Papers

Many real-world reinforcement learning (RL) problems evolve in continuous time, where decisions occur at irregular, event-driven intervals rather than at fixed discrete steps. We study episodic continuous-time Markov Decision Processes (MDPs) in which decision epochs are governed by a homogeneous Poisson process and the reward and transition dynamics vary smoothly over time. We consider both a fixed number of jumps per episode and a fixed time budget with a random number of Poisson decision epochs. Under a Lipschitz continuity assumption in time, we exploit local smoothness through discretization and extend both UCRL (Auer and Ortner 2006) and Q-learning (Jin et al. 2018) to this setting, proving $\widetilde{O}(T^{2/3})$ regret bounds for both model-based and model-free algorithms. Finally, we establish matching $\widetilde{\Omega}(T^{2/3})$ minimax lower bounds, showing that the rate is optimal up to logarithmic factors. These results provide the first tight regret guarantees for Lipschitz-smooth continuous-time episodic MDPs with Poisson decision epochs.

Activation quantisation is usually evaluated with an aggregate metric, perplexity, averaged over every token a model predicts. We ask whether that average identifies which computations a quantiser damages. Perplexity turns out to be a reliable aggregate signal: across 12 models from four families and 780 within-model comparisons, the arm perplexity prefers also retains more induction and more retrieval in all but 2.1 and 4.0 percent of cases respectively. But where perplexity has risen by only a factor of 1.2 to 1.5, induction still keeps 0.959 of its intact accuracy while retrieval has already fallen to 0.554, a gap the aggregate number does not surface. This gap has structure, not just size: a matched Gaussian-noise control of the same per-channel magnitude leaves it largely intact, and randomising only the sign of the quantisation error, every magnitude held fixed, is nearly as harmless, so magnitude alone does not explain the damage. Quantising in a rotated basis, which changes coordinate alignment without changing error magnitude, restores induction from 0.001 to 0.980 at three average bits per token in a single-block intervention, though retrieval recovers less completely at the same setting (0.694); end-to-end at four average bits, induction reaches 0.968 and retrieval 0.534. The pattern holds on two further models up to 32B parameters and, in the deployed configurations we tested, under AWQ once activations are pushed to 4 bits. A perplexity target bounds the average cost of a transformation applied to the activation; it does not, by itself, show which computations survived.

Whitening a foundation-model embedding and using its squared norm as a training-free likelihood surrogate is motivated by the observation that whitened coordinates often appear approximately standard normal. We show that this observation follows from the projection central limit theorem and therefore does not imply a Gaussian joint distribution. Across multiple encoders and three training objectives, we find systematic over-dispersion of the whitened radius relative to the Gaussian reference, including against distributional clones with identical mean and covariance. We further show that the commonly reported agreement between empirical and theoretical norm statistics is an algebraic consequence of in-sample whitening and does not constitute evidence for Gaussianity. We identify the mechanism behind this behavior: whitening reverses the encoder's spectral hierarchy, shifting the contribution to the squared norm toward near-degenerate directions that encode predominantly noise. In these directions, the dominant variability is governed by a single input-dependent scale. We estimate this scale from two moments and use it to predict, without additional free parameters, the cross-dependence between disjoint spectral halves. These results indicate that the squared whitened norm is better interpreted as a Mahalanobis measure of semantic atypicality than as a log-likelihood. This interpretation explains both its practical effectiveness and its calibration failures: the statistic can rank and detect atypical samples consistently with nonparametric density estimates and across encoders trained with different objectives, while Gaussian tail thresholds can be inaccurate by orders of magnitude. etc.

Diffusion models and transformers have supplanted GANs for multivariate time series imputation, largely on grounds of GAN training instability. R3GAN (NeurIPS 2024) removes that instability via regularized relativistic losses with provable convergence, raising a natural question: do stable, modern GANs revive adversarial imputation? We adapt R3GAN to 1D temporal data with a coarse-to-fine refinement framework and a frequency-domain discriminator, and audit 14 saved configurations across 3 datasets. Because these are heterogeneous single runs, the evidence is descriptive rather than a matched causal ablation. We report a negative result. All five saved mean/zero-start configurations improve by 48.4-70.2%. Among eight eligible non-legacy linear-start configurations, the mean change is -0.7% (range -3.0% to +1.1%); a separate -21.9% legacy logging anomaly is retained for provenance but excluded from that aggregate. In a saved Weather comparison, standalone R3GAN-1D underperforms BRITS by 5.8x. Crucially, we argue the common explanation (that GANs optimize distributional rather than point-wise objectives) cannot be the whole story, since diffusion models also optimize distributional objectives yet achieve state-of-the-art imputation. Our saved reconstruction-weight sweep is consistent with the adversarial signal being inert or harmful, but cannot identify its causal contribution; a matched discriminator-removed ablation is the key next experiment. We frame the precise reason a learned discriminator fails to provide useful refinement gradients (where a learned diffusion denoiser succeeds) as an open problem, and offer practical guidance on when adversarial refinement is worthwhile.

