We dream of a future where point clouds from all domains can come together to shape a single model that benefits them all. Toward this goal, we present Utonia, a first step toward training a single self-supervised point transformer encoder across diverse domains, spanning remote sensing, outdoor LiDAR, indoor RGB-D sequences, object-centric CAD models, and point clouds lifted from RGB-only videos. Despite their distinct sensing geometries, densities, and priors, Utonia learns a consistent representation space that transfers across domains. This unification improves perception capability while revealing intriguing emergent behaviors that arise only when domains are trained jointly. Beyond perception, we observe that Utonia representations can also benefit embodied and multimodal reasoning: conditioning vision-language-action policies on Utonia features improves robotic manipulation, and integrating them into vision-language models yields gains on spatial reasoning. We hope Utonia can serve as a step toward foundation models for sparse 3D data, and support downstream applications in AR/VR, robotics, and autonomous driving.

Many essential manipulation tasks - such as food preparation, surgery, and craftsmanship - remain intractable for autonomous robots. These tasks are characterized not only by contact-rich, force-sensitive dynamics, but also by their "implicit" success criteria: unlike pick-and-place, task quality in these domains is continuous and subjective (e.g. how well a potato is peeled), making quantitative evaluation and reward engineering difficult. We present a learning framework for such tasks, using peeling with a knife as a representative example. Our approach follows a two-stage pipeline: first, we learn a robust initial policy via force-aware data collection and imitation learning, enabling generalization across object variations; second, we refine the policy through preference-based finetuning using a learned reward model that combines quantitative task metrics with qualitative human feedback, aligning policy behavior with human notions of task quality. Using only 50-200 peeling trajectories, our system achieves over 90% average success rates on challenging produce including cucumbers, apples, and potatoes, with performance improving by up to 40% through preference-based finetuning. Remarkably, policies trained on a single produce category exhibit strong zero-shot generalization to unseen in-category instances and to out-of-distribution produce from different categories while maintaining over 90% success rates.

Achieving autonomous and versatile whole-body loco-manipulation remains a central barrier to making humanoids practically useful. Yet existing approaches are fundamentally constrained: retargeted data are often scarce or low-quality; methods struggle to scale to large skill repertoires; and, most importantly, they rely on tracking predefined motion references rather than generating behavior from perception and high-level task specifications. To address these limitations, we propose ULTRA, a unified framework with two key components. First, we introduce a physics-driven neural retargeting algorithm that translates large-scale motion capture to humanoid embodiments while preserving physical plausibility for contact-rich interactions. Second, we learn a unified multimodal controller that supports both dense references and sparse task specifications, under sensing ranging from accurate motion-capture state to noisy egocentric visual inputs. We distill a universal tracking policy into this controller, compress motor skills into a compact latent space, and apply reinforcement learning finetuning to expand coverage and improve robustness under out-of-distribution scenarios. This enables coordinated whole-body behavior from sparse intent without test-time reference motions. We evaluate ULTRA in simulation and on a real Unitree G1 humanoid. Results show that ULTRA generalizes to autonomous, goal-conditioned whole-body loco-manipulation from egocentric perception, consistently outperforming tracking-only baselines with limited skills.

The ability to conduct and learn from interaction and experience is a central challenge in robotics, offering a scalable alternative to labor-intensive human demonstrations. However, realizing such "play" requires (1) a policy robust to diverse, potentially out-of-distribution environment states, and (2) a procedure that continuously produces useful robot experience. To address these challenges, we introduce Tether, a method for autonomous functional play involving structured, task-directed interactions. First, we design a novel open-loop policy that warps actions from a small set of source demonstrations (<=10) by anchoring them to semantic keypoint correspondences in the target scene. We show that this design is extremely data-efficient and robust even under significant spatial and semantic variations. Second, we deploy this policy for autonomous functional play in the real world via a continuous cycle of task selection, execution, evaluation, and improvement, guided by the visual understanding capabilities of vision-language models. This procedure generates diverse, high-quality datasets with minimal human intervention. In a household-like multi-object setup, our method is the first to perform many hours of autonomous multi-task play in the real world starting from only a handful of demonstrations. This produces a stream of data that consistently improves the performance of closed-loop imitation policies over time, ultimately yielding over 1000 expert-level trajectories and training policies competitive with those learned from human-collected demonstrations.

