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The U.S. is shutting out more foreign-made drones and robots. China’s scale means the global competition may simply move elsewhere.
We propose QGPINNs, a physics-informed neural network framework developed in PyTorch for the numerical solution of nonlocal differential equations on quantum graphs. The framework is designed as a general computational implementation in which the solution on each edge of the graph is approximated by a neural network, while a unified graph-based loss function enforces the governing equations together with initial, boundary, and vertex transmission conditions. In particular, the formulation incorporates standard continuity and Kirchhoff-Neumann vertex conditions and Dirichlet boundary conditions into the learning process to couple the local edge-wise neural approximations into a global solution on the graph. The framework is developed for two representative classes of nonlinear models: multi-order fractional elliptic problems and time-fractional evolution equations on quantum graphs. To improve accuracy and training stability, QGPINNs integrates several graph-adapted learning strategies, including soft and hard constraint enforcement, dynamic loss balancing, Fourier feature embeddings, and a learnable singularity-capturing feature for weakly singular solutions arising in the considered problems. The framework also extends naturally to inverse problems, including the identification of the orders of fractional operators and physical parameters from noisy observational data. We validate the accuracy, computational efficiency, and physical consistency of the proposed framework through numerical experiments on benchmark graph structures and real-world networks, including the IEEE 14-bus system and an open-channel agricultural drainage network.
Tendon-driven hands are anthropomorphic, and moving the actuators off the joints is what makes a hand of this capability affordable to build. Two effects produce that saving. Routing force through a cable removes the requirement that a motor fit inside the joint it drives, so smaller and cheaper motors suffice, and one motor can drive several joints through a single cable, so fewer motors are needed. They are also harder to learn on than a direct-drive hand. The underactuated transmission that produces the saving is itself difficult to represent in a simulator, and the joints one cable drives are not independently commandable. We present Aero Hand Open, a tendon-driven anthropomorphic hand that is released simulation-ready. Three things ship with it. A simulation model reproduces the cable transmission itself. An identified actuation map connects that model to the motor commands in both directions, including the three-way coupling of the thumb. A reinforcement learning package trains policies for the hand. Together they let a policy be trained entirely in simulation and run on the hand with no fine-tuning and no state estimation. We release the mechanical design, the simulation model, the identified mapping, the training environment and the deployment stack.
Synthetic data can improve statistical inference when real data are scarce, but naively treating synthetic samples as real data can introduce bias and lead to unreliable inference. We develop a general framework for synthetic-augmented inference across a population of related tasks. It characterizes synthetic augmentation by the number of synthetic observations and their weight. Central to our framework is a size-weight frontier that specifies, for each weight, the largest synthetic sample size for which all smaller sizes attain the target task-marginal coverage. We estimate this frontier from historical tasks, and establish a finite-sample coverage guarantee simultaneously for all size-weight configurations on or below the estimated frontier. In experiments using large language model responses to augment opinion survey data, our procedure achieves target coverage and substantially narrows confidence intervals.
We study the mixing time of weighted Dikin walks for sampling from exponential distributions on polytopes and truncated positive-semidefinite (PSD) cones. Our first result gives a general total-variation mixing bound under strong self-concordance, ν-symmetry, and mixed-trace regularity on the local metric. The key idea is to control the Metropolis--Hastings acceptance probability on a high-probability region rather than at every point. Applying this framework to the Lee--Sidford, Lewis-weight, and John metrics yields an O(d^2) mixing bound for sampling from polytopes, while applying it to a hybrid barrier yields an O(d^4) mixing bound for sampling from truncated PSD cones. Our second result establishes stronger χ^2-divergence guarantees and pointwise acceptance control using a new fourth-order bootstrap condition. For a suitably scaled Lee--Sidford metric, this yields an O(d^2) mixing bound in χ^2-divergence, improving on the previous O(d^{9/4}) bound.