Internet of Things (IoT) systems are increasingly deployed in smart homes, transportation, energy systems, and critical infrastructure. This broad connectivity improves service intelligence, but also enlarges the attack surface of IoT networks. Machine Learning (ML)-based Intrusion Detection Systems (IDSs) are widely used to identify malicious network threats and protect IoT systems, but developing effective ML-based IDS models often requires human expertise and repeated manual decisions on many procedures, including data pre-processing, feature selection, model selection, and hyperparameter tuning. Automated Machine Learning (AutoML) reduces this burden by automating steps of the ML pipeline using optimization techniques, but conventional AutoML methods can consume substantial optimization time because they explore broad candidate model families and large hyperparameter spaces. This paper proposes a Large Language Model (LLM)-assisted AutoML framework for IoT intrusion detection. The proposed framework uses an LLM as a policy generator that converts dataset profiles into bounded and validated AutoML policies for automated data balancing, automated feature engineering, and Combined Algorithm Selection and Hyperparameter Optimization (CASH). Under an equal 10-trial budget, the proposed LLM-assisted policy achieves higher weighted test F1-score than traditional AutoML using the Tree-structured Parzen Estimator (TPE) on both datasets, reaching 99.680% on CICIDS2017 and 99.186% on IoTID20. Relative to the broader 30-trial Traditional AutoML-TPE baseline, the 10-trial proposed method reduces optimizer time by 63.7% and 49.9%, respectively, while achieving slightly higher F1-score. These results show that a bounded LLM policy can improve the quality of a low-budget AutoML search while retaining a clear efficiency advantage relative to a larger conventional search budget.

We study the number of prototypes needed to represent Boolean functions by nearest-neighbour classification. There are two distinct settings: the prototypes may be arbitrary points of Euclidean space, or they may themselves be required to lie in the Boolean cube. For unrestricted prototypes, we strengthen a known lower bound for almost all Boolean functions. The bound applies simultaneously to nearest-neighbour voting rules with any number of voting neighbours, and substantially narrows the gap with the known general upper bound. We obtain a VC-dimension bound for classes with a bounded number of prototypes, and show that it is sharp in order in dimensions at least four. We then study Boolean prototypes, beginning with symmetric threshold functions. A connection with covering designs expresses the minimum number of prototypes at every threshold level exactly in terms of a covering number, and leads to further exact results for related monotone functions, including disjunctive extensions and a characterisation of when a representation with a single negative prototype is possible. For a uniformly random Boolean function, the Boolean nearest-neighbour complexity, as a proportion of the cube, is asymptotically close either to one half or to one, with explicit limiting probabilities. In particular, almost every Boolean function requires at least approximately half as many prototypes as there are points in the cube, and one half is the largest proportion for which such a lower bound holds. Finally, we consider arbitrary symmetric Boolean functions. Their Boolean nearest-neighbour complexity is closely approximated by a weighted vertex-cover problem on paths. As a consequence, a uniformly random symmetric function typically requires prototypes amounting to $11/20$ of the cube. This is much larger than the upper bounds known when the prototypes are allowed to lie anywhere in Euclidean space.

Adversarial multi-objective bandits hold the potential to help us optimize choices (arms) whose reward is a multidimensional vector chosen by an adversary and whose performance is measured by Pareto regret. We define loss as one minus reward and measure the easiness of a coordinate by the smallest cumulative loss of the arms on it, and call the coordinate easier when this quantity is smaller. Existing work suggests that in theory an easier coordinate may reduce Pareto regret. However, in practice, one may not know which coordinate is easier. On the negative side, we show that this lack of information eliminates the possibility: a smaller cumulative loss does not improve the worst-case order of Pareto regret. Precisely, let \(L_d\) be the smallest cumulative loss along coordinate $d$ over $T$ rounds. For \(K\ge4\) arms, \(T\ge6\) rounds, and at least 2 coordinates, we prove that the minimax expected Pareto regret is \(\Omega(\min\{T-L_0,\sqrt{K(T-L_0)}\})\). It is monotonically decreasing in \(L_0\), even when \(L_0=\min_d L_d\) itself is known. On the positive side, this result motivates the possibility that other coordinates, not just the easy one, may suffice to attain the optimal rate of Pareto regret. When $L_0$ is known, we apply Poly-INF to a fixed coordinate and obtain an upper bound on Pareto regret that exhibits the same order and thus matches the lower bound. Without such knowledge, we develop a reward-doubling version of Poly-INF that adapts to this unknown quantity while still attaining the matching minimax rate. Another implication is that it has no extra \(\log T\) factor and is independent of the number of coordinates.