The visual world offers a critical axis for advancing foundation models beyond language. Despite growing interest in this direction, the design space for native multimodal models remains opaque. We provide empirical clarity through controlled, from-scratch pretraining experiments, isolating the factors that govern multimodal pretraining without interference from language pretraining. We adopt the Transfusion framework, using next-token prediction for language and diffusion for vision, to train on diverse data including text, video, image-text pairs, and even action-conditioned video. Our experiments yield four key insights: (i) Representation Autoencoder (RAE) provides an optimal unified visual representation by excelling at both visual understanding and generation; (ii) visual and language data are complementary and yield synergy for downstream capabilities; (iii) unified multimodal pretraining leads naturally to world modeling, with capabilities emerging from general training; and (iv) Mixture-of-Experts (MoE) enables efficient and effective multimodal scaling while naturally inducing modality specialization. Through IsoFLOP analysis, we compute scaling laws for both modalities and uncover a scaling asymmetry: vision is significantly more data-hungry than language. We demonstrate that the MoE architecture harmonizes this scaling asymmetry by providing the high model capacity required by language while accommodating the data-intensive nature of vision, paving the way for truly unified multimodal models.

Human mobility trajectories are widely studied in public health and social science, where different demographic groups exhibit significantly different mobility patterns. However, existing trajectory generation models rarely capture this heterogeneity because most trajectory datasets lack demographic labels. To address this gap in data, we propose ATLAS, a weakly supervised approach for demographic-conditioned trajectory generation using only (i) individual trajectories without demographic labels, (ii) region-level aggregated mobility features, and (iii) region-level demographic compositions from census data. ATLAS trains a trajectory generator and fine-tunes it so that simulated mobility matches observed regional aggregates while conditioning on demographics. Experiments on real trajectory data with demographic labels show that ATLAS substantially improves demographic realism over baselines (JSD $\downarrow$ 12%--69%) and closes much of the gap to strongly supervised training. We further develop theoretical analyses for when and why ATLAS works, identifying key factors including demographic diversity across regions and the informativeness of the aggregate feature, paired with experiments demonstrating the practical implications of our theory. We release our code at https://github.com/schang-lab/ATLAS.

Many complex systems and datasets are characterized by multiway interactions of different categories, and can be modeled as edge-colored hypergraphs. We focus on clustering such datasets using the NP-hard edge-colored clustering problem, where the goal is to assign colors to nodes in such a way that node colors tend to match edge colors. A key focus in prior work has been to develop approximation algorithms for the problem that are combinatorial and easier to scale. In this paper, we present the first combinatorial approximation algorithm with an approximation factor better than 2.

Tiered memory architectures have gained significant traction in the database community in recent years. In these architectures, the on-chip DRAM of the host processor is typically referred to as local memory, and forms the primary tier. Additional byte-addressable, cache-coherent memory resources, collectively referred to as remote memory (RMem, for short), form one or more secondary tiers. RMem is slower than local DRAM but faster than disk, e.g., NUMA memory located on a remote socket, chiplet-attached memory, and memory attached via high-performance interconnect protocols, e.g., RDMA and CXL. In this paper, we discuss how traditional two-tier (DRAM-Disk) virtual-memory assisted Buffer Management techniques generalize to an $n$-tier setting (DRAM-RMem-Disk). We present vmcache$^n$, an $n$-tier virtual-memory-assisted buffer pool that leverages the virtual memory subsystem and operating system calls to migrate pages across memory tiers. In this setup, page migration can become a bottleneck. To address this limitation, we introduce the move_pages2 system call that provides vmcache$^n$ with fine-grained control over the page migration process. Experiments show that vmcache$^n$ can achieve up to 4$\times$ higher query throughput over vmcache for TPC-C workloads.

