Papers

Generative modeling of time-dependent data is typically formulated on a discrete temporal grid, restricting supervision to the observed timestamps in the training data. We instead frame generation as continuous-time evolution on a learned data manifold. To this end, we leverage pretrained score-based models as geometric priors and learn a vector field that evolves data along score-induced interpolation paths. Because these dynamics follow transitions that respect the geometry learned by the score model, they support generation at arbitrary timestamps and temporal super-resolution beyond the discretization of the training data. Moreover, this geometric formulation allows us to train the vector field simulation-free through a regression objective. To improve long-horizon rollout robustness, we introduce an objective that promotes path-relative transverse exponential stability. While motivated by stability theory, it admits a practical interpretation as denoising score matching transverse to the interpolation path. Further, we extend the framework to a probabilistic setting that models a distribution over plausible future trajectories. We demonstrate the method on natural video and scientific dynamical data, including temporal super-resolution, PDE-based spatiotemporal fields, and molecular dynamics. Our results show that score-based priors provide a strong foundation for learning stochastic continuous-time generative dynamics.

How much does the noisy measurement add to learned quantum error mitigation? An accuracy table cannot say, because a model handed circuit structure can score well without reading the measurement at all. QEMScore adds the comparison that can. Each simulated circuit carries an exact ideal answer. The learned mitigator is scored beside a capacity-matched control, a model just as flexible that reads the same circuit description but never the measurement. Each method's measurement spend is accounted and not equalized. We run a controlled campaign on simulated circuits and reanalyze two published learned mitigators, Q-LEAR and QRAFT, from their released hardware data. Three findings stand out. First, under familiar within-family conditions (S0) evaluated across two spin-chain families and three seeds, continuous couplings identify the target, and the control that never reads the measurement matches 87.7 to 100.5 percent of the mitigator's gain over an affine fit to the circuit description. A plain polynomial in the coupling parameters, fitted after the campaign, beats the mitigator on all six evaluations, reflecting the selected learners' capacity. Second, for these selected learners, matching most of the gain is not matching the accuracy: on five of six evaluations the mitigator removes 19.5 to 74.5 percent of the error the capacity-matched control leaves, a learner-specific gap rather than a measurement requirement. Third, on released hardware data where descriptors only partially identify queries, the findings differ: flexible models of the descriptors show negligible mean gain over affine fits in Q-LEAR, and measurement inputs carry predictive gains in both Q-LEAR and QRAFT. These comparisons reflect representation- and protocol-specific behavior rather than an isolated cross-regime difference. A learned mitigator's accuracy should therefore be reported beside such controls.

We introduce TabPFN-3.5, our new flagship Tabular Foundation Model. It significantly outperforms its predecessor, TabPFN-3, and all existing baselines across a broad range of tabular problems. TabPFN-3.5 sets a new state of the art on standard tabular prediction in TabArena, and extends it to the data practitioners encounter in practice: non-i.i.d. data with temporal or grouped splits, tables with strings, text and images, high-cardinality categorical features, and wide tables with many features. These gains carry over to our task-specific harnesses: state of the art on relational data and stronger time-series forecasting. For faster inference, our variant TabPFN-3.5-Fast runs up to 3x faster than TabPFN-3 while keeping most of the accuracy gains. In addition, we upgrade TabPFN-3.5-Plus, expanding our multimodal capabilities with advanced text and date handling alongside proprietary inference optimizations. Finally, we release a new version of our Thinking mode, TabPFN-3.5-Thinking, which scales inference-time computation to push the state of the art further. It benefits from our stronger base model and from inference-time improvements that make it up to 12x faster than TabPFN-3-Thinking.

The manifold hypothesis suggests a natural criterion for clustering: partition data according to the manifold component from which each point is drawn. Whether two components are separable depends on a geometric tradeoff: the ambient separation between components versus the largest gap in sampling. In practice, this tradeoff is rarely assessed explicitly, leading standard methods to over-commit to a single clustering assignment even when the data do not support a unique answer. We formalize this tradeoff by combining intrinsic manifold geometry (volume growth and reach) with sample-level quantities (fill distance and density), yielding a threshold phenomenon for mutual-$k$-nearest-neighbor graphs: when the offset-to-fill ratio exceeds a conservative upper threshold, component separation is preserved; below a lower threshold, components fuse. The gap between these thresholds defines a geometric uncertainty zone in which the number of clusters is not identifiable from the data. Nevertheless, conventional approaches still seek one: sweeping parameters (an engineering approach) or fitting a generative mixture model (a model-based approach). Rather than forcing a single estimate of the number of clusters, we propose Manifold-Based Clustering (MBC), which returns an explicit bracket interval to quantify the underlying data uncertainty. This bracket acts as an empirically calibrated diagnostic: it narrows when a single resolution is supported, widens when multiple resolutions coexist, and collapses to one when no separated structure is detectable. Empirically, we find that many real datasets lie within the uncertainty zone rather than admitting one clear answer. Our results suggest that ambiguity in cluster number is often intrinsic, and should be quantified rather than resolved.