Modern Transformer design and compression both reduce to allocating capacity under a budget. The standard scalars for these decisions, #Params and #FLOPs, capture size and compute but not architectural structure: two architectures with identical parameter budgets but different depth-width, head, or FFN allocations receive identical scores yet behave differently. We propose Neural Spectral Capacity (NSC), a closed-form scalar grounded in the singular-value spectrum of each weight matrix. Under standard random initialization, the Marchenko-Pastur law renders NSC computable from the architectural specification alone, with no model instantiation, data, or gradients. Its layer-wise additive structure admits NSC-DP, an exact dynamic-programming solver returning the architecture globally maximizing NSC under resource constraints in seconds on a CPU – a guarantee that black-box search over existing training-free proxies cannot provide. Empirically, NSC outperforms #Params, #FLOPs, and representative training-free proxies in ranking across seven Transformer and CNN families (on FlexiBERT, $\tau = 0.505$ on pairs differing in #Params by less than 10%, where #Params collapses to 0.082); NSC-DP discovers a Transformer-XL architecture on WikiText-103 that beats the human-designed baseline in 2 seconds; and prunes LLaMA-7B to the best 5.7B model across eight commonsense reasoning tasks without any calibration data, about 5900x faster than the strongest training-free proxy baseline.

Large language models (LLMs) and agentic AI systems are creating rapidly growing inference energy demands as model sizes grow and reasoning trajectories extend. While in practice, many queries do not require the capabilities of the largest available model, and routinely directing such queries to a high-capability model can introduce unnecessary, considerable computation and energy consumption. In this paper, we investigate whether adaptive routing across a heterogeneous pool of LLMs can reduce this energy burden without substantially compromising task performance. We design a language-model-based router that reads in each query and selects an answer model from a fixed candidate pool. The candidate models are first profiled through an offline tournament that records their correctness, latency, power, and GPU energy for each query. Using these measurements, the router is trained through supervised fine-tuning followed by group relative policy optimization (GRPO) with the tailored paradigms. Results demonstrate that learned routing can selectively allocate expensive model capacity based on query context and improve the accuracy-energy tradeoff in multi-LLM serving. Across seven benchmark tasks, we also observe a sharp accuracy-energy phase transition among routers, providing practical insights into improving energy efficiency while maintaining LLM performance.

Over-the-air federated learning lets edge devices transmit their local updates simultaneously, reducing the communication overhead. The resulting waveform, however, has a peak-to-average power ratio (PAPR) that grows with the model dimension, and keeping the amplifier in its linear range leaves two remedies: clipping the peaks or backing off the transmit power. Neither remedy is without cost: i) the clipping distortion appears at the receiver as a bias that cannot be removed, and ii) back-off keeps the signal intact but degrades the average signal-to-noise ratio (SNR). Independent of this trade-off, the transmission remains uncompressed, spending one channel use per model parameter, which keeps large-model training out of reach. To address these challenges, we propose AirGC-CD, an over-the-air scheme that precodes each local update with a partial Gaussian circulant matrix before clipping. In AirGC-CD, the precoder's output is exactly Gaussian regardless of the update's sparsity, so the clipping function is designed for a known distribution instead of inheriting it from the data. This enables the clipping to be inverted on average by a single scalar Bussgang gain in closed form, and we prove that the resulting aggregate is exactly unbiased, with clipping adding only variance. The clipping ratio is then the only free parameter left, trading the variance of the clipping against the SNR loss from back-off, and we derive its near-optimum in closed form. Since the precoder is linear, it also acts as a compressor, reducing the transmission from the model dimension d to the sketch dimension m at a cost of only O(dlog d) via two fast Fourier transforms, whereas a Gaussian sketch costs O(md). Experiments on five image datasets show that AirGC-CD outperforms baseline over-the-air FL schemes in most settings, particularly at low SNR, while using fewer channel uses per round.

Forecasters often know an event is imminent but not the shape, size, or timing of its effect. We introduce Event Signature Transfer (EST), a training-free, model-agnostic operator that turns a completed past event into an explicit forecast scenario. EST removes a source event's own trend and seasonality, then scales and retimes the remaining event signature onto a native forecast, preserving the forecast's linked structure and reducing to it exactly at zero strength. Because it reads only output quantiles, EST applies to any quantile forecaster, with no training, no model internals, at transfer time. Across twelve real episodes and ten synthetic scenarios on Chronos-2, TimesFM-2.5 and Toto-2.0, manually configured EST reduces real-episode WQL by 21.7-90% in-sample. On Chronos-2, it leads eleven of twelve matched comparisons against covariate conditioning, activation editing and raw replay. The operator builds a scenario; it does not estimate its likelihood.

