Papers

Reasoning models do not stop when they know the answer. On DeepSeek-R1-Distill-Qwen-7B the chain of thought runs about twice as long as the model's own answer probability takes to settle, and how much of that excess is removable varies from problem to problem, so a global length penalty cannot take it out. We take it out by internalizing a causal interpretability finding into the weights. The mechanism is a halt vector: a difference-of-means direction at layer 18 of this model whose steering strength controls how long it thinks, while a replicated value axis does nothing. Installing that intervention in the weights is harder than it looks. Maximizing the scalar projection onto the direction corrupts the off-axis dimensions a frozen downstream reader depends on, and generation gets longer instead of shorter; what works is reconstructing the whole steered activation with those dimensions pinned to their natural values. Fit from 24 problems and no reinforcement learning, the halt removes about a quarter of the thinking at held accuracy across five unseen benchmarks, and the cut tracks each problem's own removable slack at 0.70. It also closes a non-termination pathology that grows with difficulty and that a decoding-time confidence hook makes worse. We do not claim to beat a well-tuned length penalty or decoding-time early exit on the raw trade-off; the contribution is how the halt is obtained.

Equivariant graph neural networks provide a principled way to model geometric systems, but efficient first-order architectures remain limited in how vector information can be transformed as it moves across a graph. We introduce ESNN, an Equivariant Sheaf Neural Network that enriches this interaction by learning directed, matrix-valued transport between neighboring vector features while preserving exact Euclidean equivariance. Rather than increasing the order of the representation, ESNN keeps scalar and vector features first-order and places the additional geometric flexibility in the edge transport itself. We characterize this transport theoretically, showing that when relative displacement is the only covariant geometric input, every linear $O(n)$-equivariant map decomposes into independent radial and tangential components, while learned covariant features enable richer feature-conditioned transformations. We also introduce controlled symmetry relaxation for systems with a preferred ambient direction, which may be prescribed or inferred from data while recovering full $E(n)$-equivariance when the directional pathway is inactive. Across particle dynamics, mesh-based simulation, point-cloud classification, and molecular property prediction, ESNN improves dynamics prediction, recovers the gravity axis when symmetry is broken, yields substantial gains on selected mesh tasks and long-horizon rollouts, and remains robust to unseen rotations. These results show that learning how geometric information is transported across edges offers a complementary route to expressive equivariant message passing without requiring higher-order representations.

Layer-skipping methods for efficient LLM inference decide, at some granularity, which transformer layers to execute for a given input. We present a rigor-matched, three-seed audit of two periodic-step, search-based methods that make this decision online at inference time and re-evaluate it every few generation steps: a confidence-gated early-exit baseline (ConfLayers) and genuine self-speculative decoding (SWIFT, Xia et al. 2024), together with vanilla autoregressive decoding, across Qwen2.5-0.5B and Qwen2.5-1.5B (Yang et al. 2024) on GSM8K (Cobbe et al. 2021) and CNN/DailyMail (Nallapati et al. 2016; See et al. 2017). SWIFT is strongest on accuracy in three of four cells, while ConfLayers is dominated everywhere, with particularly large deficits on GSM8K at 1.5B. Separating online-search overhead from pure inference cost, we find that SWIFT's true inference speed is faster than ConfLayers's in all four cells (5-21%), reversing the naive wall-clock ranking in three; ConfLayers's search overhead is small and stable (1-2% of cost), whereas SWIFT's is larger and more variable across seeds (up to 28.7%). We additionally examine two trained routing methods, LayerRoute (Sikdar, 2026), a per-sequence, input-conditioned hard gate, and LayerDrop (Fan et al. 2020), a fixed, input-independent pruning pattern, as a supplemental analysis rather than a head-to-head comparison because both operate at a coarser decision granularity. Under a verified protocol with genuine per-input gating, a genuine full-model baseline, and genuine inference-time compute skipping, both show modest real speedups (1.08-1.33x) but accuracy well below the periodic-step methods, including near-total LayerRoute collapse on GSM8K at 1.5B (0.003 mean exact-match across three seeds). We release the full audit protocol as a template for rigor-matched efficiency comparisons.