We study the problem of demonstration selection, which involves selecting a subset of examples for prepending to a query to a language model. This problem is closely related to in-context learning and language model inference. Since the inference cost of a transformer model scales quadratically with sequence length, the selection problem becomes especially challenging in a long-context scenario. In this paper, we tackle this problem by building on state space models (SSMs), which require only linear inference time given the input. Our approach involves two algorithms. The first learns a small set of SSMs through distillation of a (trained) transformer model. We partition all the layers into consecutive groups. Then for each group, we estimate a separate state space model to replicate the input-output behavior within the adjacent layers. Second, we map the distilled model outputs to a small set of tokens, and apply these embeddings for demonstration selection in downstream applications. We perform extensive experiments in both synthetic and real-world datasets to validate our approach. We demonstrate that the distilled SSMs only incur an approximation error of less than $0.7\%$ relative to the true output. In downstream evaluation, we show that on several text classification and reasoning tasks, our approach reduces FLOPs by $14.2\times$ and improves accuracy by $6.48\%$ relative to baseline demonstration selection methods.

EEG decoding tasks can rely on different temporal dynamics and cross-channel relationships. We test whether specialized modules improve a fully fine-tuned EEG foundation model by augmenting CBraMod with cross-depth Attention Residuals (AttnRes) and two soft-routed expert banks. Across matched three-seed experiments on FACED, ISRUC, SEED-V, and PhysioNet-MI, the complete model changes mean balanced accuracy relative to full fine-tuning by -0.12, +1.27, +0.77, and -1.27 points, respectively. AttnRes alone improves mean balanced accuracy on three datasets, whereas adding experts on top of AttnRes helps only FACED and SEED-V. These gains come with substantial overhead: AttnRes requires 2.11 to 2.88x runtime and 1.78 to 2.67x memory, while the complete model requires 2.41 to 3.04x runtime and 1.86 to 2.85x memory. Overall, the added modules produce dataset-dependent, sometimes opposing effects rather than consistent gains over full fine-tuning.

As unmanned aerial vehicles (UAVs) become increasingly prevalent in consumer and defense settings, classifying them reliably from limited, modality-specific data is an urgent challenge. The dominant approach, large pretrained networks fully fine-tuned on task data, carries a substantial computational and memory weight that is hard to bear in resource-constrained UAV deployments, where edge inference and rapid retraining for emerging platforms are both required. This paper systematically scales across both model architectures and fine-tuning methods for UAV audio classification, asking when that weight is justified and when lighter alternatives prevail. Using a custom dataset of 3,100 audio clips spanning 31 drone classes, we evaluate transformer (ViT, AST) and convolutional (custom CNN, ResNet-18/152, MobileNet-V3-S/L, EfficientNet-B0/B7) backbones under full fine-tuning, classifier-only fine-tuning, and four parameter-efficient fine-tuning (PEFT) methods: SSF, IA3, OFT, and selective batch-norm tuning. All configurations are evaluated with 5-fold cross-validation across accuracy, training time, trainable-parameter share, and inference-time memory footprint. Selective batch-norm fine-tuning of EfficientNet-B7 with three-fold augmentations achieves the highest validation accuracy (97.65% +- 0.30) while updating under 0.5% of model parameters. Across the sweep, lightweight CNNs consistently outperform transformers on both accuracy and efficiency. For UAV audio classification under data scarcity, scaling the method outperforms scaling the model.