Recent advances in natural language processing have led to molecular Large Language Models (LLMs) with strong performance across diverse chemistry tasks. However, they still struggle to capture fine-grained structure-property relationships, particularly how small, localized modifications alter a molecule's behavior. To address this limitation, we introduce MolSC, a dataset of substituent contributions, defined as property changes induced by attaching specific substituents to molecular scaffolds. Curated from manually annotated bioactivity records, MolSC spans structural-alert liability, target-specific bioactivity, and physicochemical descriptors, and contains 181K substituent-level examples for training. We further propose MolSC-Bench, a held-out evaluation benchmark of 1,541 examples disjoint from MolSC at the scaffold, substituent, and molecule levels. Our experiments show that existing molecular LLMs and strong proprietary models such as GPT-5.2 and Gemini-3-Flash show limited reliability in substituent contribution prediction. In contrast, training on MolSC substantially improves this ability and achieves strong performance across diverse downstream molecular tasks. These results highlight substituent contribution learning as a key component of fine-grained molecular understanding.

Chain-of-thought (CoT) can sound plausible yet be unfaithful to the model's underlying reasoning. Most prior work probes CoT faithfulness through input–output behavior or input attributions, leaving internal computation largely underexplored. We instead cast faithfulness as internal concept grounding: Does a large language model's (LLM) CoT reasoning engage the same internal concepts that support the LLM's direct prediction, and do the shared concepts causally drive its answer? Encoding a prediction pass and a CoT pass with a single shared sparse autoencoder (SAE), a reliable approximator of the latent concepts LLMs use, makes their internal concepts directly comparable. We introduce three correlational metrics of concept-level alignment and a causal metric, $\Delta p$, which ablates the shared concepts and measures the drop in answer probability. Across five LLMs and four datasets, concept alignment is generally high, as indicated by the correlational metrics; yet these only identify which concepts are shared, not how much they causally contribute. $\Delta p$ fills this gap: causal faithfulness varies substantially with model depth, peaking at mid-to-late layers rather than the final ones, and model scale reshapes the layer-wise profile. Moreover, causally important shared concepts are not always verbalized in the CoT. These dissociations suggest that faithfulness cannot be reliably assessed from surface-level or representational correspondence alone; assessing it requires causal tests of whether the internal concepts underlying a CoT actually drive the model's prediction.

Discrete diffusion models now match autoregressive language models on several benchmarks, while the question of how best to train them has received far less attention: the optimizer is inherited from one paper to the next and never compared. New optimizers, meanwhile, are validated almost exclusively on autoregressive pretraining, a different objective on a different loss surface. We present a controlled optimizer benchmark across four diffusion formulations, to our knowledge the first for discrete diffusion: seven optimizers (AdamW, Lion, Muon, SOAP, MARS, MARS-M, Schedule-Free) on masked diffusion (text8), uniform diffusion (QM9, and LM1B through the Gaussian duality) and Gaussian diffusion on images (CelebA-64), each on a task with published reference values. Every optimizer receives the same search protocol, and every winner is retrained at the full budget with three seeds. AdamW is a strong default but not always the right choice: it is beaten by a resolved margin on two of the four tasks, and the winner changes with the formulation, so the optimizer deserves the same care as the rest of the training recipe. Notably, methods validated on autoregressive language model pretraining transfer well: Muon, MARS-M and SOAP each beat the tuned AdamW on at least one diffusion formulation. The benchmark, all runs and every figure are reproducible end to end from the released code at https://github.com/armanbolatov/diffusion-baselines.

Compressed manipulation policies can pass offline evaluation while failing in closed-loop execution; this dissociation is established in prior work and is not our claim. We contribute a causal anatomy of one naturally occurring case. An 8-layer distillation of Octo-Base retains 86% of parameters, passes every offline check we applied (0.996 and 1.000 teacher-ratios on the family's own validation metrics), and collapses in closed loop: 0/72 vs. the teacher's 40/72 on a simulated WidowX pick-and-place task. The collapse is structured, not diffuse: early task stages degrade gradually (the student moves the object at 90% of the teacher's rate and grasps at 55%), while transport-to-target fails categorically, at 0% in every training variant. Paired action-trace forensics isolate the signature: a negative, late-heavy $z$ residual, roughly 10x its post-repair magnitude, and persistent across the base distillation and both continuation branches. Four standard therapies fail under matched controls: continued training and in-domain offline data leave success at zero, even though the latter measurably improves marginal action statistics; command-level compensation recovers nothing at any offset, although the same perturbations degrade healthy policies; clamping the symptom in the command channel preserves grasping, yet success stays at floor. A minimal-pair intervention that substitutes half of the training stream with deployment-distribution teacher rollouts, with every other setting held fixed, restores parity with the teacher (18/36 vs. 17/36 held-out), eliminates that signature, and recovers a teacher-like perturbation-response profile. We claim existence, not universality. Operationally, offline gates, including a family's own validation metrics, are insufficient acceptance tests for compressed policies; a few dozen closed-loop trials sufficed to find what they missed.