Ensuring a safe virtual reality (VR) experience requires systems that can predict and respond when users lose their balance. Although prior work has examined fall prediction and motion sickness, many approaches are regression-based and postural state classification remains less explored. This study compares machine learning (ML) and deep learning (DL) models for classifying postural states in VR under visual perturbations. We used a multimodal dataset containing kinematic, electromyographic (EMG), and electrodermal activity (EDA) signals. The data were prepared for a binary task to distinguish balanced from imbalanced postural states, and participant-wise downsampling addressed class imbalance. All models were evaluated with Leave-One-Participant-Out (LOPO) cross-validation to test generalization to unseen participants. Among the models, the Mamba-inspired CNN (MI-CNN) achieved the highest accuracy of 96.76%. SHapley Additive exPlanations (SHAP) analysis improved interpretability and identified the most influential classification factors. The SHAP results showed that kinematic features were dominant, indicating that body-motion patterns are informative for detecting imbalance in VR. We also evaluated MI-CNN using only the top two-thirds of features ranked by SHAP importance. Despite a 33% reduction in input dimensionality, the model maintained performance, achieving 0.957 accuracy and 0.957 F1-score, with about a 1% decrease compared with the full-feature model. These findings suggest that multimodal sensing, temporal deep learning, and explainable AI can support reliable classification of balance-related instability in VR. Accurate recognition of imbalanced postural states may raise awareness of fall risk and guide safer, adaptive VR systems that respond to instability while improving user safety and experience. Code is available at: https://github.com/NipaAnjum/MI-CNN.

We show that smooth two-layer feed-forward networks (FFNs) expose an additional structural model extraction channel under a chosen-input raw-output oracle at the FFN branch; consider transformer FFN branches with GELU or SiLU activations under chosen-input raw-output access, without access to parameters, gradients, or internal activations; exploit a second-order leakage channel in which projected input Hessians form different mixtures of the same hidden symmetric rank-one factors induced by the FFN input weights. We formalize resulting Hessian collection as a partially symmetric decomposition to establish conditions for local identifiability and stability to exploit vector-output stencil reuse to reduce the structural query cost by a factor of 16. On independently trained CIFAR-10 vision transformers, only 16 projected Hessians, corresponding to 8193 black-box queries, recover the hidden FFN directions with average absolute cosine alignment above 0.91, with 86.7.1 % of GELU and 91.1 % of SiLU directions exceeding 0.90 alignment. Recovery remains high across independently trained models, repeated extraction runs, and all transformer blocks. The recovered structure supports functional extraction too. Keeping the recovered directions fixed and fitting only the remaining FFN parameters yields high-fidelity substitutes with more than 92 % top-1 agreement, while test accuracy remains within 1.24% and 0.57% of the GELU and SiLU targets. Output rounding and Gaussian noise substantially reduce recovery under a fixed attack configuration, but adapting the finite-difference step restores average alignment to 0.9188 and 0.9081. This is an end-to-end path from black-box second-order observations to hidden FFN-structure recovery and functional replacement. Under the stated oracle model, smooth FFN curvature exposes internal parameter geometry that behavioral fidelity alone cannot reveal.

Independently trained neural networks tend to encode the same data with similar latent geometries. These latent geometries are not directly compatible, yet they can be nearly the same up to some class of transformations. While there exists many methods for alignment between different latent spaces, it is typically done using a set of shared sample correspondences, known as anchors. This leaves a fundamental question: are the geometric signatures of different latent spaces representing similar data sufficient to recover an alignment between them? To that end, we introduce HGA (Hyperspherical Gaussian Alignment), a method that directly optimizes a transformation between two latent spaces by maximizing a geometric measure of "fit" between them. Since it is driven by the geometry of the latent spaces rather than paired data, HGA can operate in both an unsupervised and weakly supervised regime. On tasks such as model stitching or multilingual word embedding correspondence recovery, HGA manages to match supervised results with minimal or no supervision.

Representation learning begins when training changes the features that define similarity between data. A frozen-kernel model only reweights a fixed geometry. We establish quantum signal processing (QSP) as a solvable quantum model of the representation-learning regime. At arbitrary depth, we compute the exact mean and variance of its quantum neural tangent kernel, revealing an input-dependent angular geometry whose diagonal remains non-self-averaging even when the underlying unitary approaches Haar randomness. We also prove a sparse-data guarantee for the full nonlinear gradient flow without freezing or ensemble-averaging the kernel: the realized dynamics converges to an integrable scalar flow with a time-dependent kernel closure and explicit convergence times. A finite-depth speed limit holds for every data set and trajectory. At higher data density, numerical results show coupled evolution beyond both the scalar and frozen-kernel descriptions. These results give a controlled theory of learned quantum data geometry with provable training dynamics beyond the frozen limit.

