Papers

Physics-Informed Neural Networks (PINNs) are trained by optimising a composite objective that combines data fitting with physics-based constraints, typically resulting in a highly imbalanced multi-task optimisation problem. Under these conditions, existing optimisation strategies are affected by conflicting task gradients, leading to slow convergence and unstable training, particularly for stiff and high-frequency partial differential equations. We analyse gradient conflicts throughout training of PINNs with standard optimiser and investigate Multi-Task Deep Learning (MTDL) optimisation methods. In our analysis across four benchmark problems we observed that PINN optimisation exhibits three distinct phases in which angle- and magnitude-based gradient conflicts alternate, with only one present at a time. Building on these observations, we propose PAM-GS, a physics-aware gradient surgery method that adaptively mitigates task interference during training according to the observed conflict types. Experiments on four representative PDE benchmarks demonstrate that PAM-GS combines competitive solution accuracy with consistently strong task-balanced performance, outperforming existing methods on most problems.

The empirical success of pretraining large language models has inspired a deeper investigation into the underlying loss landscapes and the optimization dynamics. Recent empirical and theoretical study suggest that the training loss landscape often exhibits a "river-valley" structure, which features a low-loss manifold (river) flanked by sharp orthogonal directions with higher loss (mountains). In the long term, the optimization progress is determined primarily by the progress along the river. Within such a landscape, gradient descent with large learning rates can move faster along the river despite high apparent loss due to vertical oscillations, while a subsequent sharp decay in the learning rate suppresses these oscillations, revealing genuine optimization progress. This explains the recent success of warmup-stable-decay (WSD) learning rate scheduler which, unlike cosine scheduling, keeps stable high learning rate and decays before producing intermediate checkpoints. Building on this foundation, in this work we take a step further and study the role of momentum within such a loss landscape. We establish theoretical analysis that characterizes how momentum accelerates optimization by stabilizing large learning rates that can not be tolerated by vanilla GD without deviating significantly from the river. The enabled large learning rate in-turn gives greater speed along the river and makes faster essential progress in the long run. Another intriguing observation from theory is that for a river-valley landscape with very flat and slow-spinning river, the momentum itself does not contribute directly to acceleration in terms of the speed of tracking the river, while the main acceleration comes from the admissible larger learning rate.

Hybrid language models maintain fixed-size recurrent states, but existing quantizers typically use eight bits or more. Quantization errors persist according to channel decay rates. We derive distortion weights from the observability Gramian and combine them with normalized state ranges for mixed-precision bit allocation, without calibration data, rotation, or training. We also quantize decay rates logarithmically. With per-token state quantization, a four-bit mean payload reduces excess negative log-likelihood by factors of 3.3–27.9 relative to the best of seven baselines across three hybrid models; metadata costs vary. At six bits, negative log-likelihood differs from the FP32-state baseline by less than 0.005 nats. Ablations separate gains from variable bit widths, decay weighting, and range normalization. With less frequent write-backs, gains diminish and depend on the model and budget.

The Job Shop Scheduling Problem (JSSP) is a fundamental combinatorial optimization problem in industrial optimization. This work introduces Pretrained Offline Reinforcement Learning (PORL), a hybrid approach that combines simulation-based online pretraining with offline fine-tuning on production-specific data. Reinforcement learning through online interaction enables exploration of general scheduling strategies, but typically relies on simulation environments and may suffer from a simulation-to-reality gap. In contrast, offline RL avoids direct interaction with the environment by learning from historical data, but its performance is strongly influenced by dataset quality and coverage. PORL combines the strengths of both paradigms by first learning a general scheduling policy through online interaction and subsequently adapting it offline to a target distribution. A KL-divergence-based policy constraint is introduced to limit deviations from the pretrained policy during fine-tuning. The approach is evaluated on JSSP instances with distribution shift and datasets generated from heuristic, noisy-expert, and random behavioral policies. The results show that PORL consistently achieves lower optimality gaps than standalone offline RL and the considered general scheduling baselines. Furthermore, its advantage over standalone offline RL increases as dataset quality decreases, indicating reduced sensitivity to the quality and coverage of the available offline data. The results suggest that offline adaptation of pretrained policies is a promising approach for industrial scheduling environments where direct online exploration is impractical.