Spatial reasoning is essential for vision-language models (VLMs) to understand and act in the physical world. Reasoning in dynamic environments requires VLMs to perceive local state transitions caused by object motion and viewpoint changes and integrate them over long trajectories to maintain an updated spatial state, yet existing VLMs remain limited in both capabilities. Current spatial training primarily focuses on static questions about object attributes and spatial relations, providing limited direct supervision for state transitions; in contrast, interaction trajectories naturally connect a preceding observation, an action, and a subsequent observation, offering direct supervision for local state transitions, while complete trajectories reveal dependencies among consecutive transitions. We therefore introduce Spatial-Interactor, a framework that trains VLMs to model physical-world state transitions through interaction, organizing this learning process into a three-level curriculum covering L1 passive world-state transitions, L2 active self-state transitions, and L3 long-horizon interaction trajectories. Accordingly, we construct the Learning from Spatial Interaction dataset (LSI-108K) from simulated and real interaction trajectories, with tasks aligned with the objective of each level. Our two-stage training strategy applies Supervised Fine-Tuning (SFT) to L1 and L2 for local transition modeling, and On-Policy Distillation (OPD) then uses privileged self-distillation: a teacher branch given segment-level transition descriptions supervises the student's on-policy CoT, helping the student learn to integrate consecutive transitions over L3 long trajectories. Experiments across multiple VLMs and spatial benchmarks show consistent gains in local transition modeling and long-horizon integration.

Looped language models repeatedly apply a weight-shared block to increase effective depth without increasing parameter count, but the resulting T sequential recurrent-block calls per generated token substantially increase decoding latency. To address the issue, we introduce Wavefront Decoding (WFD), a training-free self-speculative decoding framework designed for looped language models. WFD exploits two properties of these architectures: intermediate recurrence outputs provide effective draft predictions, and weight sharing allows token states at different positions and recurrence depths to be processed in one batched recurrent-block call. WFD organizes these mixed-depth states into a diagonal wavefront, continuously drafting new positions at shallow depth while advancing earlier positions toward full-depth verification. Unlike the phase-separated draft-then-verify schedule, WFD therefore concurrently batches drafting and verification within the same recurrent calls, while rejected drafts are corrected using full-depth predictions. Across six Spec-Bench task categories, WFD achieves 2.42x speedup on Ouro-2.6B and 3.54x on Huginn-3.5B over autoregressive decoding, consistently outperforming draft-then-verify. Cross-recurrence KV sharing further reduces wavefront KV traffic and increases WFD's speedup to 4.81x on Huginn-3.5B. The code is available at https://github.com/summerbro-hhj/wavefront-decoding.

Automated pollen analysis supports veterinary cytology, but brightfield microscopy is costlier and more complex than lens-less digital in-line holographic microscopy. We evaluate whether reconstructed holograms can narrow this gap and whether model explanations remain reliable under modality change. Six pollen species were imaged by brightfield and holographic microscopy. Raw, single back-propagation and iterative phase retrieval holograms were evaluated with YOLOv26s detection and MobileNetV4 classification after anchor-based annotation transfer. Six attribution methods were assessed for spatial grounding and faithfulness with the Attribution Health Inspection and Repair (AHIR) protocol, which tests model brittleness under weak noise and corrects attribution-map granularity when needed. Brightfield achieved 0.6890 mAP50-95 (0.8865 mAP50) for detection and 0.9687 macro-F1 (0.9705 accuracy) for classification. Reconstructed holograms narrowed the gap with a task-dependent split: p-type was strongest for detection at 0.5324 mAP50-95 (0.8229 mAP50), while r-type was strongest for classification at 0.7695 macro-F1 (0.7866 accuracy), both far above raw-hologram baselines. Activation-based explanations localized strongly on grains, and region-based methods retained ~60 to ~80% of faithfulness under holography. The holographic detector was highly brittle to weak perturbations, saturating deletion-based evaluation while insertion remained informative. Pixel-level gradient explanations approached random floor, yet spatial smoothing restored p-type gradient faithfulness from 0.05 to 0.51. For holographic classification, perturbation-based explanations remained faithful while gradient-based methods fell below random floor. Reconstruction improves low-cost holographic pollen analysis, while AHIR distinguishes genuine attribution failure from artifacts caused by model brittleness and map granularity.

