Papers

This paper studies real-time robust optimal control for uncertain nonlinear systems, where linear time-varying (LTV) approximations make planning tractable but require sound linearization error bounds (LEBs) to guarantee robust constraint satisfaction. We develop tight, differentiable, GPU-parallel LEBs for LTV approximations of nonlinear and neural network (NN) dynamics. For analytic dynamics, we introduce path-based Hessian bounds that are tighter than standard interval methods. For NN dynamics, we derive certified LEBs using NN verifier-generated affine relaxations and local Jacobian corrections. We adapt a GPU-parallel system-level synthesis LTV-based robust control solver to be compatible with these LEBs by extending it to handle right-invertible disturbance matrices and non-zero-centered disturbance sets for tight zonotopic uncertainty propagation. Our method, GPUSLS-LEO, enables online optimization of robust feedback policies that account for linearization error, producing tight, formally verified reachable tubes. On complex nonlinear and NN dynamics up to 168 state dimensions, our method can compute robust control policies on the GPU at rates up to 67 Hz, reducing solve times and conservativeness relative to baselines while preserving formal guarantees and real-time performance.

Quantum computing has emerged as a promising computational paradigm for machine learning (ML), with the potential to offer computational advantages over classical approaches. At this stage, the evidence supporting the performance and advantages of quantum machine learning (QML) models relative to classical models is insufficient. To address this gap, this paper presents an empirical study on the performance of QML models and their classical counterparts. We compare seven model pairs spanning supervised learning and reinforcement learning. Our results indicate that the evaluated quantum machine learning models do not yet surpass the classical baselines in overall prediction performance, policy stability, or training time. Nevertheless, QML remains a promising approach for filtering noise and controlling false positives. Our research findings summarize the challenges facing quantum machine learning across hardware environments, training efficiency, and convergence stability, providing a foundation for research into the robustness and parameter optimization of QML. This work is publicly available at https://github.com/Z-537-437/QML.

Combinatorial optimization (CO) problems are difficult because certifiable discrete structure induces exponential search. One needs to search over the set exponentially many candidates to certify optimality, however, the structural feasibility of a path, packing, or cover can be verified in polynomial time once supplied. In this study, we introduce Neural Certificate Pricing (NCP) that exploits this asymmetry under an unsupervised learning framework. A neural network is trained to predict certificate-level dual prices, while a structured recovery layer constructs the induced primal marginal. NCP can be viewed as amortized separation: instead of enumerating violated inequalities, it learns the residual prices through which their aggregate effect enters recovery. When the certificate-consistency condition holds, the recovered marginal is globally feasible, and a local theory shows that first-order errors in the predicted price induce only second-order loss in objective value. Across three classes of CO problems, NCP either outperforms state-of-the-art neural baselines by large margins or matches them at a fraction of the computation time, and shows stronger out-of-distribution generalization.

RL with verifiable rewards (RLVR) has emerged as a powerful paradigm for training LMs on tasks with well-defined success metrics, such as code generation and mathematical reasoning. However, current RLVR methods optimize only what can be objectively scored, often neglecting subjective, non-verifiable aspects of human-like outputs, such as style and structure. This limitation leads to well-documented failure modes such as diversity collapse, unnatural-sounding responses, and reward hacking. We propose an adversarial generator-discriminator framework that augments verifiable rewards with a learned signal from human demonstrations. A generator model is trained using RL to maximize both task accuracy and an adversarial reward derived from a discriminator. The discriminator, trained alongside the generator policy, learns to distinguish human-written outputs from model-generated ones. The discriminator serves as a learned proxy for the human output distribution, providing feedback on aspects of generation that are difficult to formalize as scalar rewards. Across diverse domains, including bug fixing and open-ended generation, our approach consistently improves non-verifiable properties while preserving the accuracy gains of RLVR. In bug fixing, our method produces solutions with significantly lower edit distance compared to RLVR baselines while matching end performance. In story generation, our method significantly improves win rate while producing stories that are diverse and more human-like. And in a simple reward hacking benchmark, our method nearly eliminates model misbehavior while maintaining high benchmark scores. Together, these results show that our approach bridges RL and SFT, offering a scalable path toward jointly optimizing the verifiable and non-verifiable properties of a task.