Mobile devices are frequent targets of eCrime threat actors through SMS spearphishing (smishing) links that leverage Domain Generation Algorithms (DGA) to rotate hostile infrastructure. Despite this, DGA research and evaluation largely emphasize malware C2 and email phishing datasets, leaving limited evidence on how well detectors generalize to smishing-driven domain tactics outside enterprise perimeters. This work addresses that gap by evaluating traditional and machine-learning DGA detectors against Gravity Falls, a new semi-synthetic dataset derived from smishing links delivered between 2022 and 2025. Gravity Falls captures a single threat actor's evolution across four technique clusters, shifting from short randomized strings to dictionary concatenation and themed combo-squatting variants used for credential theft and fee/fine fraud. Two string-analysis approaches (Shannon entropy and Exp0se) and two ML-based detectors (an LSTM classifier and COSSAS DGAD) are assessed using Top-1M domains as benign baselines. Results are strongly tactic-dependent: performance is highest on randomized-string domains but drops on dictionary concatenation and themed combo-squatting, with low recall across multiple tool/cluster pairings. Overall, both traditional heuristics and recent ML detectors are ill-suited for consistently evolving DGA tactics observed in Gravity Falls, motivating more context-aware approaches and providing a reproducible benchmark for future evaluation.

Post-AGI information systems won't merely distract governance from important problems. They will systematically transform how institutions make decisions in ways that progressively remove humans from meaningful participation in resource allocation. We show that policy myopia -- the tendency to prioritize visible crises over invisible structural risks -- is not a symptom of poor attention management but a mechanism producing irreversible human disempowerment. Through three entangled mechanisms (salience capture displaces consequentialist reasoning, capacity cascade makes recovery structurally infeasible, value lock-in crystallizes outdated preferences), policy myopia couples with institutional dynamics to create a self-reinforcing equilibrium where human disempowerment becomes the rational outcome of institutional optimization. We formalize these mechanisms through coupled dynamical systems modeling and demonstrate through numerical simulation that these mechanisms operate simultaneously across economic, political, and cultural systems, amplifying each other through feedback loops.

We present DuoMo, a generative method that recovers human motion in world-space coordinates from unconstrained videos with noisy or incomplete observations. Reconstructing such motion requires solving a fundamental trade-off: generalizing from diverse and noisy video inputs while maintaining global motion consistency. Our approach addresses this problem by factorizing motion learning into two diffusion models. The camera-space model first estimates motion from videos in camera coordinates. The world-space model then lifts this initial estimate into world coordinates and refines it to be globally consistent. Together, the two models can reconstruct motion across diverse scenes and trajectories, even from highly noisy or incomplete observations. Moreover, our formulation is general, generating the motion of mesh vertices directly and bypassing parametric models. DuoMo achieves state-of-the-art performance. On EMDB, our method obtains a 16% reduction in world-space reconstruction error while maintaining low foot skating. On RICH, it obtains a 30% reduction in world-space error. Project page: https://yufu-wang.github.io/duomo/

We revisit sequentialization proofs associated with the Danos-Regnier correctness criterion in the theory of proof nets of linear logic. Our approach relies on a generalization of Yeo's theorem for graphs, based on colorings of half-edges. This happens to be the appropriate level of abstraction to extract sequentiality information from a proof net without modifying its graph structure. We thus obtain different ways of recovering a sequent calculus derivation from a proof net inductively, by relying on a splitting vertex, which we can impose to be a par-vertex, or a terminal vertex, or a non-axiom vertex, etc., in a modular way. This approach applies in presence of the mix-rules as well as for proof nets of unit-free multiplicative-additive linear logic (through an appropriate further generalization of Yeo's theorem). The proof of our Yeo-style theorem relies on a key lemma that we call cusp minimization. Given a coloring of half-edges, a cusp in a path is a vertex whose adjacent half-edges in the path have the same color. And, given a cycle with at least one cusp and subject to suitable hypotheses, cusp minimization constructs a cycle with strictly less cusps. In the absence of cusp-free cycles, cusp minimization is then enough to ensure the existence of a splitting vertex, i.e. a vertex that is a cusp of any cycle it belongs to. Our theorem subsumes several graph-theoretical results, including some known to be equivalent to Yeo's theorem. The novelty is that they can be derived in a straightforward way, just by defining a dedicated coloring, again without any modification of the underlying graph structure (vertices and edges) -- similar results from the literature required more involved encodings.