An important component of urban accessibility, particularly for wheelchair users and people with reduced mobility, is sidewalk compliance with measurable requirements. We test whether effective width, longitudinal slope, cross slope, and pavement condition can be assessed reliably from pedestrian-level imagery using vision-language models (VLMs). We present the first application of sampling-based conformal prediction (CP) for VLM-based accessibility assessment. We evaluate four VLMs on 514 sidewalk images from Seoul, South Korea, with field-measured ground truth. Conformal calibration attains the nominal 90% coverage for all models and attributes, but the calibrated regions differ in informativeness. Effective width yields the most informative estimates, with a mean interval half-width of about 1.0 m for the best model. Since every model overestimates width, asymmetric calibration shortens the intervals by up to 33% at unchanged coverage. Longitudinal slope is marginally informative, cross-slope intervals are too wide to resolve regulatory thresholds, and pavement-condition sets degenerate to all five grades (A-E) for three of the four models. Uncalibrated intervals from raw sampling dispersion cover only 17-47% of field-measured values at a nominal 90% level. Among the images with the most self-consistent responses, these intervals miss the field-measured value in up to 96% of cases. Response self-consistency is therefore not evidence of accuracy, and sampling dispersion cannot be interpreted as uncertainty until it has been calibrated against field-measured ground truth. No quantitative attribute reaches the precision required for general compliance assessment, but CP identifies from calibration data alone which attributes can support screening of segments far from the thresholds. We release the annotated pedestrian-level images and their corresponding field-measured attribute values.

Real-world intelligent systems increasingly operate under open-world conditions, where user intents are not fixed or exhaustively known a priori and may evolve as new interaction patterns emerge. This paper proposes a unified uncertainty-aware probabilistic framework for continual new intent discovery under an evolving label space. Each utterance is encoded through an adaptive $\beta$-VAE into a latent mean, used for classification and density modelling and a posterior uncertainty estimate acting as a global reliability signal. Classifier confidence, posterior uncertainty and DP-GMM likelihood are combined through a multi-signal decision mechanism to distinguish known intents from potentially novel samples. Candidate novel instances are clustered through a density-based discovery module and only reliable clusters are promoted to new labels, enabling controlled label-space expansion. Replay and Elastic Weight Consolidation mitigate catastrophic forgetting and preserve previously acquired knowledge. The paper formalises continual intent discovery as a structured multi-phase open-world problem, introduces adaptive label-space expansion under stability–plasticity constraints and uses posterior uncertainty to regulate trusted-sample selection, pseudo-labelling, novelty admission and replay. Experiments show high novelty precision, stable adaptation across sequential phases and limited forgetting. Near-zero NMI and ARI indicate limited reconstruction of the complete fine-grained intent taxonomy, consistent with the framework's conservative promotion strategy. Qualitative analyses nevertheless reveal dense and locally coherent semantic clusters, showing that reliable novel structures can be discovered without exhaustive recovery of the underlying taxonomy.

Who the judge is can affect an LLM-as-judge result, but measuring that effect without confusing it with candidate quality is difficult. We study four open-weight families (Llama 3.1, Qwen 2.5, Gemma 2, and Yi 1.5) in a fully crossed pairwise design with 9,312 judgments. A common per-family statistic is strongly confounded with candidate quality and correlates with Bradley-Terry ability at r = 0.95. We derive a corrected estimator that holds the candidate family fixed and compares judges. All four families then show a positive same-family lift (3.4-8.4 percentage points), with global FPS 0.067 (95% CI [0.053, 0.084], permutation p = 0.0002). The effect remains under panel-based quality controls, an independent human-consensus anchor, and a float16 judging replication. Judge-side likelihood is closely related to the effect: adding likelihood advantage reduces the controlled coefficient by 61%, which we treat as descriptive attenuation rather than causal mediation. Position is a separate failure mode. Across the panel, 55.4% of AB/BA pairs reverse, and reversal above 50% is incompatible with a simple independent content-noise model. Relative to a family-balanced reference, panel composition changes 18.5% of pairwise outcomes. A complete reproducibility archive has been prepared for public release.

AfriSyCo studies answer switching around African-language factual content with two complementary layers: native-language follow-ups and a controlled cross-language factorial whose question, options, and target remain in the African language while the follow-up framing is English. We analyze 1,415 turn-1-correct model-language-item observations derived from 100 source questions across seven open-weight checkpoints and six languages; turn-1-correct denotes observed first-response accuracy, not demonstrated knowledge. Under native prompts, assertive endorsement produces 29.3 percentage points more any-turn false-target selection than mention-plus-verification (M+V), with a 19.0-point immediate T2 contrast. In the precommitted 2 x 2 factorial, averaged over three tested prompt families, assertive framing increases target selection by 30.4 points (95% CI [28.4, 32.3]); verification decreases it by 17.4 points, while the assertive effect rises from 20.5 points without verification to 40.2 with it (interaction +19.7). The effect remains 34.8 points among 611 observations correct after option reordering. Magnitude varies sharply by wording and checkpoint: prompt-family effects span 20.1-42.5 points, a Twi/Qwen3 paraphrase shifts target selection from 70.8% to 4.2%, and checkpoint effects span 9.2-47.0 points. Prompt realization is therefore part of the measurement problem.