Scaling inference compute, by generating many parallel attempts per problem, is a costly but reliable lever for improving language model capabilities. By default these attempts are generated independently, wasting inference compute on redundant solutions. This waste seems unavoidable. After all, independence is what makes parallel sampling trivial to scale. However, this tradeoff is not fundamental: there is a rich design space of samplers that generate correlated but exact samples entirely in parallel. We explore this design space as an avenue for improving sample efficiency in scaling inference compute and reinforcement learning (RL). Concretely, we introduce QuasiMoTTo, which uses correlated samples as a drop-in replacement for i.i.d. samples. To generate these samples, QuasiMoTTo uses a reparameterization of autoregressive sampling as inverse-CDF sampling and draws the underlying uniforms with quasi-Monte Carlo (QMC); because QMC spreads the uniforms out more evenly than i.i.d., the resulting samples cover the output space with far less redundancy. Even though the batch is correlated, each sample is marginally distributed according to the language model, so we can use the batch for policy-gradient training. Our empirical analysis focuses on understanding how efficiently QuasiMoTTo can turn compute into performance. To evaluate correlated samplers, whose dependence breaks standard pass@k estimators, we first develop an unbiased bootstrap estimator. Across four reasoning benchmarks, QuasiMoTTo matches i.i.d. pass@k accuracy with 25-47% fewer samples. Strikingly, QuasiMoTTo often saturates an upper bound on pass@k that holds for any marginal-preserving sampler. We also apply QuasiMoTTo to policy-gradient RL (GRPO) where it matches i.i.d. performance with 50% fewer training steps. These gains come from higher coverage, which yields a stronger learning signal per batch.

Sample-based generative models are increasingly used for probabilistic forecasting in high-stakes decision settings, yet their training objectives are blind to the decision maker's cost structure. These models are commonly trained with strictly proper scoring rules, such as the energy score, which allocate their training signal in proportion to data density, with no awareness of where forecast errors are most costly for downstream decisions. We therefore propose decision-aware training for sample-based generative models, augmenting the energy score objective with a differentiable decision loss that directly penalises the cost incurred by acting on the model's forecast. This combined loss is theoretically grounded, as the decision loss is itself a proper scoring rule. We compute the decision loss via a differentiable optimisation layer. Its gradient concentrates in cost-sensitive regions of the output space, making the method's effects interpretable and predictable from the cost structure. We validate the method on one synthetic and two real-world tasks. In the synthetic task, the method corrects the mode weights of a learned bimodal distribution; in a wind power dispatch task, it concentrates improvements in the rare but costly tail region, and in a frost protection task, it improves how well the decision costs are anticipated. Our method yields generative models that retain full probabilistic forecasts while being better aligned with the decision maker's specific cost structure.

Recent work has shown that implicit neural representations (INRs) can be trained to effectively compress structured and unstructured volume data, allowing for direct data querying with a reduced memory footprint. However, as existing INRs for unstructured volumes do not encode geometry, they require partial mesh storage for later sampling, limiting achievable compression. At the same time, novel view synthesis methods have shown that explicit collections of 3D Gaussians can be used to accurately visualize volume data. In this work, we introduce an explicit model for volume data compression based on 3D Gaussian primitives. We reinterpret collections of 3D Gaussians as an explicit representation of a volume's scalar field and use a sampling strategy that reconstructs scalar values at spatial locations through weighted aggregation of intersecting Gaussians. We develop optimized CUDA-accelerated pipelines for structured and unstructured model sampling, loss functions that encourage accurate domain coverage of our models, and a novel sampling-error based densification strategy. Our explicit formulation naturally encodes domain geometry, eliminating the need for mesh storage in unstructured volumes and introducing significantly higher compression opportunities. Compared to existing INRs, we demonstrate that our explicit model achieves significant training speed and reconstruction quality improvements on both structured and unstructured volumes, while enabling compression ratios much higher than previous work for unstructured volumes.

