Papers

Latent world models plan toward goal images with a frozen pretrained predictor, without task rewards or extra trained heads. However, their planners struggle with long-range goals, and prior work addresses this by training extra components such as value functions or subgoal models. We show that the planning target itself can cause this failure: even with exact dynamics and globally optimal short-horizon search, scoring predictions by their distance to the final goal rejects the first steps of a route that initially moves away from the goal. Building on this insight, we propose Anchored Planning (AP), a training-free method that reuses the world model's own offline trajectories. AP retrieves a segment that leads from the current observation toward the goal and aims the frozen planner at an observation shortly after the segment's start. Across four diverse tasks, AP substantially improves frozen LeWM planners for both action synthesis and action ranking, and it outperforms both additional final-goal search and the LeWM planner on long-range goals.

Many LLM inference problems, including model routing, prefix-cache management, prompt trimming, and test-time search, can be viewed as optimization over a tree. This structure arises naturally from autoregressive generation: every prefix defines a node, and its continuations form a subtree below it. Internal nodes of the tree provide cheap but biased estimates of a region's value, while leaf evaluations are expensive but accurate. Hierarchical bandit methods can exploit this structure, but typically require a specific smoothness schedule to be specified in advance, even though real objectives are often only piecewise smooth and their optima may lie near sharp boundaries. We introduce CANOPY, a multi-fidelity tree bandit that learns where the smoothness prior is valid rather than assuming it globally. CANOPY uses cheap random-path probes to construct an online certificate of local aggregation bias, then directs expensive leaf evaluations toward cells where the certificate detects a smoothness violation. We prove fixed-budget and regret guarantees whose additional cost is additive in the number of discontinuities, recovering the smooth-tree rate when no violations are present and approaching structure-blind search as violations become dense. Across routing, top-$k$ identification, test-time search, caching, and prompt trimming, CANOPY consistently improves matched-budget performance, including $2.9\times$ higher top-10 recall on a 1000-model pool, $1.6\times$ more SWE-bench Verified issues resolved than best-of-$N$, and $3.6\times$ lower median time-to-first-token with prefix caching.

Post-training quantization of vision–language models (VLMs) is typically assessed through aggregate task accuracy and memory savings, but preserving a headline score does not guarantee preservation of visual grounding behavior. We present GHOST-Q, a cross-precision controlled evaluation of three 8B VLM families under FP16, INT8, and NF4 across utility and hallucination-sensitive benchmarks. Rather than comparing only aggregate accuracy, we pair FP16 and quantized predictions item by-item to quantify how compression redistributes grounding successes and failures. Five of six quantized variants preserve MMStar accuracy within $\pm2$ percentage points, yet 10 of 36 paired effects remain significant after false-discovery-rate correction, nine on hallucination-sensitive conditions. Same-device A100 profiling further demonstrates that substantial memory reduction does not necessarily mean lower inference latency. Finally, an open-ended AMBER audit reveals strong generation budget censoring whose severity varies by architecture and precision. These results show that quantized VLMs should be evaluated jointly for aggregate utility, grounding reliability, generation behavior, and realized deployment efficiency.

Synthetic data can scale training supervision when real-world data are limited, but noise and distribution mismatch can reduce its value. Existing synthetic data selection methods often emphasize fidelity or diversity rather than the learner's evolving needs. We propose FROST, an online framework that estimates synthetic-data utility through gradient feedback anchored in real training data. It calibrates batch utility against recent history to determine when filtering is needed and filters samples only in out-of-band batches to determine what to retain, without an external verifier or held-out validation set. Experiments on two public benchmarks for image classification and LLM fine-tuning for text-to-SQL show that FROST filters out around 20–30% of the synthetic data while improving real-task performance compared with training on the full synthetic data pool. We further apply FROST during training in a large-scale industrial ads re-ranking system, achieving significant performance gains over a highly optimized production baseline, demonstrating its effectiveness and generalizability.