Continual fine-tuning is essential for large language models (LLMs) to dynamically adapt to real-world environments, yet it inevitably suffers from catastrophic forgetting, particularly the performance degradation of previous tasks and LLMs' general-purpose knowledge. Although existing methods, such as orthogonal gradient projection, mitigate the forgetting across various fine-tuning tasks, they fundamentally fail to preserve pre-training LLMs' inherent general-purpose knowledge because the original data and gradients of off-the-shelf pre-training LLMs required by these methods are strictly unknown and highly diverse. To bridge this critical gap, we propose EoupCT, a novel framework designed to Estimate and Orthogonalize Unknown Pre-training gradients for Continual LLM fine-Tuning. Specifically, EoupCT estimates pre-training gradients by dynamically generating pseudo data that is most susceptible to forgetting for new tasks through a learnable soft prompt equipped with Gumbel-Softmax relaxation. Furthermore, we formulate a multi-objective optimization problem and introduce a first-order efficient Pareto optimizer that jointly optimizes LLM parameters and the soft prompt, rigorously enforcing orthogonality between new task updates and the estimated pre-training gradients. Extensive experiments across multiple LLMs demonstrate that EoupCT effectively preserves both task-specific proficiency and inherent general-purpose knowledge, successfully mitigating the catastrophic forgetting.

Completed forecasts provide residual feedback, but retaining full residual blocks increases auxiliary state. We propose Endpoint-Preserving Online Correction (EPOC) with a compressed residual state. It stores low-order discrete cosine transform (DCT) coefficients and the final value of the preceding residual block. Each channel shares the endpoint across component-wise online ridge regressions using current-forecast coefficients. We evaluate eight multivariate series, DLinear and PatchTST, three seeds, and two training variants: 96 matched fixed-base conditions at a 24-step horizon. EPOC achieves mean condition-wise reductions in mean squared error (MSE) and mean absolute error (MAE) of 15.40% and 9.35% from the uncorrected base, respectively, with a median of 6,352 B in retained auxiliary arrays. EPOC also outperforms the $\delta$-Adapter, COSA, FAC, and OMPB in paired MSE on most conditions while retaining less state. Full ELF achieves the largest mean MSE reduction, 19.29%, but its median retained state is 474,048 B ($\times$75 relative to EPOC). Equal-size summary controls favor the endpoint by 1.65–2.20% in paired MSE; a coefficient-reconstructed endpoint yields similar accuracy to the observed endpoint, highlighting its role as a shared input. Increasing the retained DCT component count from 4 to 8 adds 1.00 percentage point of MSE reduction for 5,728 B. On jointly trained bases, EPOC lowers MSE by 16.69–20.15% relative to globally blended TEFL-style adapters applied to the same base. Code and numerical records are available at [https://github.com/keiotakmin/endpoint-preserving-residual-correction](https://github.com/keiotakmin/endpoint-preserving-residual-correction).

Robust counterfactual explanations promise recourse that still works after the model behind it changes. Whether they keep that promise depends on what the change is. A small perturbation of the parameters, retraining on new data, and a new architecture are different events, and each existing method is evaluated against the one it was built for. Reported robustness scores, therefore, answer different questions and cannot be compared. We propose a unified cross-family evaluation protocol that holds factual instances and generated counterfactuals fixed while testing every method against the same eight types of model change. The benchmark compares six robust methods and two standard baselines on four tabular datasets. It characterizes every changed classifier through its outputs and reports empirical robustness together with coverage, base validity, and proximity. We find that relative performance and failure modes vary across change families. Bounded parameter perturbations change 0.95% of test predictions on average, compared with 4.9% for bootstrap retraining. Methods with guarantees for these perturbations do not necessarily transfer to other changes. RobX transfers most consistently in our experiments, although greater stability can require larger interventions. We argue that robust CFE methods should be evaluated through a common protocol that specifies the model changes, measures their realized behavioral magnitude, and keeps generation performance separate from robustness.