The numerical simulation of convection-dominated transient transport phenomena poses significant computational challenges due to sharp gradients and propagating fronts across the spatiotemporal domain. Classical discretization methods often generate spurious oscillations, requiring advanced stabilization techniques. However, even stabilized finite element methods may require additional regularization to accurately resolve localized steep layers. On the other hand, standalone physics-informed neural networks (PINNs) struggle to capture sharp solution structures in convection-dominated regimes and typically require a large number of training epochs. This work presents a hybrid computational framework that extends the PINN-Augmented SUPG with Shock-Capturing (PASSC) methodology from steady to unsteady problems. The approach combines a semi-discrete stabilized finite element method with a PINN-based correction strategy for transient convection-diffusion-reaction equations. Stabilization is achieved using the Streamline-Upwind Petrov-Galerkin (SUPG) formulation augmented with a YZbeta shock-capturing operator. Rather than training over the entire space-time domain, the neural network is applied selectively near the terminal time, enhancing the finite element solution using the last K_s temporal snapshots while enforcing residual constraints from the governing equations and boundary conditions. The network incorporates residual blocks with random Fourier features and employs progressive training with adaptive loss weighting. Numerical experiments on five benchmark problems, including boundary and interior layers, traveling waves, and nonlinear Burgers dynamics, demonstrate significant accuracy improvements at the terminal time compared to standalone stabilized finite element solutions.

The accelerating adoption of language models (LMs) as agents for deployment in long-context tasks motivates a thorough understanding of goal drift: agents' tendency to deviate from an original objective. While prior-generation language model agents have been shown to be susceptible to drift, the extent to which drift affects more recent models remains unclear. In this work, we provide an updated characterization of the extent and causes of goal drift. We investigate drift in state-of-the-art models within a simulated stock-trading environment (Arike et al., 2025). These models are largely shown to be robust even when subjected to adversarial pressure. We show, however, that this robustness is brittle: across multiple settings, the same models often inherit drift when conditioned on prefilled trajectories from weaker agents. The extent of conditioning-induced drift varies significantly by model family, with only GPT-5.1 maintaining consistent resilience among tested models. We find that drift behavior is inconsistent between prompt variations and correlates poorly with instruction hierarchy following behavior, with strong hierarchy following failing to reliably predict resistance to drift. Finally, we run analogous experiments in a new emergency room triage environment to show preliminary evidence for the transferability of our results across qualitatively different settings. Our findings underscore the continued vulnerability of modern LM agents to contextual pressures and the need for refined post-training techniques to mitigate this.

AI algorithms for imperfect-information games are typically compared using performance metrics on individual games, making it difficult to assess robustness across game choices. Card games are a natural domain for imperfect information due to hidden hands and stochastic draws. To facilitate comparative research on imperfect-information game-playing algorithms and game systems, we introduce Valet, a diverse and comprehensive testbed of 21 traditional imperfect-information card games. These games span multiple genres, cultures, player counts, deck structures, mechanics, winning conditions, and methods of hiding and revealing information. To standardize implementations across systems, we encode the rules of each game in RECYCLE, a card game description language. We empirically characterize each game's branching factor and duration using random simulations, reporting baseline score distributions for a Monte Carlo Tree Search player against random opponents to demonstrate the suitability of Valet as a benchmarking suite.