Predicting heterogeneous causal effects supports informed decision-making, yet suitable inductive biases vary with treatment overlap, covariate imbalance, prognostic structure, and sample size. The Geometry-Diverse Anchor–Correction Expert Ensemble (GeoACE) addresses this variation through five complementary experts whose predictions are combined using weights estimated from validation data. Compared with ensemble designs that derive diversity primarily from sample or feature subsets, reweighting, or feature transformations, its central contribution is the coordinated design of training objectives and anchor geometries that target different prognostic and overlap structures. Following validation, each expert is refitted on the combined training and validation data, while retaining its distinctive structure. The shared architecture couples a structured outcome anchor with a learned neural correction. ACE serves as the reference estimator, while OW-ACE emphasizes well-supported covariate regions through overlap-weighted factual training. G$\Phi$-ACE constructs a global outcome-guided geometry from pooled prognostic associations, whereas A$\Phi$-ACE incorporates arm-specific outcome associations and penalties for treatment-group imbalance. O$\Phi$-ACE complements these approaches with an outcome-free, overlap-aware projection that replaces the anchor input with a lower-dimensional representation. GeoACE is evaluated against 11 comparators on eight benchmark protocols, alongside comparisons of weighting rules and aggregation controls. It achieves the lowest mean $\sqrt{\mathrm{PEHE}}$ and absolute average treatment effect error on all three IHDP protocols and closely approaches the best comparator on NEWS, although performance varies across the remaining benchmarks. The aggregation analyses show similar observed performance for inverse-DR weighting and equal averaging.

Many iterative algorithms rely on bootstrapping. A variable is updated using a second, frozen copy as a target, which is periodically replaced with the updated variable. Majorize-minimize and inexact proximal-point methods share this structure, as does temporal-difference (TD) learning. However, existing convergence guarantees for scenarios that combine sampled updates with targets refreshed only every $K$ steps rely on the specific structure of the update, such as linear approximation or gradient-based inner steps, and on uniformly bounded sampling error. We instead model the sampled update as a stochastic operator on the parameter space, which reduces the analysis to a contraction argument that needs no gradient structure and allows the sampling error to grow with the iterates. Within this framework, we derive a finite-time bound for i.i.d. samples and any target-update period $K$. We show that the iterates converge geometrically in root mean square to a ball around the fixed point, provided the sensitivity to the frozen target is smaller than the contraction slack of the inner map. Existing deterministic frozen-target contraction and stochastic-gradient-type bounds follow as special cases of our framework, and simulations of TD learning reproduce the predicted contraction rate and scaling of the error floor with the step size.

Fine-tuning large language models on new objectives can improve helpfulness, instruction following, or domain-specific performance, but it can also induce regressions on safety-critical prompts. Existing safety-preserving fine-tuning methods typically control average safety loss or use weighted auxiliary penalties, which can obscure rare but severe failures. We propose a chance-constrained formulation for safety-preserving fine-tuning that limits the fraction of safety examples whose degradation relative to a reference model exceeds a prescribed threshold. Because the resulting empirical chance constraint contains a discontinuous indicator, we introduce a differentiable majorization of the violation rate, yielding a tractable conservative constraint. We then develop a constraint-aware gradient descent method that treats the majorized constraint as a safe set in parameter space and minimally modifies the fine-tuning direction to preserve feasibility. The resulting update admits a closed form and produces a tail-aware safety correction that emphasizes examples near or above the degradation threshold. We conduct an extensive set of experiments on harmful fine-tuning across three different tasks and three models and show that our approach consistently outperforms the baselines that exist in the literature. These results suggest that safety preservation in LLM fine-tuning is better viewed as a reliability-constrained optimization problem than as average-risk regularization.

Fine-grained object detectors are commonly evaluated with confusion matrices, which show where the model is confused but not why, nor whether the confusion can be reduced. We argue that confusion can be attributed to distinct, separable sources, each quantitatively measurable, turning a passive measurement into actionable guidance. We present $A^2E^2$, a diagnostic tool that decomposes the sources of confusion along two axes, $\{$aleatoric, epistemic$\} \times \{$within-class, between-class$\}$, giving a $2\times2$ taxonomy that enumerates the source types. Each quadrant is measured by its own quantity, computed in one of three places (input geometry, output-space disagreement, and the bias-parameter posterior), so the two epistemic sources are separated by construction rather than by an empirical correlation. On fine-grained aircraft detection, the four quadrants become four named sources with their own remedy verdict: affinity (geometric similarity, irreducible from size alone), heterogeneity (geometrically heterogeneous sub-variants, pointing to re-labeling rather than more data), contested (an insufficiently trained but learnable boundary, improvable), and collapsed (a class starved of data, reducible). After attributing the confusion to a specific reducible source, we apply a targeted intervention and verify experimentally that it reduces the diagnosed source specifically while leaving the irreducible sources unchanged. $A^2E^2$ thus turns confusion measurement into a concrete, validatable and actionable "diagnosis" in which the same off-diagonal mass can carry opposite causes and opposite remedies. We also state this framework's limits, including which sources are only partially identifiable on this specific dataset and why.