Learning from human feedback has become a central paradigm for training modern AI systems, where models of human utility are used as reward models in policy learning. Existing methods typically assume a universal utility function shared across a population and treat disagreement between annotators as stochastic variation. While suitable for objective tasks, this assumption breaks down in subjective domains where preferences vary systematically across individuals. We study the problem of subjective preference learning, in which observed choices arise from heterogeneous but internally consistent utility functions. Drawing upon rational choice theory, RCT \parencite{tversky1981framing}, we introduce individuated utility functions conditioned on both the individual and their decision context, and propose a novel multi-stage architecture for estimating them from multi-modal data. We evaluate our framework on a newly collected dataset of more than $575{,}000$ pairwise aesthetic judgments from $2{,}398$ participants comparing automotive wheel designs. Our experiments show that individuated utility models substantially outperform universal utility models including foundation model baselines. Our results demonstrate that disagreement reflects meaningful preference heterogeneity rather than annotation noise. More broadly, our findings highlight the importance of collecting annotator attributes and learning individuated utility functions, enabling reward models that explicitly account for whose preferences they represent and faithfully capture human decision diversity.

Autonomous research agents aim to automate scientific workflows, from proposing ideas to conducting experiments and analyzing results. Yet current AI and research agents can propose more directions than available resources allow them to pursue. Moreover, each attempt could consume substantial resources, requiring agents to reconsider how to invest in subsequent research. Thus, deciding how to invest research effort strategically should be a defining capability of autonomous research agents. Accordingly, we introduce PrimeScientist, which jointly determines research direction and resource investment across successive research attempts. Specifically, we formulate this challenge of strategic research effort allocation as a sequential decision problem where remaining resources should explicitly guide the research policy. We first introduce an executable plan tree that preserves competing plans and their outcomes across attempts. Building on this representation, we propose an adaptive MCTS-based allocation policy that balances exploration and exploitation using experimental feedback and remaining resources. Comprehensive evaluations across AI research, systems and code optimization, and machine learning engineering show that strategic allocation improves research quality and sample efficiency together. Across 12 AI research tasks, PrimeScientist improves average reward by 10.3% with 50.6% fewer research attempts than AutoResearch under the same resource budget. We believe making research effort allocation an explicit optimization target establishes effective resource use as a core research capability for autonomous agents to drive scientific breakthroughs at scale.

Let the exact homogeneous hard-margin support vector machine be trained on \(m\) independent observations from a Borel probability law on a real Hilbert space. We prove that, with score zero counted as an error, there is a universal numerical constant \(C\) such that \[ \Pp\left( \gamma_m>0,\quad \Risk(u_m)> \frac{C}{m} \left( K_m+\log\frac1\delta \right) \right) \le \delta . \] Here \(\gamma_m\) is the empirical homogeneous margin, \(u_m\) is the exact minimum-norm unit-margin separator, \(r_m\) is the largest training radius, and \(K_m:=r_m^2\norm{u_m}^2=r_m^2/\gamma_m^2\) on \(\{\gamma_m>0\}\). The proof is driven by a deterministic deletion problem. Given vectors \(x_1,\ldots,x_n\) in the unit ball, delete a set \(B\) of constraints and let \(u_B\) be the closest point to the origin that satisfies every retained unit-margin constraint. Suppose that \(\norm{u_B}^2\le k\) and that every deleted vector has nonpositive score under \(u_B\). We prove that a family of such deletion sets of cardinality \(q\) has size at most \(\exp(8k+2q)\). The conceptual step is an exact identity obtained from the KKT representation of \(u_B\). For a random deletion set, the identity converts the mean squared spread of the separators into a weighted sum of score deficits. It therefore forces a coordinate whose deletion status separates the two conditional means by a quantitatively large amount. Revealing that coordinate decreases the conditional separator variance enough to control the binary entropy of the split. An entropy induction gives the deletion count, and an exact factorial ghost-sample identity converts that count into the stated high-probability SVM bound.