We establish quantitative convergence to the target and uniform-in-time propagation of chaos for Langevin-regularized Stein variational gradient descent. The Stein interaction need not be small relative to the confining Langevin drift and does not generally yield a contractive particle coupling. At the mean-field level, the Stein and Langevin components dissipate the same relative entropy in the kernel-induced Stein and $2$-Wasserstein geometries, producing the squared kernel Stein discrepancy and relative Fisher information. Under a log-Sobolev inequality for the target, this yields exponential last-iterate convergence. We also derive a finite-particle entropy identity relative to the product target, giving exponential-in-time convergence of the empirical measure up to polynomial sampling errors. For propagation of chaos, we develop two complementary finite-time approaches. A synchronous coupling, combined with exponential moment estimates for the nonlinear mean-field diffusion, yields explicit single-exponential bounds in Wasserstein distance and kernel Stein discrepancy (KSD). Moving-product entropy gives joint-law relative entropy control relative to the evolving mean-field product law and, through entropy superadditivity and concentration, fixed-marginal relative entropy and total variation bounds and empirical KSD estimates. Under an additional $T_2$ inequality for the initial law, it also yields Wasserstein bounds. Combining these finite-time estimates with target convergence at a logarithmic cutoff time gives polynomial uniform-in-time propagation of chaos rates in expectation for empirical KSD and $W_2^2$, and for fixed-marginal total variation and $W_2^2$. All bounds control the last iterate in physical time. We also compare the two finite-time mechanisms and identify regimes in which each gives the sharper polynomial exponent.

Separable nonnegative matrix factorization (SNMF) has been widely used for low-rank representation and clustering of nonnegative data, owing to its ability to produce part-based and interpretable decompositions. In particular, SNMF is closely related to graph clustering and community detection. To enhance sparsity and identifiability of the learned factors, we propose an $\ell_1^p/\ell_2$-regularized SNMF model based on a powered ratio-of-norms regularizer. The resulting formulation is nonconvex and nonsmooth, which poses significant challenges for optimization. To address this, we develop efficient algorithms based on the difference-of-convex function algorithm (DCA) and the alternating direction method of multipliers (ADMM). The proposed methods decompose the original problem into tractable subproblems, leveraging closed-form proximal operators associated with the powered norm terms. We establish descent and limiting criticality properties for the DCA scheme and convergence under standard assumptions for the ADMM scheme. Extensive numerical experiments on synthetic datasets and hand gesture classification tasks demonstrate that the proposed approach achieves competitive or improved performance in anchor identification and classification accuracy compared with existing SNMF methods, while maintaining competitive computational efficiency.

Technical operations teams resolve large volumes of incidents by synthesizing fragmented evidence from ticket text, historical cases, system logs, and technical documentation. Existing automation often relies on monolithic generation without explicit evidence modeling or provenance, making outputs difficult to verify when critical signals are sparse across sources. We propose ASTRA, an agentic system for ticket resolution in which a central orchestrator coordinates three specialist information-gathering agents and drives a judge-orchestrator refinement loop to produce evidence-backed troubleshooting reports. TicketSimilarityAgent retrieves relevant historical precedents through dense retrieval and LLM reranking; LogAgent distills hundreds of thousands of log lines into structured, quote-grounded findings using deterministic filtering and constrained LLM analysis; and DomainKnowledgeAgent retrieves relevant technical knowledge via the Model Context Protocol (MCP). Their outputs are transformed into a claim-evidence representation linking each claim to a verbatim source passage, assigning a support level, and preventing cross-attribution. A JudgeAgent scores the report on five criteria, while the OrchestratorAgent converts low scores into targeted follow-up queries for bounded iterative refinement. Evaluated on 987 real-world telecom fault tickets across seven product lines, ASTRA achieves a mean quality score of 4.13/5.0, with 59.9% of reports identifying the fault area at the component-family level or better. Relevance and Clarity scores are 4.88 and 4.94, respectively, while fabricated technical details remain below 3% of error cases. Stratification by fault type reveals that hardware faults remain substantially harder than software or configuration faults (Cohen's d=0.80), pointing to a fundamental limitation of text-based evidence channels for hardware fault diagnosis.