We study a matching mechanism where agents and objects are described by features rather than complete rankings. A single spectral projection reduces the problem to a one-dimensional sort, computable in O(N log N) time. We prove that on descaled features and preferences, our algorithm obtains the exact Nash Social Welfare (NSW) optimum within the projected space, with an unconditional utilitarian-welfare guarantee and a conditional NSW guarantee. The proposed mechanism is stable against exogenous noise but not strategy-proof; we provide an explicit profitable misreport. On an agentic AI shopping application, the diagnostics correctly anticipate both a success and a failure case. A 100-instance robustness study confirms the findings.

State tracking requires composing a sequence of updates, but accuracy alone does not reveal what a model has learned. We study neural networks trained to predict the running product of group elements. We identify quotient solutions in Transformers, where models recover the quotient class while predicting nearly uniformly among its members. The reciprocal of class size predicts partial accuracy without a fitted parameter, extending parity-based accounts to non-parity quotients. Our baseline Transformers' predictions change little under prefix reordering beyond the exact-tracking frontier. We prove that, for finite groups under uniform i.i.d. full-group inputs, optimal order-blind exact accuracy converges to the reciprocal of abelianization class size as prefix length grows, consistent with the observed abelianization plateaus. Sequential updates permit more: any partition into right cosets of a subgroup, normal or not, survives sequential updates. In our census of standard Transformers, every recovered coset partition comes from a normal subgroup, whereas parameter-matched recurrent networks pass through both normal and non-normal right-coset stages during training. On $A_5$, we identify low-dimensional subspaces of the recurrent state that encode non-normal cosets. In the three-dimensional cases, coset mean vectors form approximate dodecahedra, and swapping the state components in these subspaces transfers the donor's coset state through a shared input suffix. Our results connect partial accuracy, learning stages, and internal computation through the subgroup cosets that models learn to track.

Robust control under delayed sensory feedback remains a key challenge in both robotics and neuroscience. Classical cerebellar models explain delay compensation through forward prediction but fail to account for fast online corrections and rapid adaptation observed in biological systems. We propose a cerebellum-inspired control framework that combines multiplexed predictive representations with internal feedback. By jointly encoding kinematic variables and task-relevant error signals, the model enables accurate online correction despite delayed feedback. Furthermore, incorporating feedback within the cerebellar loop significantly accelerates adaptation, reducing learning time by an order of magnitude. Our results show that single-signal predictions are insufficient under delay, while multiplexing and feedback together provide a unified mechanism for online control and rapid learning.

Many real-world optimization problems rely on expensive simulations or experiments, making the efficient use of available data essential. Multi-fidelity optimization of high-dimensional black-box functions subject to black-box constraints is increasingly relevant as the cost of objective evaluations continues to rise in applications such as machine learning, engineering, and control. To our knowledge, no existing method simultaneously addresses high-dimensionality, black-box constraints, an arbitrary number of fidelity levels, and non-nested sampling. In this work, we extend the Scalable Constrained Bayesian Optimization method to the multi-fidelity setting, resulting in the MF-SCBO method. The proposed approach is evaluated on standard benchmark functions as well as challenging problems. The experimental results demonstrate that MF-SCBO generally achieves better convergence than both the single-fidelity SCBO and the other multi-fidelity method considered in this high-dimensional and constrained settings.

A central goal when designing treatment policies is often to "do no harm", that is, to avoid interventions that improve average outcomes while worsening outcomes for some individuals. A widely used notion for harm is the fraction of negatively affected (FNA), defined as the probability that an intervention decreases an individual's outcome. However, in many applications, treatments operate through mediators, and a single "total" FNA can obscure whether harm arises primarily through direct pathways or indirect (mediator-induced) pathways. In this work, we introduce a path-specific analogue of the FNA. For this, we disentangle total harm into direct and indirect harm in causal mediation settings. However, these quantities depend on joint distributions of potential outcomes that are not point-identified even in randomised controlled trials. As a remedy, we develop a novel partial identification framework for direct and indirect FNA. In our framework, we (i) derive sharp Makarov bounds for the FNA, and (ii) propose a semiparametrically efficient estimator with valid confidence intervals for these bounds under mild margin conditions. We demonstrate our framework across various numerical experiments. To the best of our knowledge, we are the first to study path-specific decomposition of causal harm and to develop an orthogonal inference framework for its analysis.