Language models deployed in online communities must adapt to norms that vary across social, cultural, and domain-specific contexts. Prior alignment approaches rely on explicit preference supervision or predefined principles, which are effective for well-resourced settings but exclude most online communities -- particularly those without institutional backing, annotation infrastructure, or organized around sensitive topics -- where preference elicitation is costly, ethically fraught, or culturally misaligned. We observe that communities already express preferences implicitly through what content they accept, engage with, and allow to persist. We show that this acceptance behavior induces measurable geometric structure in representation space: accepted responses occupy coherent, high-density regions that reflect community-specific norms, while rejected content falls in sparser or misaligned areas. We operationalize this structure as an implicit preference signal for alignment and introduce density-guided response optimization (DGRO), a method that aligns language models to community norms without requiring explicit preference labels. Using labeled preference data, we demonstrate that local density recovers pairwise community judgments, indicating that geometric structure encodes meaningful preference signal. We then apply DGRO in annotation-scarce settings across diverse communities spanning platform, topic, and language. DGRO-aligned models consistently produce responses preferred by human annotators, domain experts, and model-based judges over supervised and prompt-based baselines. We position DGRO as a practical alignment alternative for communities where explicit preference supervision is unavailable or misaligned with situated practices, and discuss the implications and risks of learning from emergent acceptance behavior.

Unified multimodal models have recently demonstrated strong generative capabilities, yet whether and when generation improves understanding remains unclear. Existing benchmarks lack a systematic exploration of the specific tasks where generation facilitates understanding. To this end, we introduce UniG2U-Bench, a comprehensive benchmark categorizing generation-to-understanding (G2U) evaluation into 7 regimes and 30 subtasks, requiring varying degrees of implicit or explicit visual transformations. Extensive evaluation of over 30 models reveals three core findings: 1) Unified models generally underperform their base Vision-Language Models (VLMs), and Generate-then-Answer (GtA) inference typically degrades performance relative to direct inference. 2) Consistent enhancements emerge in spatial intelligence, visual illusions, or multi-round reasoning subtasks, where enhanced spatial and shape perception, as well as multi-step intermediate image states, prove beneficial. 3) Tasks with similar reasoning structures and models sharing architectures exhibit correlated behaviors, suggesting that generation-understanding coupling induces class-consistent inductive biases over tasks, pretraining data, and model architectures. These findings highlight the necessity for more diverse training data and novel paradigms to fully unlock the potential of unified multimodal modeling.

We investigate geometric regularization strategies for learned latent representations in encoder--decoder reduced-order models. In a fixed experimental setting for the advection--diffusion--reaction (ADR) equation, we model latent dynamics using a neural ODE and evaluate four regularization approaches applied during autoencoder pre-training: (a) near-isometry regularization of the decoder Jacobian, (b) a stochastic decoder gain penalty based on random directional gains, (c) a second-order directional curvature penalty, and (d) Stiefel projection of the first decoder layer. Across multiple seeds, we find that (a)--(c) often produce latent representations that make subsequent latent-dynamics training with a frozen autoencoder more difficult, especially for long-horizon rollouts, even when they improve local decoder smoothness or related sensitivity proxies. In contrast, (d) consistently improves conditioning-related diagnostics of the learned latent dynamics and tends to yield better rollout performance. We discuss the hypothesis that, in this setting, the downstream impact of latent-geometry mismatch outweighs the benefits of improved decoder smoothness.