We introduce Acacia, a graph foundation model, trained on the web graph. Acacia (i) supports arbitrary feature dimensionalities and semantics without additional training, (ii) supports a wide range of tasks, including node classification, link prediction, node clustering, and graph generation, without additional training, (iii) has in-context learning capabilities, and (iv) does not rely on pretrained LLMs. In particular, existing graph foundation models often require training additional classification heads or feature projectors to accommodate new graphs or new labels, whereas Acacia does not. Moreover, existing graph foundation models often gain their capabilities by being stitched together with pretrained LLMs, whereas Acacia is trained from scratch using only the Common Crawl web graph. This is also an important result because it provides evidence that graph models can acquire emergent capabilities from scratch like LLMs.

Conformal prediction can lose coverage when the data distribution changes after deployment. We study adaptation using labeled source data and unlabeled target inputs, allowing both the input distribution and its relationship with outcomes to change. We use Exponential Tilt Reweighting Alignment (ExTRA), introduced for classification by Maity et al. (2023), to estimate structured distribution shifts. We compare using its estimated weights in conformal calibration with additionally tilting the source predictive distribution. Shared learned predictors, estimated weights, calibration samples, and test observations isolate the effect of tilting. Existing theory gives both procedures target coverage with true weights and a common coverage bound with estimated weights. Identification calculations and an analysis of how scoring interacts with weight estimation error help explain why their performance can nevertheless differ. In a synthetic regression setting where the assumed models match the data-generating process and target inputs are informative about the shift, tilting reduces mean set length by about $30\%$ relative to weighting alone, with both methods attaining coverage near nominal. Tilting can instead cause substantial coverage losses in synthetic classification and in regression when target inputs provide little information about the response shift. Real-data experiments also show no consistent benefit. Good coverage from weighted calibration alone does not ensure that adding predictive tilting will preserve coverage. Deciding when to apply this additional adjustment using only source labels and target inputs remains an open problem.

We introduce a framework for retraction-based convex optimization on Riemannian manifolds, which includes a notion of retraction-specific convex sets and retraction-based gradient projection algorithms. The standard theory of gradient projection algorithms generalizes easily to this framework. Within this framework, we establish convergence results for retraction-based gradient projection algorithms with various stepsize rules. As an application, we use our framework to study the weighted low-rank approximation. We also provide numerical validation of our convergence results on the image completion task.

Large language models rely on KV caching to reduce repeated prefill computation in long context and interactive applications. As lightweight adapters evolve, cached states reflect earlier versions, so stale reuse distorts current model outputs, while complete affected suffix recomputation restores fidelity at substantial cost. We seek minimal recomputation that recovers current adapter behavior. Existing systems track token, context, or stable adapter identity, but neither represent caches from earlier adapter versions nor distinguish update propagation from the recomputation required for behavioral recovery. To address these gaps, we introduce CacheReforge, which represents stale KV caches as layerwise mixed-version objects. It combines per-layer adapter anchors, calibrated sensitivity, accumulated drift, and executable restart boundaries to select direct reuse, bounded recomputation, or complete affected-suffix recovery. We distinguish dependency depth from the functional recomputation horizon and use cumulative tail influence to characterize when bounded recovery preserves current-model behavior. We evaluate CacheReforge on Qwen2.5-1.5B and Qwen2.5-7B with continual LoRA updates, including 16K HotpotQA and 2WikiMQA workloads. CacheReforge reduces mean KL divergence by 92.4% relative to stale reuse, while recomputing only 5.44% of layers and reducing cache-maintenance time by 93.2% relative to fresh full prefill. These results show that version-aware recovery preserves model fidelity and most KV caching gains.

Time series foundation models (TSFMs) are pretrained on series from diverse domains, where demand series make up only a small fraction. Demand data has properties that such corpora rarely contain: Short histories, frequent zeros, censoring by stock-outs, and exogenous events that the series does not record. To this end, we propose EXAONE Demand, built on 1) a demand-specific corpus and 2) a demand-aware adapter. For the corpus, we assemble 11.3M series and 48.4B observations from 73 sources, and a synthetic generator supplies the behaviour that open demand data under-represents. For the adapter, we attach low-rank branches to a frozen general-domain backbone, one for each of the four demand classes (smooth, intermittent, erratic, and lumpy), and a router that reads eight scale-free statistics of the input series decides how much each branch contributes. We build EXAONE Demand in two versions, one trained on real-world and synthetic demand together and one trained on the synthetic corpus alone. On 22 held-out datasets, both versions outperform 36 TSFMs, and real-world demand adds a gain over synthetic data alone.