Wearable human-activity recognition (HAR) models operate across sensors, subjects, and backbones, yet a smooth waveform may appear temporal while exploiting a persistent sensor offset primarily. We introduce SpectrumAudit, a label-sealed audit that fits a phase-randomized full-window stimulus on calibration windows from subjects held out from training and testing. After selection, it replays its exact DC projection and budget-constrained zero-mean residual on the same frozen victim without refitting. Across 27 victims from three datasets and three backbones, the selected waveforms cause 2.87-40.83-point three-phase robust accuracy losses. Under this replay budget, DC is more damaging than AC on 24/27 victims and recovers at least 90% of the full drop on 22/27; all 5 failures occur on WISDM. In a held-out UTD-MHAD check, the selected waveform causes 13.49-pp accuracy and 11.68-pp macro-F1 losses, versus -0.66 pp for matched random changes. The audit diagnoses offset versus zero-mean variation under a common peak-budget cap. The code will be released upon acceptance.

We study the detection of LLM-generated text under editing and contamination. Modeling human and machine text as finite-order Markov processes with Huber contamination, we characterize an exact boundary for reliable detection under our assumptions. Detection is impossible when contamination is sufficiently large relative to clean-source separation. Below this boundary, a collection of clipped likelihood-ratio tests achieves vanishing worst-case errors. This construction motivates clipping as a simple modification of existing statistical detectors. For a broad class of additive scores, we identify conditions under which the clipped test is consistent while the raw test's worst-case power tends to zero. We evaluate seven detectors across three datasets and three generation models, and on the RAID benchmark. Clipping improves robustness in both studies, with gains varying across detectors and contamination settings. For example, at a target false-positive rate of 5%, clipping improves the log-likelihood–log-rank ratio (LRR) detector's true-positive rate by a median of 8.3 percentage points in the controlled study and 2.1 and 4.3 points in rate- and attack-specific RAID evaluations, respectively.

Radiology AI systems increasingly inform clinical decisions such as triage, follow-up imaging, and treatment planning. For these decisions to be made safely, model outputs must be well calibrated, meaning predicted probabilities accurately reflect true risk. Many standard techniques for improving calibration, such as MC Dropout and Deep Ensembles, require access to model parameters or retraining. However, proprietary clinical AI systems operate as black boxes, preventing access to the model's internals. To that end, we propose a model-agnostic framework for improving calibration of black-box models using clinically grounded test-time augmentation (TTA). Our framework applies geometric and physics-inspired 3D CT perturbations and learns probability-level aggregation strategies without access to model internals or the original training data. Across pulmonary embolism and intracranial hemorrhage detection tasks, DualTTA achieved the strongest overall calibration among TTA methods, reducing the Expected Calibration Error by 54% (0.239 -> 0.109) and 43% (0.051 -> 0.029), respectively, while requiring only input-output access. Additionally, DualTTA outperformed uncertainty estimation techniques that require access to model internals, such as Temperature Scaling, MC Dropout, and Deep Ensembles, in most calibration metrics. These results demonstrate that learned TTA aggregation can improve the calibration of clinical AI systems, providing a practical approach for improving the reliability of black-box medical AI.

The estimation of Annual Average Daily Traffic (AADT) is vital for transportation planning and infrastructure maintenance, yet obtaining accurate values for an entire urban network across multiple years remains challenging due to the high cost and spatial sparsity of physical sensors. This research proposes a novel spatio-temporally complementary feature propagation framework that leverages the strengths of two distinct data sources: spatially sparse but temporally dense loop detector data, and a spatially complete but temporally sparse macroscopic transportation model. The methodology highlights a feature propagation algorithm on directed graphs, formulated as a Poisson energy minimization considering residues. The standard binary adjacency matrix is replaced with flow ratio matrices to capture real-world vehicle turn ratios at intersections. Validated in the city of Zurich, the algorithm demonstrates high computational efficiency, achieving convergence within minutes. Results indicate that the framework effectively reconciles theoretical models with empirical ground truths, yielding a normalized mean absolute error below $10\%$. This scalable approach provides a feasible solution for spatio-temporal network-wide AADT estimation through combining real-world limited sensor coverage and traffic models.