Data analysis in the medical domain often encounters scenarios involving a limited target dataset and a large, unannotated dataset with a general distribution. Under such circumstances, self-supervised learning (SSL) methods are highly effective for utilizing large datasets, making them a popular choice for electrocardiogram (ECG) analysis. This work presents the Event Reconstruction Joint-Embedding Predictive Architecture (ER-JEPA), a lightweight SSL framework for multivariate time series, whose name and two-fold hierarchical structure are inspired by the diagnostic approach of cardiologists. At its core, ER-JEPA features: (1) a two-stage structure that constructs representations for each time interval and subsequently processes these representations as a univariate time series, (2) the hierarchical integration of two Joint-Embedding Predictive Architectures (JEPAs), and (3) a Vision Transformer (ViT) backbone. The structural concatenation of two JEPAs categorizes the model as a Hierarchical JEPA (H-JEPA), designed to encode multiple levels of abstract representations for enhanced prediction on complex tasks. This study reports a successful application of H-JEPA to 12-lead ECG data as a multivariate time series, alongside an analysis of the sensitivity of hierarchical representation during the pretraining stage. Furthermore, this study provides a qualitative demonstration that the intermediate representations produced by the first module of ER-JEPA excel at local feature extraction, as they are structurally free from over-smoothing. Pretrained on approximately 180,000 10-second recordings, the model achieves state-of-the-art downstream performance on the ST-MEM benchmark, with rapid computation and minimal resource usage.

While generative models have enabled training-free reward alignment, existing particle-based methods are fundamentally constrained by their propensity to local exploration within narrow regions of the underlying distribution, severely restricting sample diversity. This limitation becomes especially acute under tight reward-feedback budgets, where effective search demands broad, strategic exploration to uncover high-utility regions. To address this, we propose Sequentially-Controlled Interactive Multi-Particle Flow-Maps (IMPFM), a framework for feedback-efficient search. IMPFM progressively transports a group of interactive particles toward the target distribution, maintaining the broad coverage essential for heterogeneous preference alignment. IMPFM leverages a principled and efficient posterior sample-sharing mechanism across particles powered by flow maps. By correcting individual particle drift with the collective value gradient from the entire ensemble's posterior samples at each correction step, the framework maximizes sample utility to enable global exploration while actively mitigating reward over-optimization, typical of standard control frameworks. Paired with a principled exploration-exploitation reweighting mechanism involving multi-particle interaction, this sequentially corrected multi-particle dynamics explicitly preserves structural diversity and overcomes the weight degeneracy inherent to standard Sequential Monte Carlo (SMC) samplers. Crucially, we prove that the resulting sampling framework yields a multi-particle interaction-aware Feynman-Kac corrector that progressively steers the multi-particle system toward a KL-tilted target distribution, facilitating global exploration and preventing mode collapse. Extensive empirical evaluations and ablations across diverse search and alignment tasks confirm the efficacy of IMPFM over existing baselines.

Operator learning for partial differential equations (PDEs) on arbitrary geometries builds fast neural surrogates for large-scale simulation. Although recent geometry-adaptive neural operators have made substantial progress, they are mainly designed for forward problems in which inputs and outputs share the same spatial domain. This limits their applicability for boundary value problems (BVPs) and inverse problems, where inputs and outputs may live on different domains. We introduce the Geometry-Adaptive Integral Autoencoder (GAIA), an operator learning model that encodes the domain boundary and the interior field distribution into geometry tokens, and conditions integral transform layers on these tokens via cross-attention, allowing the kernel to adapt locally to geometric features. This yields a single architecture for forward (including BVPs) and inverse problems on arbitrary domains in one pass, without retraining, iterative optimization, or graph construction. We evaluate GAIA on seven 2D and 3D benchmarks, four of which are new or substantially extended benchmarks for inverse problems and BVP: electrical impedance tomography, optical tomography, 3D Darcy flow on varying geometries, and a modified setting of Poisson BVP on mechanical components benchmark (MCB). GAIA sets new state-of-the-art results on every inverse and BVP task, reducing median relative $L^2$ error by 64% on airfoil flow reconstruction and 27% on EIT relative to the next best amortized method, and outperforming all baselines on every shape category of MCB. On other forward problems, GAIA is competitive with specialized solvers while maintaining stable accuracy across point resolutions on which transformer-based baselines degrade.