Deep learning models are powerful but opaque. As quantum machine learning matures, the field faces a defining choice: build quantum models that are equally opaque, or exploit the mathematical structure of quantum mechanics to make them inherently interpretable. We show that the latter is possible. By tracking quantum mutual information~(MI), entanglement entropy, and state fidelity through the layers of a Quantum Transformer Block (\qtb{}), a fully-coherent variational circuit with quantum analogues of both attention and feedforward, we gain direct insight into how the model processes information: which tokens it attends to, when correlations form, and why predictions fail. On four tasks with known dependency structure we show that (i)~learned MI matrices align with ground-truth task structure (AUC$\,{=}\,0.69$ on lookup), (ii)~disabling entangling gates collapses accuracy from 100% to 15% while MI$\to 0$, proving entanglement is the mechanism, (iii)~accuracy and MI co-evolve during training ($\rho\,{=}\,0.92$ on lookup), and (iv)~per-sample MI predicts prediction correctness on the conditional task with ROC AUC$\,{=}\,0.84$. All results are validated on IBM Quantum hardware (ibm\_kingston, Heron~r2): the circuit's reasoning process, from product state through structured entanglement, is directly observable on a superconducting processor. These proof-of-concept results, obtained on small synthetic tasks, suggest that the physics of quantum computation can provide intrinsic interpretability signals with no direct classical counterpart, motivating study of whether this advantage persists at scale.

Multi-class open-set anomaly detection requires a model to characterize the normal acceptance domain formed by multiple heterogeneous subdistributions using only class-labeled samples from known normal classes, and to identify previously unseen anomalies at test time. Existing single-hypersphere methods cannot explicitly represent class-specific locations and acceptance ranges, while current multi-hypersphere or multi-class approaches do not fully integrate inter-class boundary constraints, learnable acceptance ranges, and interpretable decisions. To address these limitations, we propose Interpretable Multi-Hypersphere Deep Anomaly Detection (IMHD-AD). IMHD-AD constructs an independent hypersphere for each known normal class in a shared feature space. With target-inside and non-target-outside constraints, IMHD-AD embeds the class-specific hypersphere centers and radii directly into the final network layer and jointly optimizes them with the shared representation. The minimum signed boundary score across hyperspheres simultaneously determines open-set acceptance or rejection and provides a faithful geometric explanation of each decision. On MNIST, Fashion-MNIST, and CIFAR-10, IMHD-AD achieves the highest AUC in 28 of 30 open-set comparisons. A two-dimensional synthetic study further shows that model architecture must balance the compactness of known normal classes against the separability of unknown anomalies.

Apple Silicon machines with large unified memory make it possible to hold large tensors on a desktop GPU. However, we found that PyTorch's Metal Performance Shaders (MPS) backend silently returns wrong results for batched matrix multiplication with more than $2^{32}$ elements. torch bmm, including its wrappers matmul and eager attention, returns relative errors above 1 without an exception or a warning in every PyTorch release tested (2.4.1 to 2.14.0). We sweep bmm over dtypes, memory layouts, shapes and batch sizes around $2^{31}$ and $2^{32}$ elements, and judge every result against a float64 computation on the CPU. Three rules account for every outcome on 2.14.0. When the output exceeds $2^{32}$ elements and an operand is a transposed view, the entire output is wrong and equals a computation that ignores that operand's strides. Otherwise, a view with at least $2^{31}$ elements raises an exception, and a contiguous input above $2^{32}$ elements makes exactly the batches beyond that point wrong, equal to a computation whose index wraps at $2^{32}$. A slightly larger problem can thus turn an explicit error into a silent failure. The rules extend to the backward pass, where a correct forward pass can return silently wrong gradients. A second machine with another chip, under two macOS versions, reproduces all 6156 results, including the wrong values, and the same sweeps on an NVIDIA A100 are correct in all 2530 runs. In a public sentiment classifier, one oversized batch corrupts a third of the outputs, which collapse onto one class. All findings come from observable behavior, without access to the backend's closed-source kernels; we release the harness, raw results and a guard that stops any MPS operation touching $2^{32}$ or more elements at jniimi/mps-silent-failures (https://github.com/jniimi/mps-silent-failures).

We study the symmetric and antisymmetric parts of bilinear forms in the attention heads of trained large language models. We introduce an orthogonally invariant profile map from real bilinear forms to a three-dimensional simplex and observe that profiles of trained bilinear forms accumulate near profiles of rank-one bilinear forms. We prove that the symmetric part of a bilinear form in an attention head is the sum of a hyperbolic form and a zero form for a Zariski-dense subset of query-key matrices.