We study kernel ridge regression under anisotropic Gaussian data, where the input covariance decays as a power law with exponent α0 for polynomial inner-product kernels. We derive asymptotically sharp expressions for the kernel spectrum and the generalization error in the polynomial high-dimensional regime n=Θ(d^κ), revealing how anisotropy reshapes the learning curves. For weak anisotropy (0<α<1), the problem remains effectively high-dimensional and retains some features of the isotropic case, while departing from it in others: the variance still peaks at integer sample complexities κ{N}, but these peaks are progressively damped as α grows; meanwhile, for targets strongly aligned with the data's principal directions, the bias drops at fractional sample complexities, decoupling the bias transitions from the interpolation peaks. For strong anisotropy (α> 1), the effective dimension of the problem is constant, and the variance stops depending on sample size altogether, plateauing under ridgeless interpolation or vanishing at an explicit rate under fixed ridge penalty. The bias undergoes a sharp transition governed by the target's decay rate: below a threshold, learning is abrupt rather than gradual; above it, the bias decays as a power law that recovers the classical source and capacity rates. We finally specialize these results to single-index targets, showing how the alignment of the index with the data's principal directions determines the effect of anisotropy on learning. Together, our results clarify how the input geometry shapes the kernel features and fundamentally impacts its generalization properties.
Can a listener recover what a speaker means from the form of an utterance alone? We answer this question information-theoretically, and for a listener given by any featurizer of text, including the hidden states of contemporary large language models. Modeling language use as a joint distribution over meanings, contexts, and utterances, we derive upper bounds on the probability that a decoder recovers a speaker's intended meaning from a representation of the utterance. The bounds are governed by the uncertainty that form leaves about meaning, which splits into an irreducible part and a part that only (extralinguistic) context, but never the utterance alone, can resolve. Because these quantities are intrinsic to language, no representation, however much text or supervision produced it, can surpass them; the bounds hold whether the space of meanings is discrete or continuous. Experiments on artificial languages, Mandarin zero-pronoun resolution, and color reference provide empirical evidence in support of the theory.
Neural-network optimization in 2025-2026 is no longer well described as a succession of new Adam variants. The design space has expanded from coordinates to matrices and layers, from fixed training horizons to policies over time, and from mathematical update rules to state representations that must survive sharding and low-precision computation. This survey organizes recent optimizers and training optimization methods along four largely independent axes: temporal estimation, update geometry, horizon management, and representation and systems. It connects the spectral normalization of Muon, the historical matrix statistics of Shampoo and SOAP, adaptive and hybrid matrix methods, memory-efficient optimizers, schedule-free training, small-batch corrections, and quantized optimizer states. The central empirical conclusion is deliberately non-triumphal: matrix-aware methods represent a genuine advance, but there is no context-independent replacement for AdamW. Rankings change with model scale, data-to-parameter ratio, batch size, schedule, parameter partition, tuning budget, and whether the target metric is tokens, FLOPs, wall-clock time, or memory. The practical consequence is a compositional view of optimizer design and a stricter protocol for evaluating optimizer claims.
Modern agent systems assemble capabilities at runtime, and this dynamic composition has recently received a complete formal treat ment in the spatiotemporal-composability calculus, in which a capability is a component carrying a tracked inverse, and agents are assembled as plugins. This plugin form is carried by a single process sharing one context, a carrier that places all components in one physical failure domain, a fault suspends every component at once, and process death interrupts every session the process hosts. This paper shows that neither the modeling nor the calculus binds an agent to one process, the statelessness of the language model keeps all cross-step state outside the model, and the soundness invariant is defined on the state space alone. These observations condense into four lemmas whose premises are the hypotheses of the calculus and the statelessness of language-model inference. On these lemmas this paper constructs Logos, a ROS-like cross process agent harness in which a plugin is a process and the only shared state is an append-only transcript. Eighty sessions resume with no repeated effect after kills placed at the four boundaries of the tool-call cycle, and a same-fault comparison with a single process reference configuration shows one fault interrupting every co-resident session while under the peer-process construction one fault ends at one node.
As a precursor to high-dimensional biomedical data modeling, reliable feature selection can reduce computational expense, improve modeling performance, and yield simpler, more interpretable models. However, most filter-based feature selection methods struggle to detect feature interactions, while wrapper or embedded feature selection methods are computationally expensive. Relief-based algorithms (RBAs) are filter methods that are sensitive to feature interactions while mitigating these other limitations. This study (1) refactors, optimizes, and expands the scikit-rebate Python package with existing and newly proposed RBA variants and (2) conducts rigorous RBA benchmark comparisons across diverse genomic simulations. We expand scikit-rebate to include SWRF*, mu-Relief, and 5 novel RBA variants implementing alternative strategies for neighbor selection and feature scoring. All RBAs were evaluated to compare predictive feature ranking and runtime across simulated genomic datasets varying in sample size, number of features, heritability, and underlying association type (e.g. main effects and interactions). All RBAs, except mu-Relief, were proficient in detecting 2-way interactions in noisy data. RBAs utilizing 'far' scoring were best at detecting 2-way interactions - with MultiSWRFDB* top-performing - but were far less sensitive to main effects. SWRF, MultiSWRF, MultiSURF, and MultiSWRFDB yielded top performance across main effect and 2-way interaction datasets with MultiSWRFDB performing best when also considering 3-way interactions. Refactoring of scikit-rebate resulted in 10 to 35-fold reductions in RBA runtimes. The newly introduced RBAs were among the strongest performing, and by robustly retaining both main effects and 2-way epistatic interactions, these algorithms preserve predictive signals for downstream modeling.