A new proposal called DM-SMC (Diffusion Model - Sequential Monte Carlo) is investigated, which samples ensembles defined in terms of an action, using diffusion models trained on samples from the ensemble. The SMC setup allows for accurate sampling in spite of an approximate diffusion model and the finite stepsize used in the numerical solution of the stochastic process. Improved update strategies are also investigated. Results are presented for a $Z_2$ symmetric scalar field theory in 2 dimensions near its 2nd order phase transition.

This paper investigates cost-sensitive online window size selection for portfolio management under changing market conditions. Specifically, we propose a two-level framework that constructs portfolios using candidate window sizes and dynamically aggregates them through online learning. By treating candidate window sizes as “experts,” we dynamically update their aggregation weights using turnover-inclusive losses. Moreover, we derive finite-horizon cost-sensitive tracking-regret bounds that account for turnover of the aggregated portfolio, with static regret as a special case. Under bounded losses and cost rates, suitably tuned Fixed Share achieves asymptotically no tracking regret for sublinear switching budgets, with Hedge covering the static case.

Choosing Shellsort gaps is a well-known open problem. For over sixty years, successful sequences have relied on human-designed formulas, numerical searches, or number-theoretic constructions. Although stronger general bounds exist for dense or mainly theoretical families, the worst-case upper bound for a short, sparse, and practically competitive construction has not advanced beyond $N^{4/3}$ for decades. We ask whether the sequence itself can instead be learned from execution. We present an RL-driven, self-supervised system that searches over executable gap generators. Every proposal is valid by construction, and executed candidates return exact comparison and move counts; no classical sequence is used as a target. Across five independent searches, the system discovers a common rational-geometric family. A second self-supervised stage tunes only a finite prefix, producing the practical sequence $1,3,8,20,47,116,300,585,1416,3303,\ldots$. Once frozen, it obtains the lowest equal-task average operation count among seven classical baselines on 25 large tasks with $10^7<N\leq 10^8$. We complete the learned tail without changing its practical behavior: only beyond $10^{1000}$, a zero-density set of unit companions $h_s+1$ removes the remaining congruence barriers. The resulting sparse sequence has matching polynomial upper and lower exponents, up to polylogarithmic factors: $\Omega(N^{1.024296451657\ldots}) \leq T(N) \leq O(N^{1.024296451657\ldots}\operatorname{polylog} N)$. The lower bound follows from Zang's recent theorem for rational-geometric sequences; our contribution is the matching upper bound. Thus one exact sequence connects self-supervised discovery, large-scale practical performance, and a substantial step below the classical $N^{4/3}$ bound for sparse practical Shellsort sequences.

Generative modeling approaches often focus on recovering broad statistical characteristics from the training data. In the context of graph generation, this may refer to degree distributions, clustering coefficients, or spectral properties. However, generating usable distribution feeders when detailed feeder models are unavailable requires more than matching generic graph statistics: the sampled topology must also obey electrical compatibility and radiality rules. We therefore formulate feeder synthesis as a constraint-guided graph generation problem and propose the Power-Grid-constrained Discrete Denoising Diffusion model, PG-DiGress, which learns categorical node and edge patterns from feeder data, while respecting domain-specific rules. Specifically, it injects feeder constraints into the reverse diffusion process through soft masks that suppress incompatible edge classes during denoising, followed by a final projection step that rebuilds a connected, rule-compliant feeder graph. We evaluate PG-DiGress using graph-distribution similarity, feeder-rule satisfaction, structural validity, and downstream model construction. Compared with the unconstrained baseline, PG-DiGress increases the strict feeder pass rate from 13.7% to 96.8%. We also successfully convert the generated graphs into executable feeder models for downstream analysis.

Deep learning-based speech enhancement is increasingly deployed on-device in hearing aids, headsets, and earbuds. Most of these devices, however, can only accelerate static int8 graphs, so a depth-varying network must be implemented as several graphs, orchestrated by a policy. In this paper, we supervise every intermediate depth of one causal model, then we fine-tune its output heads to guarantee that deeper outputs are never worse than shallower ones. Using this training protocol, we can derive a family of static models that are more Pareto-efficient than their equivalently-sized counterparts trained from scratch on the same budget. Specifically, we achieve up to 0.11 higher PESQ for equivalent compute, and match the best PESQ at 30% less compute. We then quantize the models to int8 and measure the latency-quality frontier on an STM32N6 microcontroller. On VoiceBank-DEMAND, the dynamic enhancer lies on the same frontier as the static models, rather than trading quality for dynamic execution. Running the policy on the companion Cortex-M55 takes only 26 $\mu$s per frame, while splitting the enhancer into separate NPU graphs adds 2.2% latency overhead. The cost of dynamic execution is therefore small.