Physics-informed neural networks (PINNs) use one shared representation over the computational domain, which can become difficult to optimize on long domains and for high-order operators. We study a minimal alternative: multiply the first hidden activation of an otherwise unchanged dense PINN by input-dependent localization functions, giving first-layer units receptive fields without partitioning the domain or adding interface losses. We screen 13 families of localization functions, in up to three parameterizations each, on a nonlinear harmonic oscillator (HO), a heat equation on a long spatial interval, and a manufactured four-dimensional (4D) fourth-order problem, with ten paired seeds throughout. Three configurations give large reductions in solution error at matched budgets: (i) Fixed Gaussian localization functions on the $2\pi$ HO domain cut mean solution RMSE from $4.8369\times10^{-1}$ to $8.83\times10^{-3}$ at 3k epochs. (ii) The inverse-quadratic family with learnable centers and widths cuts it from $2.896\times10^{-1}$ to $3.06\times10^{-2}$ on the $8\pi$ heat domain at 10k epochs. (iii) Fixed bump localization functions cut it from $1.75947\times10^{1}$ to $2.260\times10^{-1}$ on the $4\pi$ 4D domain at 10k epochs. Every paired seed improves in these three comparisons. The screen also shows that the mechanism is not a free win: on HO only 2 of 13 families beat the baseline, and 10 of the remaining 11 are 9 to 23 times worse; on 4D four families are non-finite and five are more than three orders of magnitude worse than the baseline. The inverse-quadratic family is the only one that beats the baseline on all three equations. Overall, these results show that first-layer localization can provide measurable improvements to baseline PINNs on long-domain and high-order problems.

Robotic grasping is typically formulated as the problem of identifying successful actions from a space of candidate grasp poses. However, the organization of successful actions within this space has received less attention. We study the multiscale structure of viable robotic grasps in $SE(3)$ and investigate whether this structure can be exploited for more efficient exploration. Using a large-scale grasp dataset, we show that successful grasp sets exhibit heterogeneous and reproducible connectivity structure across objects. We then introduce a connectivity-aware sampling strategy that incrementally explores the currently observed grasp space by prioritizing potential bridges between components, structural frontiers, boundary extensions, and geometric novelty. In controlled reconstruction experiments, the method recovers the connectivity structure of successful grasp sets substantially more efficiently than random sampling and farthest-point sampling. We further evaluate whether connectivity acquired under hidden grasp viability can improve subsequent grasp discovery, and whether structural experience from previously explored objects can be retrieved and transferred to unseen objects. These results suggest that the spatial organization of viable actions provides information relevant to grasp-space exploration beyond the viability of individual candidate actions. More broadly, they motivate structure-aware exploration as a means of exploiting the geometry of viable action spaces in robotic manipulation.

Similarity-based retrieval is the dominant rule for conditioning large language models (LLMs) in in-context learning, retrieval-augmented generation, and prompt-based time series forecasting. The rule concentrates on near-duplicate candidates, an issue that has motivated diversity-aware retrieval but remains unexamined in other retrieval-conditioned pipelines. We study this issue using prompt-based time series forecasting as a test bed, where a learned prompt pool is retrieved by similarity. Dominant methods in this setting retrieve top-K entries by cosine similarity without redundancy control, producing a bias toward dominant temporal patterns while overlooking rare but informative events. We propose CASP-LLM, a coverage-aware semantic prompting framework that addresses this prompt selection bias by combining usage-tracking and saturating-gate techniques into a coverage regularizer that adds no learnable parameters. On six long-term benchmarks and the M4 short-term benchmark, CASP-LLM matches or improves on similarity-based LLM forecasters on most dataset-horizon settings, with the exceptions of Electricity, M4-Monthly, and the few-shot long-horizon setting. A controlled study locates the failure mode at the cross-batch usage level rather than per-retrieval redundancy: within-retrieval diversification such as MMR does not help, whereas regularizing anchor usage across training does.

The medications prescribed to a patient often change during a hospital admission as clinicians start, stop, or continue therapies. We study whether models can predict which medication classes are added or removed between 24 hours after admission and discharge. Metrics that compare the complete discharge regimen can reward models for copying medications that remain unchanged, even when they identify no actual changes. We therefore introduce a leakage-controlled benchmark that predicts net ATC3 additions and removals using only prior completed admissions and information available within the first 24 hours of the current admission. Addition candidates are classes not active at 24 hours, whereas removal candidates are classes active at that time. We also introduce R-GEAN, an asymmetric candidate-scoring network with independent addition and removal predictors. Across 240,480 admissions from 82,286 patients, R-GEAN achieves the highest predefined summary of addition, removal, changed-regimen, and action-pattern performance, termed the edit composite (0.464), compared with 0.435 for the strongest primary comparator. Reimplemented RETAIN, GAMENet, and MICRON baselines obtain 0.428, 0.420, and 0.288, respectively. R-GEAN's advantage is concentrated in correctly identifying medication classes no longer active at discharge, while rare additions and admissions with multiple medication changes remain difficult. Rankings based on micro-F1 over the reconstructed discharge regimen and the edit composite correlate weakly across the evaluated models (Spearman r = 0.20). The continuation baseline achieves the highest complete-regimen score despite predicting no additions or removals. These results show that complete-regimen and edit-level evaluation measure different aspects of medication prediction. The benchmark evaluates observed prescribing changes, not treatment appropriateness