Zeroth-order (ZO) optimization enables fine-tuning large language models when backpropagation is unavailable or memory-prohibitive, but existing methods often perturb full model weights or randomly constructed low-dimensional subspaces, yielding high-variance estimates and limited performance. We propose ZO-Act, an activation-informed ZO fine-tuning method that restricts perturbations to a fixed low-rank subspace derived from input activations. For each linear layer, ZO-Act computes a small activation basis once at initialization and optimizes only lightweight coefficient matrices using forward-only loss evaluations. This reduces the effective perturbation dimension, exposes explicit trainable variables compatible with momentum-based optimizers such as Adam, and naturally supports quantized LLM fine-tuning by keeping low-bit weights frozen. We analyze ZO-Act as zeroth-order optimization over a restricted coefficient space and show that perturbing the low-dimensional coefficients reduces both the variance-dependent convergence term and the finite-difference error of the ZO estimator, at the cost of a controlled subspace approximation bias that is mitigated by the low-rank structure of LLM activations and gradients. Experiments on Llama-3-8B, OPT-13B, and INT4 Llama-3-8B show consistent gains over strong ZO fine-tuning baselines across language understanding, question answering, and commonsense reasoning.

Muon has recently emerged as one of the most effective optimizers for training large neural networks, yet its empirical success has been explained from several different perspectives. In this paper, we propose a simple mechanistic interpretation: Muon can be understood as an implicit residual connection during training. Specifically, orthogonalizing the update can sacrifice some immediate gradient fidelity while improving representation preservation for downstream layers. We study this trade-off in controlled linear optimization settings, where Muon can learn representations that are slower to fit a local target but easier for downstream layers to exploit. Our results suggest a conceptual explanation for Muon and a design perspective for optimizers that balance local descent with downstream usability.

Robot policies inevitably encounter failures when deployed in real environments. Naive retries often repeat the same mistakes, while many existing recovery methods rely on human intervention. In this paper, we propose Failure-Aware Retry (FAR), a framework that enables robots to learn from previous failures at test time, adapt their behavior accordingly, and eventually complete the task autonomously. FAR combines Failure-Contrastive Preference Adaptation, which constructs preference learning data from failures to steer the policy away from previously unsuccessful behaviors, with lightweight action perturbations during retries to encourage local exploration. We further incorporate successful recovery trajectories into a training loop for continual policy improvement. Experiments in both simulation and real-world manipulation tasks show that FAR substantially improves success rates and robustness, with average gains of 17.6% over the standard diffusion policy in simulation and 11.7% in the real world. In addition, FAR improves data efficiency under both reset and timestep budgets during continual policy improvement by exploiting informative failure cases. Videos and code are available at https://hoar012.github.io/FAR-Project.

We present SynLaD, a latent diffusion framework for small-molecule generation that unifies ligand-based drug design objectives (what to make) with synthetic accessibility (how to make it). Current models typically optimize one objective at the expense of the other, creating a bottleneck for discovering high-scoring and synthesizable molecules. SynLaD combines reaction-constrained generation with pharmacophore-conditioned 3D design by learning a latent space that decodes to both 3D structures and synthesis pathways. An encoder maps molecules to a latent representation used by two decoder heads: (i) a geometric head that reconstructs atom types and coordinates and (ii) an autoregressive synthesis head that outputs synthetic routes in a serialized, reaction-based notation. A diffusion transformer generates novel latents in the learned space, conditioned on pharmacophore profiles. Across analogue generation tasks for bioactive ligands, SynLaD outperforms existing baselines in synthesizable and diverse hit generation, demonstrating that a single model can produce shape-aligned molecules with feasible synthesis plans.

In Large Language Model (LLM) training, data mixing plays a pivotal role in determining model performance. Recent methods optimize mixture weights via proxy models, but they rely on the assumption of static data distributions. As a result, when the underlying data pool shifts, these methods require costly retraining from scratch. This limitation restricts their ability to scale seamlessly from small settings to larger data pools and model sizes. In this paper, we propose CausalMix to address this limitation by casting data mixture optimization as a causal inference problem. We formulate the statistical features of the data pool as covariates and the domain mixture as the treatment. After fitting a causal model on 512 runs of Qwen2.5-0.5B to estimate the Conditional Average Treatment Effect (CATE), we extrapolate the optimal mixture for an 800K data pool and apply it to train a 7B model. Furthermore, we successfully generalize the framework to long chain-of-thought data on Qwen3-4B-Base. By leveraging causal modeling to isolate confounding biases, CausalMix infers state-dependent data mixtures offline, with the selected mixture fixed during each training run. Extensive experiments show that the mixture guided by CausalMix achieves competitive performance across downstream tasks compared with other baselines. The CATE Interpreter visualizes the learned mixing strategy. Overall, CausalMix offers a causal and interpretable framework for optimizing LLM data mixtures.