Deploying real-time speech enhancement on resource-constrained devices requires meeting strict latency, memory, and energy constraints. Microcontroller NPUs can accelerate neural inference under these constraints, but only through a restricted set of operators in static, integer-quantized graphs. Recent speech-enhancement networks have reduced parameter counts and MACs to levels nominally suitable for microcontrollers, but their operators and execution patterns often remain incompatible with restricted NPUs. We address this gap by redesigning LiSenNet, a 37k parameter sub-band dual-path model, for the STM32N6570-DK Neural-ART accelerator. We replace its recurrent bottleneck with convolutional frequency and temporal mixers, reformulate unsupported operations as static int8-compatible primitives, and use bounded decoder activations to preserve quality after quantization. On VoiceBank-DEMAND, the final NPU-compatible model matches or exceeds the recurrent LiSenNet baseline, reaching PESQ 3.08 versus 3.01 in FP32 and 3.01 versus 2.93 in int8. Deployed on a microcontroller, it processes each 16 ms input hop in 4.83 ms, corresponding to a real-time factor of 0.30. Stateless receptive-field recomputation is an order of magnitude slower at the same frame rate despite higher accelerator utilization. These results show that parameter count and operator compatibility, quantization range, and persistent streaming state must be co-designed to achieve efficient real-time speech enhancement on restricted NPUs.

High-resolution digital elevation models (DEMs) support Earth observation applications, but paired training references are often available only at coarser output resolutions. Reconstructing finer terrain grids therefore requires both effective transfer beyond the supervised scale and control of dense-query computation. To address this problem, SCOPE learns a continuous terrain representation from coarser-resolution pairs. It predicts a latent coefficient field on the low-resolution grid and reuses local Fourier residual functions through basis evaluation and geometry-guided ensemble fusion. This separates high-dimensional coefficient prediction from output-grid construction. Experiments on geographically distributed land–ocean samples assess supervised reconstruction, unseen-scale inference, cross-domain generalization, and theoretical computation. SCOPE leads the compared methods across six metrics in the main supervised-scale evaluation. At an unseen factor three times the training factor, land reconstruction reduces RMSE and MAE by approximately 12% relative to bicubic interpolation, with errors close to target-scale fine-tuning. Ninefold output density increases counted multiply–accumulate operations by only about 2%. Frozen-model validation on held-out external marine regions reduces RMSE relative to the DEM-specific implicit baseline EBCF-CDEM by approximately 19% under self-downsampling and 2% with cross-product inputs, while also yielding lower RMSE than LIIF-MS in both settings. These results demonstrate the value of reusable coefficient fields for accurate reconstruction beyond the supervised resolution with low incremental arithmetic cost.

The Brinkman penalisation method embeds boundary-value problems on complex domains into a simple computational box by modeling the solid region as a strongly dissipative medium, avoiding body-fitted mesh generation. We show that multi-symplectic Hamiltonian PDEs regularised by Brinkman-type penalisation retain a multi-conformal symplectic structure under a compatibility condition linking the symplectic matrix and the penalisation projection. This yields an exact local conservation law, under which the multi-symplectic two-form is conserved in the fluid region and decays exponentially inside the solid. The linear wave equation with Brinkman friction and Maxwell's equations with artificial Ohmic conductivity satisfy this condition, with explicit modified Hamiltonian densities. Building on this, we propose (i) structure-preserving numerical integrators via Strang splitting that satisfy a discrete conformal conservation law, and (ii) conformal symplectic neural operators that interleave exact dissipative flows with learnable multi-symplectic evolution operators, allowing geometry-dependent operator learning. Numerical experiments on wave and electromagnetic scattering demonstrate that our methods reproduce correct local energy budgets and avoid unphysical energy drift, providing a principled framework for physics-consistent scientific machine learning on complex domains.