Video anomaly detection (VAD) is an actively studied task, having wide applications in typical scenarios such as public surveillance and road traffic safety. The task is also relevant for robotic arm interactions, where it has several downstream applications, including learning better interaction and manipulation abilities, triggering recovery procedures when anomalies occur, etc. Despite its relevance, the exploration of anomaly detection in robotic arm manipulation videos is limited by the low number of available resources. To this end, we introduce RoboVAD, a large-scale benchmark for video anomaly detection that comprises challenging cross-domain evaluation scenarios, where certain actions (tasks executed by a robotic arm) and anomaly types (mistakes that occur while performing certain tasks) remain unseen during training. RoboVAD is designed to benchmark VAD methods in realistic scenarios, where robotic arms can perform unforeseen tasks, and thereby encounter new anomaly types. We train and evaluate several state-of-the-art VAD methods, including a novel method specifically adapted for robotic arm manipulation. While the proposed method outperforms many state-of-the-art competitors, all methods remain below a micro-averaged frame-level AUC threshold of 70% in the most challenging evaluation setup, confirming the difficulty of the proposed benchmark. We publicly release our dataset and code at https://zenodo.org/records/22754659.

We develop a hybrid modeling framework for coupling pre-trained numerics-informed neural networks (NINNs) with classical full order models (FOMs) using the overlapping Schwarz alternating method. We consider the two-dimensional advection-diffusion equation in the advection-dominated, Peclet-number 10^6 regime. We first demonstrate that, unlike the corresponding physics-informed neural network (PINN), a monolithic NINN can be accurately trained on our model problem without domain decomposition. We then employ overlapping multiplicative Schwarz as a deployment mechanism for coupling a pre-trained, subdomain-local NINN with a neighboring FOM, with the NINN weights held fixed throughout the Schwarz iteration. We consider two training approaches for the subdomain-local NINNs: a top-down approach, in which boundary data are obtained from a coupled Schwarz solve on the full domain with a FOM on each subdomain (FOM-FOM Schwarz), and a bottom-up approach, in which boundary traces are generated synthetically on the NINN subdomain without requiring any full-domain solves. The resulting hybrid NINN-FOM solutions agree closely with the corresponding FOM-FOM Schwarz solutions, with the top-down and bottom-up training approaches yielding comparable accuracy.

Low-energy nuclear structure is encoded in a broad body of experimental information across the chart of nuclides. Learning how this information is organized across observables and nuclei can provide a data-driven empirical baseline for theoretical extrapolations and experimental design. Here, we develop held-out ensembles based on NuCLR (Nuclear Co-Learned Representations), a multi-task model of nuclear data, to study charge radii and electric-quadrupole transition strengths. Out-of-fold (OOF) validation shows that shared representation improves performance over single-task learning, yielding a charge-radius $\mathrm{RMS}$ deviation of $0.0147~{\rm fm}$ and a $\mathrm{B(E2)}$ $\mathrm{RMS}$ deviation of $0.192~e^2{\rm b}^2$ across hundreds of nuclides, competitive with state-of-the-art nuclear models. Our error bars estimate the expected prediction accuracy across the nuclear chart, highlighting regions where new data would encode information beyond the learned patterns. NuCLR thus serves as a data-driven surveyor of nuclear structure and a step toward a shared, multi-observable foundation model of the nuclear chart.

Hybrid domain decomposition methods provide a flexible framework for coupling full order models (FOMs) and reduced order models (ROMs), but typically assume the model assigned to each subdomain is fixed throughout a simulation. This is limiting for transient problems in which localized features propagate through the domain and the regions requiring high-fidelity resolution change over time. We introduce a reinforcement learning (RL)-based approach for online adaptation of FOM-ROM models coupled via the overlapping Schwarz alternating method (O-SAM), an iterative domain decomposition method that solves subdomain-local problems while exchanging solution information through transmission boundary conditions on overlapping interfaces. Deep Q-networks (DQNs) are trained offline to select among subdomain-local FOMs and pre-trained Operator Inference (OpInf) ROMs using a reward balancing accuracy, cost, and model-switching frequency. Once trained, the policies are deployed predictively on problem instances not seen during training, without requiring a reference FOM solution. We demonstrate the approach on two examples: a 1D advection-diffusion problem with a moving front, and a 3D linear elastic wave propagation problem implemented in the Norma.jl solid mechanics code. For the advection-diffusion benchmark, the learned policy dynamically allocates high-fidelity resolution as the front propagates and outperforms static FOM/ROM assignments; letting the agent also adapt the domain decomposition provides no further benefit. For the elastic wave benchmark, learned policies for two and three subdomain decompositions track the propagating wave by assigning FOMs to subdomains containing the wave and ROMs elsewhere, as expected. Our results demonstrate the potential of RL to enable predictive online adaptation of model fidelity within Schwarz-based hybrid simulations.