Recent generative approaches to geometry estimation adapt pretrained image diffusion models and treat the task as image-conditioned generation. Leveraging off-the-shelf image diffusion models, they either (i) train task-specific geometry models (for depth and surface normal estimation) independently, losing the opportunity of exploring the intrinsic correlation of these geometric targets, or (ii) jointly fine-tune modified image diffusion backbones (e.g., altered self-attention), which typically demands substantial labeled data. To overcome these limitations in a principled fashion, we repurpose pretrained video generative models as a unified and data-efficient framework for geometry estimation, formulated innovatively as a next-frames prediction task. Our method, GeoNeXt, inherits naturally structured knowledge and richer priors from the video model, while further adapting them for joint modeling of images and geometry targets (image <-> geometry), enabling more data efficient and effective learning of geometry. Extensive experiments validate our method for zero-shot monocular depth and surface normal estimation across diverse datasets, outperforming both previous task-specific and unified generative competitors while using substantially less training data. Notably, our method rivals discriminative state-of-the-art approaches trained on over 100x more data and even standouts on several benchmarks.
Model merging combines multiple task-specific fine-tuned LLMs into a single multi-task model without additional training. However, merged models are known to suffer from representation bias: systematic drift between the merged model's hidden states and those of each individual source model. Prior work (Yang et al., 2024a) study and mitigate this bias for encoder-based vision models using a lightweight correction module trained with L1 loss. However, such bias is not studied for decoder models due to their autoregressive nature. We analyze the problem of representation bias in decoder models, and show two challenges absent in encoders: (1) the causal attention mask causes bias to accumulate across token positions, requiring position-dependent correction; and (2) not all token positions are equally important, i.e., high-entropy (decision-critical) positions matter far more than low-entropy ones. To address these challenges, we propose Decoder-Aware Representation Tuning via Surgery (DARTS). DARTS employs a novel entropy-weighted L1 loss to upweight correction at high-entropy positions where errors most affect generation quality, and a per-position additive bias that captures position-dependent error without overparameterization. We perform extensive evaluation on three domains: code generation (HumanEval), mathematical reasoning (GSM8K), and instruction following (AlpacaEval) on Llama-2-7B models, and show DARTS achieves significant improvement over the standard surgery approach while adding negligible parameters (0.1\% of total parameters).
A code world model accepted by a sampling gate can be exactly right on everything the gate can see and arbitrarily wrong beyond it. We characterize what a certified model can know, and what its errors can cost, when the omission is an annular freeze mode enclosing an unreachable interior. The gate quotient makes the question precise: acceptance-with-certainty determines the model exactly on the reachable query set; beyond reach is gauge. On a minimal ring instrument we prove the extreme case (a wrong-topology filled-disc artifact unfalsifiable by any sampling gate and bitwise harmless at play) and measure, with LLM synthesis across three model families, how one knob (a channel of width gamma) walks the same artifact through three regimes: unfalsifiable-and-harmless, falsifiable-and-costly, and instantly falsified. Three principles organize the empirics. First, danger is topology relative to reach: a channel the planner can use collapses the blind model's exploitation (play cost 1.09 to ~0 over a knee at gamma ~ 0.1), while a hidden channel with the same first Betti number keeps it at full strength (1.12). Second, repair is parameter-bound and sensor-bound: no family recovers the region from outside evidence; from inside, models pose the right topology but cannot pin its parameters, and the posed topology tracks the guiding persistent-homology summary's wrong beta_1 (a sensor with a measured geometric resolution limit), not the truth. Third, mitigation must match the error's dimension and direction: point fences fail against the one-dimensional boundary, a dimension-matched persisted fence collapses exploitation to a two-lesson transient (0.999 to 0.058), and the dual freedom certificate collapses the invented-mode failure symmetrically (1.769 to 0.029). In n dimensions the shell makes misidentification near-certain while the danger stays fully exploitable: the two axes are independent.