Enterprise agentic systems that route every trajectory step to a frontier model waste 60-80% of their inference budget on subtasks that smaller models handle equally well. Existing routing solutions optimize single-turn query assignment but ignore a property unique to agentic workflows: subtask complexity varies widely within a single trajectory. A planning step may require frontier-class reasoning while a subsequent formatting step needs only a 7B model. We formalize step-level model routing as a sequential assignment problem over agent trajectories and propose AgentRouter, a lightweight classifier (12M parameters, <5ms overhead per step on an A100 GPU) that maps each trajectory step to one of four model tiers using five features extractable at routing time. Trained on 50,000 annotated agent trajectory steps spanning planning, coding, research, and data analysis tasks, AgentRouter achieves 72% cost reduction relative to frontier-only baselines, retaining 97.3% of frontier-only quality (less than 3% degradation in end-to-end task completion); per-step routing accuracy reaches 91% on minimal-complexity steps and 85% on efficient-tier steps, with 76-82% on the harder mid-range and frontier tiers. On the same benchmarks, RouteLLM and FrugalGPT (applied per-step) achieve only 31% and 44% cost reduction respectively, because their single-turn training signal misses trajectory-level quality dependencies.

While compressed-sensing regularizers enable interpretable reconstruction of 4D Flow CMR through transparent variational objectives, their hand-crafted nature is too restrictive under high acceleration. State-of-the-art learning-based approaches mitigate this, but typically encode regularization implicitly through unrolled network modules, which limits their interpretability. To address this limitation, we propose CLEAR, designed to combine the interpretability of compressed sensing with the flexibility of learned models. To the best of our knowledge, it is the first learned regularizer for a 4D reconstruction task. In the ultra-accelerated \(10\times\)–\(50\times\) regime of the CMRx4DFlow2026 challenge, CLEAR outperforms compressed sensing locally low-rank (LLR) and the popular variational network FlowVN, while using less than 10k parameters and preserving an interpretable regularization structure.

Token selection for instruction tuning is coupled: supervision utility depends on retained context, and vice versa. Existing methods largely optimize prompt compression or response supervision separately. Combining selectors can value supervision using removed context, or context using excluded supervision, creating selection-state mismatch. BRIDGE (Budgeted Response-Prompt Interaction via Directional Gradient-guided Efficient Token Selection) models selection-conditioned token utility through a shared validation-directed surrogate objective. BRIDGE routes response utility to supporting prompt tokens through attention, then alternates budgeted selection to revalue each side under the other's retained subset. Updates reuse precomputed interactions without repeated model scoring, while structure-aware projection promotes coherent supervision spans. Across three model families and three task domains, BRIDGE performs best overall among evaluated selection methods. Its MATH advantage over independent selection grows with compression, reaching 1.66 percentage points on Llama-3.2-3B.

Federated learning (FL) enables collaborative model training without centralizing private data, but performance often degrades under feature skew: clients share labels while the conditional input distributions $p_i(x\!\mid\!y)$ vary due to latent, client-specific appearance factors. We propose Joint Domain-Class Federated Learning (JDFL), a lightweight, optimizer-agnostic extension that makes this latent domain variation usable without sharing raw data. JDFL first infers domain clusters called pseudo-domains from brief local update signals. It then expands the classifier head to output $M\times C$, joint (domain-class) logits. This allows the model to represent domain-conditioned appearance while keeping a shared backbone. To train the expanded head we introduce two complementary supervision strategies based on simple intuitions: a similarity-aware soft-labeling that transfers evidence between nearby inferred domains while allowing domain-specific specialization, and a per-sample randomized target assignment that perturbs supervision across the joint outputs and serves as a low-cost training-time regularizer. JDFL integrates with existing standard FL methods (e.g., FedAvg, SCAFFOLD) with minimal changes. Empirically, both supervision modes consistently improve global test accuracy on standard domain-shifted image benchmarks; ablations and sensitivity studies show the gains stem from the proposed supervision and parametrization rather than mere capacity increase.