Molecular property prediction is often limited by the small size of labeled downstream datasets, motivating pretraining on large corpora of unlabeled molecules. In this work, we ask whether useful inductive biases can instead be learned from abstract, procedurally generated data before a model sees any molecular data. We introduce a three-stage training pipeline consisting of procedural pretraining, molecular pretraining on SMILES, and downstream fine-tuning, and evaluate several procedural tasks spanning sequence structure, cellular automata, and graph reasoning. We find that procedural pretraining can improve molecular property prediction even after subsequent molecular pretraining: on Lipophilicity, Reverse reduces test error by 4.8%. For context, the magnitude of this improvement is roughly 90% of the performance difference between our 250K-molecule baseline and the publicly released MoLFormer checkpoint pretrained on approximately 100M molecules. Our analysis shows that the benefit is strongest under downstream data scarcity, depends on the structure of the procedural data rather than only surface-level statistics, and does not increase monotonically with additional procedural training. Instead, transfer typically peaks at an intermediate procedural budget and deteriorates as the model approaches convergence on the procedural task. We further find that, for several tasks, much of the transferable information is localized in the attention layers, while feed-forward layers can contribute to over-specialization. These results show that procedural data can provide transferable structure for molecular learning and offer a complementary route to improving performance when labeled molecular data are limited.

Understanding how deep neural networks make decisions remains a fundamental challenge. We present NObSP (Nonlinear Oblique Subspace Projections), a framework that decomposes predictions into explicit per feature contribution functions and an interaction residual. NObSP exploits the linear final layer of a trained network and uses oblique projections in sample space to reduce double counting when learned feature subspaces overlap, thereby supporting both local explanations and global functional analysis. We establish connections to functional ANOVA and the Kolmogorov-Arnold representation theorem and derive an efficient partial regression algorithm for out of sample evaluation. For convolutional networks, NObSP-CAM produces class activation maps without backward passes after a one time calibration. Experiments on tabular and vision benchmarks show faithfulness comparable to established attribution methods. On a synthetic benchmark with known component functions, NObSP obtains a Function Reproduction Score of 0.989, compared with 0.966 for KernelSHAP and 0.922 for Integrated Gradients. On TinyImageNet, contribution vector embeddings improve mean nearest neighbor class purity from 0.654 for raw activations to 0.713 and reduce mean neighbor distance by more than half. These results indicate that NObSP complements scalar attribution methods by recovering functional contribution profiles with separable positive and negative evidence.

Many proteins function through transitions between conformational states, yet rare states are rarely sampled by diffusion models trained on an equilibrium ensemble, demanding better sampling methods. We introduce METALICA, which implements Metadynamics on a pretrained diffusion model via Replica Exchange. It accumulates a bias potential along a Collective Variable, repels new samples from previous ones through biased sampling, and reweights samples onto the unbiased distribution. METALICA holds one replica per diffusion level, forming a Markov Chain that evolves through inter-replica communication and is refined in place as the bias grows. METALICA is the dual of sequential control, in which Sequential Monte Carlo parallelizes the sampler over a batch of particles. Parallelism over the levels of the diffusion-time schedule instead allows METALICA to generate samples from long chains, essential for the discovery of rare events, with accuracy set by run length rather than by the memory available. We validate on a bimodal target with known free energies, then apply METALICA to the unfolding of a protein. At a budget for which sequential control yields no unfolded structure, METALICA populates the basin and resolves a second free energy minimum.

Solomonoff induction frames prediction as a mixture over computable hypotheses, typically leading to identification of the true environment. In a finite meta-reinforcement learning setting with nested constraint families, in our previous work, we observe a different regime: a value-mixture (VM) agent achieves near-optimal, zero-collision navigation without identifying the true environment, a phenomenon we call Free Inference. This regime persists up to a sharp density threshold, beyond which performance degrades and posterior-mode selection (PMS) becomes preferable. We formalize this behavior via the Free Inference dimension dFI(S,N), a combinatorial measure of the environmental complexity a VM agent can handle while preserving trajectory coherence. We prove dFI is strictly smaller than the VC-dimension and relates to the Natarajan dimension up to a path-length factor, capturing the cost of non-decomposable loss. A PAC-style relaxation yields generalization bounds driven by dFI^(epsilon,delta). We also define a complementary PMS identification dimension and show that a hybrid strategy—averaging until the first collision, then switching to selection—is optimal, with links to Littlestone-type dimensions supported by grid-world experiments.