Active learning reduces labeling cost by querying the most informative unlabeled samples, but standard coreset methods ignore known data symmetries and can waste budget on transformed versions of the same instance. We propose GRINCO, a group-invariant coreset framework that performs acquisition in the quotient space induced by a transformation group, so that selection operates on orbits rather than raw samples. The method uses either canonical representatives or learned orbit-separating invariant embeddings to define practical quotient metrics, and combines quotient-space k-center selection with invariant training through an orbit-averaged loss. We further derive a generalization bound that relates excess orbit-averaged risk to quotient-space coverage, label uncertainty, and intra-orbit variability. Experiments on synthetic scale-invariant data and image benchmarks with rotation-induced redundancy show that GRINCO improves orbit coverage and achieves stronger label efficiency than conventional coreset baselines, especially when group-induced redundancy is substantial.

Asynchronous reinforcement learning improves the throughput of large language model post-training by decoupling rollout generation from policy optimization, but introduces a mismatch between the behavior and learner policies. How the resulting policy staleness couples with the learning rate to govern training stability and collapse time remains poorly understood. We investigate this coupling in vanilla GRPO through controlled sweeps of the synchronization interval $S$ and constant learning rate $\eta$ on Llama-3.2-1B/3B, complemented by experiments on Qwen3-8B. We identify two empirical scaling laws: (i) Stability-boundary scaling: the largest stable learning rate scales approximately as $S^{-1}$, yielding a stability boundary characterized by an approximately constant product $S\eta$. (ii) Collapse-time scaling: among collapsing runs, estimated collapse times scale approximately as $\eta^{-1}$, corresponding to a model- and setup-dependent cumulative learning-rate budget that aligns across synchronization intervals in the Llama sweeps. We interpret these laws through a local analysis of the behavior-dependent GRPO surrogate and a complementary mean-field model. Under local regularity conditions, the analysis yields an $O(S\eta)$ upper bound on the staleness-induced update bias that resets at synchronization. The mean-field model shows how sufficiently strong positive feedback can sustain directional drift when update directions persist across synchronization cycles. When drift speed saturates under optimizer normalization, this mechanism predicts exit from a local surrogate-validity region after an approximately fixed cumulative learning rate. Together, these findings motivate a practical calibration rule: estimate the stability threshold and collapse budget from a coarse sweep, then jointly select $S$ and $\eta$ for the intended training horizon.

Spatio-temporal point-process models must often generalise across space when local event histories are sparse. We study whether exogenous spatial context can compensate in such regimes. Using a fixed log-Gaussian Cox process backbone, we compare an event-only model with the same model augmented by AlphaEarth embeddings as linear spatial context. We evaluate spatial transfer on emergency medical services (EMS) forecasting across eight held-out regions, fixed forecast anchors, and a sweep over history length $w$, using only AlphaEarth (AE) embeddings available strictly before each anchor. AE improves out-of-region predictive performance across all history regimes, with the largest gains under scarce histories: approximately $2$–$6\times$ multiplicative improvements at $1-2$ weeks, tapering to roughly $10$–$20\%$ at $w=20$–$104$ weeks. These results show that contextual information can substantially stabilise spatially transferred point-process forecasts when event history is limited.

We investigate Gaussian process (GP) bandit optimization with quantum kernels, assuming the mean reward function lies in the reproducing kernel Hilbert space (RKHS) induced by the quantum kernel. This setting is motivated by NISQ-era tasks such as quantum control, state preparation and variational quantum algorithms. While quantum kernels can offer a `quantum advantage' via domain-specific inductive biases, naïvely using full, high-dimensional kernels increases model complexity and information gain, leading to higher cumulative regret and poor learnability. To address this, we propose projected quantum kernels and classical kernel approximation techniques that reduce feature dimensionality while preserving key quantum properties. Using these approximate kernels, we develop misspecified GP bandit algorithms and derive regret bounds that characterize the trade-off between approximation error and information gain. The regret bounds provide principled guidance for selecting the optimal model complexity. Empirically, our methods outperform full quantum kernels in sample efficiency, while substantially reducing computational overhead, enabling scalable GP optimization for quantum-native applications.