Autonomous vehicles (AVs) rely on accurate camera-LiDAR calibration for multimodal sensor fusion. In practice, calibration can drift due to vibration, temperature variation, or minor sensor displacement, motivating online calibration algorithms that detect and correct misalignment at runtime while allowing the vehicle to continue operating without a factory visit. Existing AV attacks largely assume correct calibration. We instead identify online sensor calibration as a new attack plane. A corrupted calibration update can persist across subsequent fusion operations, causing system-wide errors that propagate from perception to planning and control. We present Adversarial Calibration Attack (ACA), the first physical attack against camera-LiDAR online calibration. Using a single adversarial poster, ACA first spoofs the miscalibration detector to trigger the calibration process and then steers the calibration estimator toward an incorrect transformation. A unified optimization jointly designs the poster's geometry and texture for both objectives. We evaluate ACA across benchmark datasets, simulation, and physical experiments. On benchmark datasets such as KITTI and nuScenes, ACA induces up to 33.9 degrees mean rotational calibration error, thereby severely degrading object detection. In the CARLA simulator, the attack causes a collision when the corrupted calibration is accepted in vulnerable scenarios crafted by the attacker. On a real Husky robot, a printed adversarial poster successfully reproduces the calibration error. These results demonstrate that online calibration is a practical and safety-critical attack surface for AVs.

Large reasoning models achieve strong performance on complex tasks by generating extended chain-of-thought (CoT) traces via reinforcement learning with verifiable rewards (RLVR). While current RLVR methods have achieved strong results with correctness-based reward signals, they provide limited guidance on the quality of the reasoning process itself, leaving the internal reasoning structure largely unoptimized. Through empirical analysis across multiple model families, we identify a consistent pattern: correct reasoning trac es exhibit more frequent and larger token-level entropy drops within the thinking phase than incorrect ones. We propose ERR+, a two-phase RLVR framework grounded in this observation. The first phase trains with the Entropy Relief Reward (ERR), a bonus proportional to cumulative token-level entropy drops in the thinking phase, log-normalized by response length. Unlike prior methods that suppress entropy, ERR rewards the resolution of uncertainty while leaving exploratory high-entropy states unconstrained. The second phase introduces the Robust Relative Efficiency Reward, which scores each response's length against co-generated peers via a $\tanh$-transformed within-group $z$-score. We provide a formal analysis showing that joint optimization of the two objectives induces gradient conflict in early training, motivating the sequential design . Experiments on five datasets demonstrate consistent improvements in both accuracy and response conciseness across model backbones. Our code is available at https://github.com/XrkArul/err_response

Indoor 3D Scene Graphs (3DSGs) represent environments as multi-layer hierarchies that connect observed geometric primitives (e.g., planes) to higher-level metric-semantic concepts (e.g., rooms, floors, buildings), enabling incremental spatial reasoning for robotic perception and SLAM. However, classical high-level concept generation approaches rely on hand-crafted rules for specific concept classes, while learning-based methods require separate models for graph structure and spatial node features (e.g., centroids), which limits scalability to novel classes and more complex hierarchies. We propose a unified autoregressive diffusion-based graph generative model that jointly learns structure and features, constructing complete 3DSGs bottom-up from observed vertical planes across arbitrary hierarchy depths. Our method consistently surpasses all learning-based and random baselines across 3DSG datasets spanning synthetic scenes, real architectural floor plans, and robotic sensor data, with varying layout complexity and hierarchy depth, and surpasses a one-shot model with oracle access to the target graph size on the largest hierarchy and on real single-floor data. Finally, we propose an adaptation of the Fused Gromov–Wasserstein distance for principled graph-level evaluation of generated 3DSGs against ground truth.

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, $\bar{\nu}$-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 $\widetilde O(d^2)$ mixing bound for sampling from polytopes, while applying it to a hybrid barrier yields an $\widetilde O(d^4)$ mixing bound for sampling from truncated PSD cones. Our second result establishes stronger $\chi^2$-divergence guarantees and pointwise acceptance control using a new fourth-order bootstrap condition. For a suitably scaled Lee–Sidford metric, this yields an $\widetilde O(d^2)$ mixing bound in $\chi^2$-divergence, improving on the previous $\widetilde O(d^{9/4})$ bound.