The Koopman operator has been widely used for time-series prediction in dynamical systems. However, prior work that learns latent “Koopman spaces” using neural networks often did not construct a valid Koopman space for forecasting, as these representations may be mathematically inconsistent with the operator-theoretic formulation and fail to capture the intrinsic low-rank structure of system dynamics. To address this issue, we introduce K$^2$SVD, a method that explicitly learns the leading singular functions of the Koopman operator by optimizing a Hilbert-Schmidt objective. This yields a well-defined low-rank approximation of the Koopman operator with an interpretable linear combination, featuring a compact latent space with less than $10\%$ of the dimensions used in previous work. In the learned Koopman space, K$^2$SVD further captures temporal evolution with a linear Gaussian state-space model and performs inference via Kalman filtering, mitigating noise accumulation during multi-step prediction. Empirical results show that K$^2$SVD outperforms state-of-the-art methods across multiple datasets, with significantly faster prediction speeds and lower computational cost than previous efficiency-focused models. This highlights the benefits of principled low-rank Koopman representations and opens up broader potential for applications.

The increasing adoption of electric vehicles (EVs) is expected to place significant additional demand on residential distribution networks, creating a need for realistic charging datasets for planning and simulation studies. However, access to real-world EV charging data is often limited due to privacy constraints, incomplete records, and restricted availability. This paper proposes a conditional variational autoencoder (CVAE) for the generation of synthetic EV charging sessions from real transaction-level charging data. The model is trained on engineered session features describing plug-in duration, charging duration, delivered energy, charging delay, and cyclical time-of-week, while conditioning on day of week and managed charging status. A Gaussian negative log-likelihood (NLL) reconstruction loss is employed to model feature-wise heteroscedastic uncertainty, and the latent space is regularised using a Kullback-Leibler (KL) divergence term. The statistical fidelity of the generated data is evaluated using distributional metrics and downstream task performance through the Train-on-Synthetic-Test-on-Real (TSTR) protocol. Results demonstrate that the proposed approach produces synthetic EV charging sessions that preserve key statistical properties of the original dataset while supporting predictive modelling tasks.

Large language models solve grade-school math word problems with high accuracy, yet a single irrelevant clause inserted into the problem can collapse it. We reconcile these observations with a mechanistic account. We show that the model's internal computation decomposes into a four-stage sequential pipeline, Schema Abstraction, Operation Planning, Operand Binding, and Computation, each stage producing a distinct intermediate representation in an identifiable band of layers. Using the same scaffold to diagnose distractor-induced failure, we localize the corruption to a single stage, Operation Planning, implemented by a set of attention heads whose causal role we validate bidirectionally. In short, we provide a mechanistic interpretation of math word problem reasoning in LLMs, and their failure when distracted.

We present SAiFE_gym, a Python module that provides a collection of simulation environments for studying trading problems in Constant Product Markets (CPMs) with Concentrated Liquidity (CL). These markets give Liquidity Providers (LPs) granular control over how their capital is allocated and enable them to adjust their range of liquidity provision dynamically based on market conditions, which in turn, dictates how they earn fees. We decompose the microstructure of CPMs with CL in interactive components that allow researchers and practitioners to capture various economic settings. We employ a vectorized approach to optimize our environments, making them scalable for high dimensional Reinforcement Learning (RL) workflows that best describe sequential decision problems. We demonstrate the benefits of our environments by evaluating the performance of RL agents in CPMs with CL under uncertainty in market parameters.