Tabular foundation models (TFMs) provide a promising route to time-series classification, but their effectiveness depends on how sequential data are converted into tabular representations. Existing representations face two challenges: global aggregation can lose the order of temporal evolution, while features computed in independently fitted coordinate systems may not have consistent meanings across sequences. We therefore view representation design for TFMs as a problem in its own right: the representation should preserve local temporal transitions while maintaining a shared feature definition across samples. We propose SwitchPFN, which learns a shared projection and regime codebook from the training sequences, making local dynamic operators and transition features directly comparable across samples. Across the evaluated benchmarks, SwitchPFN achieves the highest mean accuracy among the evaluated methods, improving over the strongest baseline by 4.47% relatively. Ablation studies, parameter sensitivity analyses, and reduced-training-data experiments further examine the contributions of the representation, its main design choices, and its behavior when labeled data are limited.

Looped Transformers have attracted substantial attention as a parameter-efficient approach to increasing computational depth through repeated application of shared Transformer blocks. However, their practical advantages over conventional Transformers remain under debate: each additional loop incurs another Transformer pass and requires caching another set of KV states, causing inference FLOPs and KV-cache memory to grow continuously with loop depth. This overhead becomes particularly severe at large loop counts and long context, preventing the parameter efficiency of Looped Transformers from translating into practical inference efficiency. In this paper, we find that much of the additional computation and storage introduced by looping is redundant. As recurrence proceeds, state changes become increasingly concentrated on a small subset of tokens; attention-output differences are dominated by a sparse and stable subset of key columns; and KV residuals between adjacent loops become progressively more amenable to low-bit quantization. Building on these observations, we introduce FlashLoop, a training-free inference framework that reduces cross-loop redundancy through token-sparse updates, sparse attention, and KV-residual quantization. Across several Looped Transformers models, FlashLoop delivers lossless accuracy while achieving up to 1.64$\times$ end-to-end speedup and up to 6$\times$ KV-cache memory reduction, substantially improving the practicality of scaling Looped Transformers to greater computational depths and longer context.

A large language model (LLM) can turn a text into a distribution over an ordered scale, but that distribution is a noisy measurement: saturated, compressed or exaggerated, and biased in a consistent direction. We propose CORDIAL, which treats the model's output as a noisy reading of the true label and corrects it with a channel of five interpretable parameters. The channel is small enough for its posterior to be averaged from a handful of labels, and we prove that the resulting calibration preserves first-order stochastic order. On Amazon reviews and CMU-MOSEI transcripts with four LLMs, CORDIAL has the lowest log loss among nine calibrators in 76 of 80 settings with 5 to 100 labels; with 20 labels and the main 7B reader, it matches the strongest baseline using 28-54 labels. The same posterior lets us learn priors from other tasks and fuse several LLMs. Unrestricted calibrators such as Dirichlet calibration overtake it only as the calibration set grows into the hundreds or thousands.

Auxiliary learning is an optimization paradigm in which a neural network's performance on a target task is improved by jointly training it on additional tasks. However, the mechanisms behind this improvement remain poorly understood. We study this problem using a teacher-student framework and derive a closed system of differential equations describing the dynamics of online stochastic gradient descent in the large-input limit. For linear networks, we obtain a closed-form expression for the generalization error to leading order in the learning rate, quantifying how task correlations and label noise determine the benefit of auxiliary learning. For non-linear activation functions, we develop a fluctuation-dissipation analytical theory that establishes a general relation linking the main and auxiliary errors to the corresponding single-task error. Numerical experiments support the theoretical predictions and show how auxiliary tasks improve generalization by balancing the forcing dynamics towards the optimal solution with gradient noise.

Radar nowcasting is essential for short-term warning and emergency response, yet conventional systems mainly return future radar fields and provide limited support for operational communication and post-event verification. We formulate radar nowcasting as an evidence-grounded forecast–bulletin–audit task, in which a numerical forecaster produces both future radar fields and structured diagnostic evidence. Forecast-time bulletins use only model-available evidence, whereas post-event audits incorporate future radar truth only after the forecast horizon is observed. Based on this task formulation, WeatherDiagFlow predicts motion, growth and decay, heavy-echo risk, and uncertainty to condition rolling flow refinement, while frozen-scaffold residual calibration improves long-lead strong-echo preservation. A multi-agent layer converts the structured evidence into operational bulletins and independently generates verification audits without feeding textual outputs back into the forecaster. Experiments on FJRADAR demonstrate competitive overall performance and improved strong-echo event skill. WeatherDiagFlow therefore connects numerical prediction, evidence-grounded reporting, and auditable verification under a leakage-controlled protocol.