Learning diagnosis is a critical task that monitors students' cognitive state during educational activities, with the goal of enhancing learning outcomes. With advancements in language models (LMs), many AI-driven educational studies have shifted towards conversational learning scenarios, where students engage in multi-turn interactive dialogues with tutors. However, conversational learning diagnosis remains underdeveloped, and most existing techniques acquire students' cognitive state through intuitive instructional prompts on LMs to analyze the dialogue text. This direct prompting approach lacks a solid psychological foundation and fails to ensure the reliability of the generated analytical text. In this study, we introduce ParLD, a preview-analyze-reason framework for conversational learning diagnosis, which leverages multi-agent collaboration to diagnose students' cognitive state over multiple dialogue turns. Specifically, ParLD comprises three main components: (1) Behavior Previewer, which generates a student behavior schema based on previous states and learning content; (2) State Analyzer, which diagnoses the tutor-student dialogue and behavior schema to update the cognitive state; and (3) Performance Reasoner, which predicts the student's future responses and provides verifiable feedback to support ParLD's self-reflection with the Chain Reflector. They operate sequentially and iteratively during each interaction turn to diagnose the student's cognitive state. We conduct experiments to evaluate both performance prediction and tutoring support, emphasizing the effectiveness of ParLD in providing reliable and insightful learning diagnosis.

Selecting the number of clusters remains a fundamental challenge in unsupervised learning. Existing criteria typically target a single ``optimal'' partition, often overlooking statistically meaningful structure present at multiple resolutions. We introduce ElbowSig, a framework that formalizes the heuristic ``elbow'' method as a rigorous inferential problem. Our approach centers on a normalized discrete curvature statistic derived from the cluster heterogeneity sequence, which is evaluated against a null distribution of unstructured data. We derive the asymptotic properties of this null statistic in both large-sample and high-dimensional regimes, characterizing its baseline behavior and stochastic variability. As an algorithm-agnostic procedure, ElbowSig requires only the heterogeneity sequence and is compatible with a wide range of clustering methods, including hard, fuzzy, and model-based clustering. Extensive experiments on synthetic and empirical datasets demonstrate that the method maintains appropriate Type-I error control while providing the power to resolve multiscale organizational structures that are typically obscured by single-resolution selection criteria.

While deep neural networks (DNNs) have achieved remarkable performance in tasks such as image recognition, they often struggle with generalization, learning from few examples, and continuous adaptation - abilities inherent in biological neural systems. These challenges arise due to DNNs' failure to emulate the efficient, adaptive learning mechanisms of biological networks. To address these issues, we explore the integration of neurobiologically inspired assumptions in neural network learning. This study introduces a biologically inspired learning rule that naturally integrates neurobiological principles, including sparsity, lognormal weight distributions, and adherence to Dale's law, without requiring explicit enforcement. By aligning with these core neurobiological principles, our model enhances robustness against adversarial attacks and demonstrates superior generalization, particularly in few-shot learning scenarios. Notably, integrating these constraints leads to the emergence of biologically plausible neural representations, underscoring the efficacy of incorporating neurobiological assumptions into neural network design. Preliminary results suggest that this approach could extend from feature-specific to task-specific encoding, potentially offering insights into neural resource allocation for complex tasks.

Large Language Models (LLMs) demonstrate potentials for automating scientific code generation but face challenges in reliability, error propagation in multi-agent workflows, and evaluation in domains with ill-defined success metrics. We present a Bayesian adversarial multi-agent framework specifically designed for AI for Science (AI4S) tasks in the form of a Low-code Platform (LCP). Three LLM-based agents are coordinated under the Bayesian framework: a Task Manager that structures user inputs into actionable plans and adaptive test cases, a Code Generator that produces candidate solutions, and an Evaluator providing comprehensive feedback. The framework employs an adversarial loop where the Task Manager iteratively refines test cases to challenge the Code Generator, while prompt distributions are dynamically updated using Bayesian principles by integrating code quality metrics: functional correctness, structural alignment, and static analysis. This co-optimization of tests and code reduces dependence on LLM reliability and addresses evaluation uncertainty inherent to scientific tasks. LCP also streamlines human-AI collaboration by translating non-expert prompts into domain-specific requirements, bypassing the need for manual prompt engineering by practitioners without coding backgrounds. Benchmark evaluations demonstrate LCP's effectiveness in generating robust code while minimizing error propagation. The proposed platform is also tested on an Earth Science cross-disciplinary task and demonstrates strong reliability, outperforming competing models.