While inference-time scaling has improved the reasoning abilities of large language models (LLMs), the need to generate long chains-of-thought (CoTs) is a computational bottleneck. Thus, in contrast to sequential scaling methods like CoT, recent parallel scaling techniques instead use fork and join (FJ) primitives to divide work across multiple LLM threads. However, in the fork-join paradigm, threads are typically transient and do not communicate pointwise with one another which limits scalability. To tackle this, we introduce Message Passing Language Models (MPLMs), a framework for LLM reasoning in which threads communicate directly via lightweight send and receive primitives. MPLMs enable efficient scaling through two key mechanisms: (1) reduced communication costs, achieved by avoiding redundant context sharing, and (2) preemption, which allows threads to terminate early based on partial information from their peers. We demonstrate the promise of MPLMs on 3 classes of tasks. First, on Sudoku puzzles, we show that MPLMs require an asymptotically smaller context than both serial CoT and parallel FJ. We then fine-tune a single model to solve 25 x 25 puzzles that remain challenging for standard CoT and FJ approaches, as well as frontier reasoning models without tools. Second, on 3-SAT puzzles, the capability of preemption allows termination of unpromising branches, which results in improved efficiency. Finally, we show that appropriately prompted large pre-trained models follow the MPLM protocol, achieving competitive results on long-context question answering relative to popular fork-join approaches.

The deployment of Large Language Models (LLMs) with extended context windows is increasingly constrained by the linear growth of Key-Value (KV) cache memory. Vector Quantization (VQ), particularly Residual Quantization (RQ), is a promising approach for pushing KV cache storage toward the sub-1-bit regime by progressively encoding residuals with small codebooks. However, most VQ methods still rely on standard $\ell_2$ $K$-means as the core codebook-learning primitive. We identify a subtle high-dimensional issue of this primitive: Euclidean centroid averaging can induce centroid shrinkage, which weakens the angular alignment term in the $\ell_2$ distortion and makes directional preservation harder. To address this issue, we propose Gain-Shape $K$-means (GSKM), a drop-in replacement for $K$-means that improves directional fidelity while matching, and in some regimes improving, $\ell_2$ distortion. We then build Gain-Shape Residual Quantization (GSRQ) by incorporating a weighted extension of GSKM into an RQ pipeline. On LLaMA-3-8B, GSRQ substantially improves over strong KV cache quantization baselines across bit rates. At 1-bit, it improves the average accuracy across LongBench tasks from 11.34 to 33.54, a gain of 22.20 percentage points over VQLLM.

We study a broad class of graphical models whose independencies correspond to vertex separation in mixed graphs with directed, undirected, and bidirected edges, that are capable of encoding independence structures arising from feedback, latent and selection mechanisms. In particular, we introduce separable graphs, in which each missing edge implies the existence of a separating set for its endpoints, and essentially separable graphs, those graphs separation equivalent to a separable graph. We show that these models include many existing graph families used to define graphical models an provide several characterizations of separable graphs and essentially separable graphs. We also provide multiple characterizations of separation equivalence for separable graphs. One is a graphical characterization in terms of ordinary graph properties, extending earlier results for specific subfamilies Another is a separational characterization depending only on graph separation properties. Finally, we provide a canonical representation for the equivalence classes of essentially separable graphs and develop an algorithm that, under suitable assumptions, identifies the equivalence class of any essentially separable graph.

Model organisms (MOs) - language models trained to exhibit undesired or unnatural behaviours - are frequently used as testbeds for evaluating white-box interpretability techniques. Current MOs are typically constructed via post-hoc supervised fine-tuning (SFT). Prior research has shown that interpretability methods can easily identify hidden behaviours in these MOs. However, recent work suggests that such post-hoc training methods may make interpretability unrealistically easy. We investigate this claim by constructing a suite of 61 $\verb|OLMo2-1B|$- and $\verb|gemma-3-1b-it|$-based MOs trained with seven different techniques, including standard post-hoc SFT, post-hoc DPO, and more realistic integration of MO data into the OLMo post-training DPO phase. We also use these to train 96 further variants via knowledge distillation. We use these MO variants to benchmark activation oracles, activation steering, the logit lens, and the Jacobian lens. Our findings show that (i) MO interpretability depends strongly on training objective, target behaviour, model architecture, and training data generation pipeline; (ii) substantial variance remains even after controlling for differences in the strength of target behaviour expression; and (iii) both our more realistic $\textit{integrated training}$ and knowledge distillation often yield less interpretable MOs than standard post-hoc methods. Our results cast substantial doubt on the validity of current MOs as interpretability proxies and suggest actionable steps towards more robust benchmarks.

