with native mixed-state diffusion backbones for heterogeneous data, combining Gaussian and masked categorical components without one-hot relaxations. In exact settings, we characterize the update and show that the observed mask-indexed marginals match the targets at the limit, while making explicit that the full data distribution is generally non-identifiable from incomplete observations alone. Empirically, Impute-EM delivers the best distributional fidelity on mixed-type tabular imputation, on which downstream modeling relies, with text imputation serving as a controlled validation of the native discrete backbone.

We introduce a fully–discrete variational approximation of Mather measures and sets for Tonelli Lagrangians on the flat torus, together with a numerical procedure for approximating the entire Mather set. The scheme is based on a fully–discrete Lax–Oleinik operator with integer winding labels. We prove an $O(\tau+h/\tau)$ error estimate for the critical value, convergence of critical solutions, and a finite-dimensional characterization of fully–discrete Mather measures. Accumulation points of the reconstructed minimizing measures are continuous Mather measures, while the supports satisfy complementary upper and lower convergence results involving the Mañé and Mather sets. To avoid the selection of only some minimizing components by exact discrete minimizers, we introduce a mass-threshold approximation based on almost-minimizing holonomic measures. This yields a finite-dimensional constrained optimization procedure designed to recover the whole Mather set.

We investigate the $k$-variation bounding property of the discrete-time Hankel operator, i.e., its invariance under the set of signals with a variation (number of sign changes) of at most $k$. Building on existing sign-consistency criteria, it is shown that this property is equivalent to the external positivity of $k+1$ explicitly realized linear discrete-time systems. Thus, making the property tractable via numerical and analytic certificates. We also derive dominant-pole restrictions for the case of $k=1$. A three-node thermal example illustrates the results and distinguishes variation bounding from variation diminishing.

Entrepreneurial cognition is a foundation of entrepreneurship research. Yet the growing involvement of large language models (LLMs) in entrepreneurial work extends the cognition question beyond human actors to systems whose internal representations remain largely unexplored. We introduce artificial entrepreneurial cognition, the functional organisation of entrepreneurship-relevant representations and computations inside artificial intelligence (AI) systems. We bring mechanistic interpretability into entrepreneurship research through representation engineering. Focusing on opportunity recognition (OR), we construct 636 matched OR-present and OR-absent scenario pairs and recover an OR direction in Llama 3.1 8B-Instruct. Rather than infer the construct from outputs, we intervene directly on this direction, steering the model up and down along what we call the opportunity recognition dial, and its opportunity judgments shift with it. To our knowledge, this is the first causal intervention on an internal representation of an entrepreneurship construct inside an LLM. Held-out tests, lexical and topical controls, behavioural ablation, and geometric comparisons show that the direction is recoverable, consequential, and distinct from the opportunity evaluation and exploitation directions, although steering it also shifts judgments about these neighbouring stages. Recovery, signed steering, and geometric separation hold across four additional LLMs spanning different scales and families. These results give the contested distinction between opportunity recognition and evaluation a concrete representational form inside AI systems. More broadly, they establish internal representations as a new object of entrepreneurship inquiry and show how entrepreneurship theory can guide their identification, causal manipulation, and interpretation.

This paper presents a low-clearance hinge joint mechanism based on the 3D printing on sheet fabrication method. This approach simplifies the fabrication of hinge mechanisms and overcomes limitations of conventional origami manufacturing by eliminating the need for adhesives commonly used during assembly, making it suitable for robots at the tens-of-centimeters scale. The advantages and disadvantages of three types of hinge joint mechanisms are compared, and a hinge joint that can be designed with low clearance for various facet thicknesses is selected. Based on the selected hinge joint, the twisting angle and bending force are analyzed, leading to the implementation of a clearance of 0.1 mm. Torsional resistance is experimentally evaluated to measure the torque required for twisting caused by plastic deformation and clearance. The results show that the torque associated with plastic deformation is sufficient to constrain the undesired degrees of freedom of the hinge joint, while the torque required for twisting due to clearance is minimal. Based on the analyzed data, the proposed hinge joint mechanism is applied to a 3-degree-of-freedom delta robot manipulator, demonstrating precise motion with low clearance.