We study kernel ridge regression under anisotropic Gaussian data, where the input covariance decays as a power law with exponent $\alpha\geq 0$ for polynomial inner-product kernels. We derive asymptotically sharp expressions for the kernel spectrum and the generalization error in the polynomial high-dimensional regime $n=\Theta(d^\kappa)$, revealing how anisotropy reshapes the learning curves. For weak anisotropy ($0<\alpha<1$), 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 $\kappa\in\mathbb{N}$, but these peaks are progressively damped as $\alpha$ 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 ($\alpha > 1$), 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.

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.

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.

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.

To determine the real-world effectiveness of machine learning based malware detection, it is vital to evaluate its robustness against highly capable adversaries. However, state-of-the-art attacks do not effectively model realistic adversaries, as they often assume access to privileged information such as the training data, feature space, or confidence scores of the target. In this work, we present Replicant, a deep reinforcement learning framework that learns the realistic task of evasion under a strict label-only black-box threat model. Replicant learns a reusable policy on how to modify a malware sample and when to query the target, which transfers across samples, detectors, and feature spaces. Across seven Android malware detectors and three feature spaces, Replicant is the strongest and most query-efficient approach achieving a mean attack success rate of 78.8%, a relative improvement of 20.9%-39.2% over the state-of-the-art. Furthermore, when used for adversarial training, Replicant also outperforms the state-of-the art by producing detectors with more generalizable robustness. With Replicant we demonstrate that learning the task of evasion not only results in stronger attack performance but, crucially, provides a better signal for hardening malware detectors.

This paper evaluates how reward function choice shapes the performance and behavior of LLM forecasters. We compare five proper scoring rules as training objectives for binary forecasts of resolved real-world events. Although the rules share the same theoretical incentive for truthful probability reporting, the resulting models differ in calibration, probability use, and estimated profiles of bias, information, and noise, with smaller differences in aggregate accuracy and discrimination. The Brier-trained model has the lowest observed Brier score and highest AUC-ROC, while the log-trained model has the highest observed log score and lowest calibration error. Models with similar aggregate performance also reach that performance through different combinations of bias, information, and noise. Proper scoring rules therefore need not behave interchangeably as training objectives. Reward choice may shape not only how well an LLM forecasts, but how its forecasting errors are structured.

Interactive dialogue games test a capability that static benchmarks largely leave implicit: a model must carry state across turns, interpret feedback, and choose valid actions under changing constraints. We study this setting in the LM Playschool Challenge with a 2B open-weight model, and find that many failures are not only broad knowledge failures but also local decision failures: repeated guesses, malformed actions, and violations of feedback that the model has just seen. These diagnostics motivate a training recipe organized around three steps: acquire broad game participation through supervised fine-tuning, repair mechanically verifiable failures within one targeted dialogue-game family using turn-local preference pairs, and preserve general capabilities beyond these dialogue games. In the official final evaluation, our submission improves public clemscore from 10.67 to 38.92 and closed in-domain score from 13.41 to 41.17, while approximately preserving aggregate static performance (44.14 vs. 44.24 for the baseline). Out-of-domain clemscore remains low at 7.88, with the largest gains concentrated in unseen variants of the targeted family. Our results suggest that broad SFT brings most of the model's capability improvement; turn-local supervision can be effective when failure detection is precise, with observed transfer concentrated primarily within-family.

For finite-dimensional linear inverse problems where the variables are Gaussian, it is well-known that the minimum-mean-square error estimator takes the form of a regularized least-squares data fit. In this chapter, we show that this equivalence extends to a much broader infinite-dimensional setting where generalized splines take the role of linear regressors and generalized Gaussian processes on a nuclear space $S$ are the counterpart of Gaussian random vectors. The scope of this extension is of the same nature as the switch from the classic notion of function to that of a distribution, also known as a "generalized function." Our formalism involves a whitening/regularization operator $L: S\to S'$ whose continuous extension induces a native Hilbert space $H\subset S'$ that plays a central role in our characterization. The presentation is self-contained for the most part and remarkably general and powerful. It allows for the recovery of all known instances of such equivalences; in particular, the methods involving innovations and reproducing-kernel Hilbert spaces developed by Kailath and his students, and the mathematical correspondence between fractional splines and Mandelbrot's fractional Brownian motion (fractals), with the former being the optimal estimators of the latter. It also covers general Bayesian methods for the resolution of infinite-dimensional inverse problems.