Radio-frequency (RF) sensing is a central modality for counter-unmanned-aerial-system (counter-UAS) defence because it exploits the control, telemetry, and video links between a drone and its operator. Reported accuracies for RF-based drone detection and identification are often very high, but many are obtained using cross-validation that splits a small number of continuous recordings into short segments. This can place near-duplicate slices of the same recording in both training and test partitions, creating data leakage. We study this leakage problem through theory and measurement. We formalise the optimism of segment-level cross-validation and show, using Cover's function-counting theorem, that a classifier can exactly memorise the recording-to-label map when the number of independent recordings, R, is small relative to the feature dimension, d. In particular, this can occur when 2R is less than or approximately equal to d. Under these conditions, naive accuracy approaches 1, and the inflation gap approaches 1 - ACC*, where ACC* is the Bayes accuracy. The inflation eases only once R grows beyond this separability threshold. A controlled synthetic experiment with 10 seeds confirms the predicted curves: naive balanced accuracy rises from the Bayes level toward 1.0 as recording-specific nuisance variation grows, while honest recording-grouped evaluation declines to chance, with a gap reaching about 0.5. On the public DroneRF dataset, pooled leave-one-recording-out cross-validation shows drone type identification, AR versus Bebop, collapsing from a naive macro-F1 of 0.74 to 0.46, the two-class chance level. A leakage-pathway ablation attributes essentially all of the inflation to segment-level leakage.

Spatiotemporal point processes (STPPs) model event data in continuous time and space, with applications in mobility, epidemiology, and public safety. Recent neural STPPs span expressive intensity models, conditional density models, continuous-time latent dynamics, normalizing-flow spatial decoders, and score-based generative mechanisms. Yet comparison remains fragile because implementations differ in preprocessing, coordinate normalization, splits, likelihood conventions, and evaluation protocols. We present SEAHORSE, a unified framework for reproducible STPP experimentation. SEAHORSE formalizes neural STPPs through a common encode-evolve-decode interface and trains, tunes, and evaluates every model family under a single executable benchmark protocol with raw-coordinate likelihood reporting. This enables fair comparisons but, more importantly, controlled diagnostic studies. We pair SEAHORSE with HawkesNest, a synthetic stress-test suite, and show that increasing event-pattern complexity exposes each family's inductive bias, degrading some models sharply and leaving others stable. Code: https://github.com/YahyaAalaila/seahorse.

Data assimilation models state dynamics conditioned on sequential observations, and has wide-ranging scientific applications. In the filtering setting, the goal is to model the posterior over the current state given all observations so far. Classical solutions typically make simplifying distributional or functional assumptions, e.g., linear-Gaussian systems, which can be inaccurate in many scenarios. In principle, particle filters (PFs) remove these assumptions, yet often collapse in high dimensions. Recent generative approaches learn conditional state transitions, but without principled Bayesian updates they do not recover the correct filtering posterior and can accumulate error over long horizons. In this work, we introduce Flow Proposal Particle Filters (FPPF), which learn a conditional generative model based proposal approximating the variance-minimizing optimal proposal for particle propagation. Conditioning on observations steers particles toward high-likelihood regions before weighting, reducing weight variance and delaying degeneracy. Since our proposal admits tractable likelihood evaluation, FPPF computes accurate importance weights and retains a Bayesian update step. We further extend FPPF to high-dimensional problems through localization strategies, adressing another standard PF failure mode. Extensive experiments on a variety of dynamical systems show that FPPF outperforms statistical baselines and other generative methods in non-linear, non-Gaussian, and high-dimensional regimes.