We introduce a novel representation and optimization framework for discrete geodesics on triangle meshes that reduces artifacts of linear methods on uneven and coarse discretizations. Our method computes squared geodesic distances from point and curve sources using piecewise-quadratic elements, exactly reproducing flat distances regardless of mesh quality while improving accuracy over existing approaches on curved meshes. The formulation naturally supports sources placed anywhere on the mesh, not just at vertices.

The electric vehicle routing problem with time windows (EVRPTW) extends the classical VRPTW by introducing battery capacity constraints and charging station decisions. Existing benchmark datasets are often static and lack verifiable feasibility, which restricts reproducible evaluation of learning-based routing models. We introduce SynthCharge, a parametric generator that produces diverse, feasibility-screened EVRPTW instances across varying spatiotemporal configurations and scalable customer counts. While SynthCharge can currently generate large-scale instances of up to 500 customers, we focus our experiments on sizes ranging from 5 to 100 customers. Unlike static benchmark suites, SynthCharge integrates instance geometry with adaptive energy capacity scaling and range-aware charging station placement. To guarantee structural validity, the generator systematically filters out unsolvable instances through a fast feasibility screening process. Ultimately, SynthCharge provides the dynamic benchmarking infrastructure needed to systematically evaluate the robustness of emerging neural routing and data-driven approaches.

Categorical deep learning (CDL) has recently emerged as a framework that leverages category theory to unify diverse neural architectures. While geometric deep learning (GDL) is grounded in the specific context of invariants of group actions, CDL aims to provide domain-independent abstractions for reasoning about models and their properties. In this paper, we contribute to this program by developing a coalgebraic foundation for equivariant representation in deep learning, as classical notions of group actions and equivariant maps are naturally generalized by the coalgebraic formalism. Our first main result demonstrates that, given an embedding of data sets formalized as a functor from SET to VECT, and given a notion of invariant behavior on data sets modeled by an endofunctor on SET, there is a corresponding endofunctor on VECT that is compatible with the embedding in the sense that this lifted functor recovers the analogous notion of invariant behavior on the embedded data. Building on this foundation, we then establish a universal approximation theorem for equivariant maps in this generalized setting. We show that continuous equivariant functions can be approximated within our coalgebraic framework for a broad class of symmetries. This work thus provides a categorical bridge between the abstract specification of invariant behavior and its concrete realization in neural architectures.

Differential Privacy (DP) is becoming central to large-scale training as privacy regulations tighten. We revisit how DP noise interacts with adaptivity in optimization through the lens of stochastic differential equations, providing the first SDE-based analysis of private optimizers. Focusing on DP-SGD and DP-SignSGD under per-example clipping, we show a sharp contrast under fixed hyperparameters: DP-SGD converges at a Privacy-Utility Trade-Off of $\mathcal{O}(1/\varepsilon^2)$ with speed independent of $\varepsilon$, while DP-SignSGD converges at a speed linear in $\varepsilon$ with an $\mathcal{O}(1/\varepsilon)$ trade-off, dominating in high-privacy or large batch noise regimes. By contrast, under optimal learning rates, both methods achieve comparable theoretical asymptotic performance; however, the optimal learning rate of DP-SGD scales linearly with $\varepsilon$, while that of DP-SignSGD is essentially $\varepsilon$-independent. This makes adaptive methods far more practical, as their hyperparameters transfer across privacy levels with little or no re-tuning. Empirical results confirm our theory across training and test metrics, and empirically extend from DP-SignSGD to DP-Adam.