Due to the nature of quadratic attention, Large Language Models (LLMs) consume a lot of memory and energy: every new token costs more than the previous one, and its keys and values must be stored in memory indefinitely, which is unsustainable. Two main lines of work address this: compressing the KV cache, e.g., by evicting or quantizing keys and values, and retrofitting LLMs to use Linear Attention, which replaces the KV cache with a fixed-size state. Retrofitting has attracted a lot of attention, given its promise to solve the quadratic scaling problem with state-of-the-art performance at low cost. However, it has not been properly compared to the simplest form of KV-cache eviction: Sliding Window Attention (SWA) with attention sinks. In this work, we show that SWA with sinks performs as well or better than most retrofitted Linear Attention models across multiple LLMs and downstream tasks, with the largest gains on long-context and generative tasks. On long-context reasoning tasks (Needle-in-a-Haystack and BABILong), SWA achieves massively higher performance (2 to 10 times higher than linear attention). SWA requires no additional training, is extremely fast, and requires little memory, making it an extremely cheap and reliable solution. When the training budget is limited, switching to SWA is a much more effective way to reduce inference memory cost than retrofitting linear attention. Linear attention models have shown promise, but they require training from scratch or extensive retrofitting to reap their architectural benefits and come close to SWA.

Pretraining accounts for a large fraction of the total computational cost in LLM training. However, noise-dominant gradients and the highly ill-conditioned loss landscape bring severe challenges. Although modern adaptive optimizers such as AdamW and Muon have achieved great success in large-scale pretraining, their reliance on gradient normalization offers limited mitigation of the ill-conditioned curvature. The progress along flat directions (eigen-directions of small eigenvalues), which dominates the final loss reduction, remains relatively slow. To enhance training dynamics along flat directions, we propose a curvature-conditioned multiscale momentum method with sphere constraints, delivering steady acceleration in LLM pretraining. This multiscale momentum, applied only along flat directions, pairs a slow-decay component for noise reduction with a fast-decay component for rapid curvature adaptation, harnessing their complementary strengths. Crucially, we employ a sphere constraint technique to prevent parameter inflation and excessively rapid effective learning rate decay that would otherwise arise from a naive combination. Extensive experiments show that the proposed method significantly accelerates Muon across diverse architectures (dense, MoE) and model sizes (0.12B–2.3B parameters). Theoretically, we verify the acceleration effect and provide insight into the design principles underlying the flat-direction multiscale momentum.

Fourier neural operators (FNOs) provide an efficient framework for learning mappings between function spaces as they are, by construction, independent of the grid resolution at which they are trained and evaluated. However, FNOs are not independent of the periodic domain they are applied to: their discrete spectral weights are indexed by integer Fourier mode numbers, which correspond to physical wavevectors. When applied to a different domain, the same trained weights act at different wavevectors, and the FNO silently represents a different operator. This makes FNOs unsuitable for tasks where transfer across domains is crucial. We propose Euclidean Fourier neural operators~(EFNOs) as a domain-independent alternative to FNOs. By parameterizing the spectral kernel as a continuous function of the physical wavevector, the EFNO can learn operators that act consistently across periodic domains of varying shape and size. We evaluate the EFNO on a simple heat equation and on a practically relevant materials science task of learning exchange-correlation potentials across different crystal structures, and demonstrate that the EFNO is able to generalize to unseen grid sizes and domains.

Tabular data, as a core data format in machine learning, often lacks the discriminative power needed for high-performance modeling due to insufficient feature informativeness. Automated Feature Engineering (AutoFE) overcomes this by automating feature generation and selection, ensuring both model performance and operational efficiency. However, traditional AutoFE often yield features with poor interpretability because they rely on blind mathematical transformations, while large language models (LLM)-based AutoFE faces challenges in requiring costly multi-round iterations to generate high-utility features to effectively enhance model performance, compounded by inherent risks of bias and hallucination. In this paper, we combine symbolic regression with LLMs for feature engineering (SymboLLM-FE) to solve these challenges. We extract mathematically expressive formulas strongly correlated with the target via symbolic regression, which can enhance model performance, then refine them by LLMs with rich prior knowledge to ensure interpretability. Empirical results on six real-world datasets and four Kaggle competitions demonstrate that SymboLLM-FE outperforms existing AutoFE. SymboLLM-FE also addresses the dual challenges of poor interpretability and numerous iterations by employing a statistical prior-grounded LLM refinement mechanism and single-digit LLM calls.