On-policy self-distillation (OPSD) provides dense teacher targets, but evaluates them only along student-sampled rollouts. When the privileged teacher favors an alternative action at a visited prefix, OPSD can provide a target for the branch decision but cannot supervise the successor contexts induced by that action unless the student samples it. This creates a training-time data-collection bottleneck and suggests a different role for teacher-student disagreement: proposing a trajectory branch rather than identifying a sufficient local repair. Our diagnostic framework using controlled token interventions reveals that a teacher-preferred token at peak disagreement can improve student continuation success, while its local corrective value is limited. Motivated by this finding, we introduce a simple branch-regenerate-distill algorithm, Trajectory-Intervention Self-Distillation (TISD). TISD forces a teacher-selected branch action, returns suffix generation to the student, and distills the full trajectory under the privileged-context-conditioned teacher. Across the coding models, TISD improves average Avg@4 over SDPO by 1.2 percentage points. Across the science domains, it improves average Avg@128 by 0.8 points under an equal-step budget and by 0.3 points under an equal-time budget. These results support teacher-guided branching as a way to expose useful successor contexts for self-distillation.

We study whether the linear condition-number dependence in the stochastic complexity of SAPD+ is necessary for nonconvex-strongly-concave minimax optimization. For jointly $L$-smooth objectives with dual strong-concavity parameter $\mu$, we prove a lower bound that matches the SAPD+ upper bound under the same Moreau-envelope stationarity criterion and the same primal-dual initialization gap. Specifically, when $\sigma\ge\varepsilon$, the worst-case complexity of zero-respecting algorithms is $\Theta(\kappa LG\sigma^2\varepsilon^{-4})$ in the stated accuracy regime, where $\kappa=L/\mu$, $G$ bounds the initial primal-dual gap, and $\sigma^2$ bounds the variance of a general unbiased first-order oracle. The lower bound is realized on a smooth problem class with a bounded dual box. Our construction routes each link of a nonconvex zero-chain through a dual gradient of magnitude proportional to $\varepsilon/\sqrt{\kappa}$, while an undiscovered primal coordinate prevents stationarity. It also yields the primal-gradient lower bound $\Omega(L\Delta(\sqrt{\kappa}\varepsilon^{-2}+\kappa\sigma^2\varepsilon^{-4}))$ after combination with the known deterministic bound, where $\Delta$ bounds the initial primal function gap.

Contingency analysis using the AC power flow (AC-PF) model is a critical tool for accurate grid security assessment, but its computational burden increases with the number of operating scenarios and outage configurations to evaluate. Recent ML-based approaches typically require outage-specific training data, leading to offline training costs that scale with the number of contingencies. This work proposes a framework that reuses a single ML model trained solely on basecase AC-PF data to estimate post-contingency operating states under arbitrary single-line outages. The proposed approach formulates post-contingency state prediction as a fixed-point iteration. If the ML model is a deep neural network (DNN), we derive sufficient conditions that guarantee convergence and develop semidefinite programming (SDP) formulations to certify these conditions for a given DNN. Numerical tests on the IEEE 118-bus system demonstrate that the proposed SDP formulations are tight, that the certified conditions hold for all tested contingencies, and that the resulting method produces accurate post-contingency state estimates within only a few iterations.

Safe reinforcement learning (RL) commonly enforces expected-cost constraints, but such expectation safety may fail to control the probability of rare high-cost trajectories. Chance-constrained MDPs (CCMDPs) impose a stronger probability-level requirement, but are widely viewed as harder because the chance constraint is nonconvex and depends on the full trajectory rather than a Bellman-linear expectation. In this paper, we reveal that this computational difficulty does not necessarily imply a higher statistical price. For tabular discounted CCMDPs with fixed bounded successor support and access to a certified planning oracle, we establish a model-based upper bound, with a matching lower bound up to logarithmic terms. Technically, our key idea is the Bellman distributional certificate, which constructs a Bellman recursion for constraint violation probabilities before policy selection. The certificate can be reused across candidate policies; combined with shared row-wise reverse-KL confidence sets, it gives a policy-uniform trajectory-KL transfer without a union bound over policies or time–budget Bellman tables. For stochastic policies, we give a model-free variance-reduced policy-gradient algorithm with a finite-sample expected KKT-residual guarantee and independent validation of every accepted policy. Numerical experiments on synthetic CCMDPs and an IEEE 14-bus energy storage control benchmark illustrate the safety and mechanism behavior of the proposed algorithms.