Multiparty quantum key agreement (MQKA) enables $n \geq 3$ mutually distrustful users to establish a shared secret key through collaborative quantum protocols. In this paper, we provide a comprehensive review where we argue that MQKA is best understood as a design space organized along three orthogonal but tightly coupled axes: (1) network architecture, which determines how quantum states flow between participants; (2) quantum resources, which encode the physical degrees of freedom used for implementation; and (3) security model, which defines trust assumptions about devices and infrastructure. Rather than treating MQKA as a linear sequence of isolated protocols, we develop this three-axis perspective to reveal recurrent patterns, sharp trade-offs, and unexplored design spaces. We classify MQKA protocols into structural families, map them to underlying quantum resources, and analyze how different security models shape fairness and collusion resistance. We further identify open challenges in composable security frameworks, network native integration, device-independent implementations, and propose a research roadmap toward hybrid-resource, bosonic-code-encoded, and fairness-aware MQKA suitable for the future quantum internet deployments in the post-NISQ era.

Physics-Informed Neural Networks (PINNs) have been recognized as a mesh-free alternative to solve partial differential equations where physics information is incorporated. However, in dealing with problems characterized by high stiffness or shock-dominated dynamics, traditional PINNs have been found to have limitations, including unbalanced training and inaccuracy in solution, even with small physics residuals. In this research, we seek to address these limitations using the viscous Burgers' equation with low viscosity and the Allen-Cahn equation as test problems. In addressing unbalanced training, we have developed a new adaptive loss balancing scheme using smoothed gradient norms to ensure satisfaction of initial and boundary conditions. Further, to address inaccuracy in the solution, we have developed an adaptive residual-based collocation scheme to improve the accuracy of solutions in the regions with high physics residuals. The proposed new approach significantly improves solution accuracy with consistent satisfaction of physics residuals. For instance, in the case of Burgers' equation, the relative L2 error is reduced by about 44 percent compared to traditional PINNs, while for the Allen-Cahn equation, the relative L2 error is reduced by approximately 70 percent. Additionally, we show the trustworthy solution comparison of the proposed method using a robust finite difference solver.

Real-time proactive agentic system, capable of modeling Human State of Mind, using foundation EXG model and text embeddings model, running fully offline on the edge. Unlike all previously known systems, the NeuroSkill(tm) system leverages SKILL.md description of Human's State of Mind via API and CLI provided by the system, directly from the Brain-Computer Interface (BCI) devices, which records Human biophysical and brain signals. Our custom harness - NeuroLoop(tm) - utilizes all of the above to run agentic flow that manages to engage with the Human on multiple cognitive and affective levels of their State of Mind (e.g., empathy), by providing actionable tool calls and protocol execution with explicit or implicit requests from the Human. GPLv3 open-source software with ethically aligned AI100 licensing for the skill markdown.

Shape optimization under uncertainty (OUU) is computationally intensive for classical PDE-based methods due to the high cost of repeated sampling-based risk evaluation across many uncertainty realizations and varying geometries, while standard neural surrogates often fail to provide accurate and efficient sensitivities for optimization. We introduce Shape-DINO, a derivative-informed neural operator framework for learning PDE solution operators on families of varying geometries, with a particular focus on accelerating PDE-constrained shape OUU. Shape-DINOs encode geometric variability through diffeomorphic mappings to a fixed reference domain and employ a derivative-informed operator learning objective that jointly learns the PDE solution and its Fréchet derivatives with respect to design variables and uncertain parameters, enabling accurate state predictions and reliable gradients for large-scale OUU. We establish a priori error bounds linking surrogate accuracy to optimization error and prove universal approximation results for multi-input reduced basis neural operators in suitable $C^1$ norms. We demonstrate efficiency and scalability on three representative shape OUU problems, including boundary design for a Poisson equation and shape design governed by steady-state Navier-Stokes exterior flows in two and three dimensions. Across these examples, Shape-DINOs produce more reliable optimization results than operator surrogates trained without derivative information. In our examples, Shape-DINOs achieve 3-8 orders-of-magnitude speedups in state and gradient evaluations. Counting training data generation, Shape-DINOs reduce necessary PDE solves by 1-2 orders-of-magnitude compared to a strictly PDE-based approach for a single OUU problem. Moreover, Shape-DINO construction costs can be amortized across many objectives and risk measures, enabling large-scale shape OUU for complex systems.