Next-day wildfire prediction requires models whose forecasts can be evaluated alongside the assumptions and historical evidence used in their computation. Although deep learning can learn spatial patterns from remote-sensing data, predictive performance alone does not establish physical fidelity or operational trustworthiness. This study investigates three modular augmentations for next-day active-fire prediction: wind- and slope-conditioned attention biases, physics-feature retrieval-augmented output correction, and fire conditioned dual-stream gating. The attention biases expose prescribed directional preferences, while the retrieval module selects historical tiles using a nine-dimensional environmental and fire-state descriptor and applies a learned correction to a frozen model's logits. The modules are evaluated across five backbones on the Next Day Wildfire Spread benchmark, using staged ablations, directional audits, retrieval perturbations, calibration measures, and computational comparisons. The three-seed mean F1 score and area under the precision–recall curve (AUC-PR) of a SwinUNETR model with all three augmentations are 0.4216 and 0.3673. Then, a mixed ensemble (two augmented architectures and one non-augmented architecture) model achieves 0.4292 and 0.3790. Benefits vary across architectures, and retrieval-related improvements in AUC-PR do not consistently translate into higher F1. The constructed wind bias aligns closely with input wind, but its alignment with observed next-day fire displacement is much weaker, distinguishing prior inspectability from predictive physical fidelity. The study contributes a framework for exposing and evaluating selected domain-informed components within wildfire prediction models. Together, the results presented show that predictive performance, operational trustworthiness, and computational practicality need not be competing objectives.

Muon updates matrix-valued neural-network parameters by orthogonalizing a gradient-based momentum matrix. Its reliance on derivatives limits its use when gradients are unavailable or unreliable. We develop a derivative-free framework that constructs Muon-style updates from structured finite differences. Four variants are considered: full entrywise recovery, random low-rank surrogates, basis-aligned rank-one probing, and direct structured search. Exhaustive basis-aligned probing is equivalent, up to positive scaling before ideal polar orthogonalization, to coordinate finite differences. Matrix-regression experiments show that random rank-one probing can reduce the number of function evaluations substantially, at the cost of less accurate updates. Controlled noisy-gradient experiments on regression and a neural network illustrate when accurate function values can compensate for an unreliable gradient oracle. A small CartPole study further examines orthogonal rank-one probes under a fixed episode budget. These results support structured probing as a practical option for selected black-box problems; they do not establish a general convergence guarantee or an advantage over accurate, inexpensive gradients.

Deep neural networks that are independently trained to similar performance can be connected by low-loss parametric curves in weight space, a phenomenon known as Mode Connectivity (MC). This geometric property underpins practical techniques such as weight averaging, model ensembling, and model merging. We argue that low-loss connectivity is an incomplete geometric criterion: it controls loss only along a one-dimensional trajectory while leaving the surrounding weight-space neighborhood unconstrained, so the optimized curve may traverse sharp ridges that become fragile under distribution shift. We therefore reformulate mode connectivity as a neighborhood-robust path optimization problem, seeking a curve whose entire local neighborhood maintains low loss. We propose Sharp Mode Connectivity (SMC), which applies a first-order sharpness-aware approximation to the resulting minimax functional, enforcing flatness along the entire curve rather than only on it. We derive a practical optimization algorithm for connectivity paths under this sharpness-aware objective. Under severe blur corruptions from CIFAR-10-C, SMC achieves up to 6.09% absolute accuracy improvement over standard MC. Remarkably, SMC produces negative loss barriers, meaning that models obtained at interior points of the optimized path can outperform the average endpoint loss. These results, validated across ResNet-18, VGG16-BN, and ViT-Tiny on CIFAR-10 and ImageNet-100, establish path-wise flatness as a practical principle for robust weight-space interpolation.

A central goal of autonomous reinforcement learning is continuous policy training without external resets. However, existing paradigms largely depend on underlying environmental reversibility, a property absent in real world manipulation, where events such as pushing objects off tables or spilling granular substances cannot be undone. We introduce REVERSAL-BENCH, a benchmark that controls reversibility via a continuous parameter $\rho \in [0, 1]$ and provides a reset oracle, a ground-truth verification mechanism to test state recoverability across eight manipulation settings in five physics engines. Evaluating a broad spectrum of policy architectures, including standard actor-critic algorithms, safe RL, and specialized reset-free frameworks, reveals a sharp reversibility cliff: reset-free agents are consistently absorbed into irrecoverable states as $\rho$ increases, whereas episodic agents maintain steady learning. We see this failure mode across autonomous reset-free baselines and constrained RL. Because reset-free agents lack external resets, any transition into an irrecoverable state results in permanent absorption, leaving the agent trapped where further learning halts. We show that this absorption phenomenon persists in full physics simulations under learned manipulation policies. By evaluating against geometrically identical reversible counterparts, we confirm that this breakdown is causally driven by irreversibility rather than obstacle complexity. We release the benchmark suite, a large multi-simulator dataset labeled with recoverability and a reset oracle. We also evaluate a safety shield that intervenes before irreversible failures occur, showing that while recoverability can be predicted accurately, active recovery primarily succeeds only when the agent can physically steer clear of the trap