The success of deep learning models in classification and regression is widely attributed to the low-dimensional structure that real-world data tend to exhibit, despite their high-dimensional representation. This work attempts to provide a mathematical framework for binary classification on low-dimensional data, building on Cover's (1965) function-counting theory. With our framework, we aim to address the question of how the low-dimensional structure of the data affects the classification capabilities of learning models. Cover's theory relies on a general position assumption that blinds it to the underlying data structure. We refine this assumption to account for the low-dimensionality of the data and derive dichotomy counts that reflect the data structure. We further extend Cover's separation capacity and problem of generalization to the low-dimensional setting, enabling the impact of the underlying data structure on both to be analyzed.

In long-context use, large language models frequently synthesize answers from the meaning of a relevant context span rather than literally copy-pasting them. Identifying which attention heads perform this synthesis matters for interpreting long-context model behavior. Yet existing detectors miss these heads by construction: they reward heads whose attended token matches the generated token, a literal-copy criterion that captures where a head reads but not what it writes through its output-value (OV) circuit, the very mechanism that carries non-literal retrieval. We introduce Logit-Contribution Scoring (LOCOS), a write-aware detector that scores each head by the projection of its OV-circuit output onto the answer-token unembedding direction, contrasting needle and off-needle source positions in a single forward pass. Across three model families (Qwen3, Gemma-3, OLMo-3.1), mean-ablating the top LOCOS heads on the NoLiMa non-literal retrieval benchmark collapses ROUGE-L at lower head counts than prior attention-based detections; on Qwen3-8B, ablating 50 heads drives ROUGE-L from 0.401 to 0.000 while the strongest baseline still retains 0.292. The selected heads are retrieval-specific: parametric recall and arithmetic reasoning stay at baseline under the same ablation. On Qwen3-8B, the same ablation also drops MuSiQue from 0.55 to 0.08 and BABI-Long from 0.62 to 0.20, while a random-heads control stays within 0.05 of baseline.

Radiomics is the established approach for CT-based lung cancer phenotyping, yet comparisons with foundation models rarely isolate contributions of feature extractor, classification head, and segmentation choice, or test cross-cohort robustness. We benchmark five feature extractors (Curia, Curia-2, DINOv3, Radiomics2D, Radiomics3D), seven classification heads (TabPFN, TabICL, XGBoost, CatBoost, Random Forest, logistic regression, Ridge), and three segmentation regimes on five tasks: tumor volume and stage classification, 2-year survival prediction, histology classification, and age prediction. Models are trained on LUNG1 (n=338) and evaluated on an internal test set (n=84) and the external LUNG2 cohort (n=211), with worst-case cross-cohort performance as the primary metric. The dominant design factor is task-dependent: segmentation drives volume and stage classification, while classifier choice drives survival, histology, and age prediction. Radiomics is competitive for tumor volume, tumor stage and survival (partly due to label-derivation effects for the former); Curia variants reach comparable peak scores for survival; DINOv3 falls slightly short across tasks. Patch and slice aggregation have negligible impact. We recommend Curia with tumor segmentation and a CatBoost head as a safe default, achieving the best mean rank across the three primary clinical tasks, though task-specific selection consistently outperforms any cross-task default. When tumor delineations are unavailable, Curia-2 with lung segmentation and logistic regression offers a competitive alternative. All pipelines use a two-stage design suited to small cohort sizes where end-to-end fine-tuning would risk overfitting.

Most existing multitask learning approaches are limited by their reliance on task-specific loss functions tailored to the scale and type of each outcome. When outcomes differ across tasks, these losses are generally not directly comparable, which makes it difficult to formulate a unified objective and may limit information sharing across tasks. We propose a multitask transformation framework in which task-specific responses may differ through unknown monotone transformations. Motivated by high-dimensional biological applications in which the predictor dimension may diverge with the sample size while only a common subset of predictors is informative, we consider shared sparsity across tasks. Under this framework, we estimate the target functions and identify important predictors by optimizing a smoothed rank-based criterion with a group-Lasso penalty, implemented through a multitask deep neural network with a shared first layer. We establish the nonasymptotic excess-risk bounds, and variable-selection consistency for the proposed estimator. Simulation studies show that the proposed method achieves competitive prediction and variable-selection performance compared with competing approaches. Analyses of gene-expression studies with continuous, binary, and mixed outcomes further illustrate that the proposed method improves prediction and identifies biologically meaningful shared predictors.