Autoregressive LLM inference at long context is bounded by memory bandwidth, not arithmetic throughput, and the binding resource shifts from model weights to the Key-Value (KV) cache as sequence length grows. For Llama-3-70B in BF16, the 140 GB weight footprint exceeds the 80 GB HBM of a single accelerator, and one 128k-token sequence adds 42 GB of KV cache. Techniques that compress, evict, page, share, or offload KV state have proliferated, but reported gains use inconsistent workloads, hardware, and quality metrics, preventing cross-paper comparison. This SoK paper unifies the field analytically, with a protocol that strictly separates derived and reported claims. We derive closed-form arithmetic intensity as a decaying function of context length, parameterized by hardware topology for NVIDIA H100, NVIDIA B200, and AMD MI300X, including per-die bandwidth partitioning and the crossover lengths where KV traffic overtakes weight traffic. We classify the literature into five domains, quantization, token eviction, KV paging, prefix caching, and heterogeneous tiering, evaluating one method per domain at 128k context under a single protocol. The central finding is a three-regime structure: below a hardware-specific crossover, weight traffic dominates and KV compression yields negligible speedup; beyond it, KV traffic dominates and each domain trades quality for bandwidth savings approaching the roofline bound. Paging and prefix sharing are lossless but address capacity, not bandwidth. Quantization and eviction cut bandwidth directly, with degradation that accelerates below 4-bit precision and turns discontinuous for eviction on position-sensitive tasks. Tiering converts the bandwidth wall into an interconnect problem bounded by PCIe or NVLink rather than HBM. We close with design rules for selecting a compression domain given hardware, context length, and quality budget.

One-step generators enable high-quality visual generation with a single network evaluation, but their post-training is difficult: general implicit generators provide neither tractable likelihoods nor denoising trajectories, and many rewards are non-differentiable. We introduce Reward-Weighted Transport Distillation (RWTD), a post-training method that requires only generated samples and scalar reward evaluations. Rather than aligning solely to the conventional reward-tilted reference distribution, RWTD constructs an adaptive target that mixes separately tilted current and reference distributions. The current component incorporates improvements discovered during training, while the reference component anchors the target to the pretrained generator. RWTD realizes this target through feature-space optimal transport and fixed-point regression. Theoretical analysis shows that the fixed-point distributions of RWTD interpolate between off-policy reward tilting of the reference and on-policy tilting of the current model, providing a principled approach to balancing reward adaptation with retention of prior knowledge. Empirically, RWTD substantially improves the GenEval score of the one-step SANA Sprint 1.6B backbone from 0.73 to 0.80, while separate preference alignment experiments demonstrate strong cross-reward generalization that yields balanced improvements and preservation of compositional capabilities.

Simultaneous speech-to-text translation (Simul-S2TT) consists of generating partial translations while the incoming audio frames are processed by the system. However, the streaming nature of this setup creates the challenge of deciding the best moment to perform an accurate translation while minimizing the delay. To address this challenge, we utilize the cross-attention mechanism of the encoder-decoder architecture to find the right alignment between the input speech frames and the target text tokens. In this paper, we propose the Recent Frame Attention Policy (RFAP) and the Dual-Condition Attention Policy (DCAP) that allow offline trained speech-to-text translation models to be used in streaming scenarios without requiring additional training. Results on three different language translation pairs over the CVSS-C corpus show that the RFAP is able to surpass other policies with gains of up to 4.0 BLEU while reducing the translation delay by almost 1 second. Moreover, the DCAP is able to preserve a high translation quality when the latency is very low.

Effective behavioral intervention in chronic disease management requires not a single prescription but a sequence of incremental steps, each grounded in what real, similar individuals have demonstrably achieved. Counterfactual explanation offers a natural computational route to such guidance, answering what change in behavior would have produced a better outcome. But existing methods return a target state without a route to it, guarantee no monotone health improvement along the way, and draw no evidence from peer behavior – asking a patient to close a wide gap in one move, which is precisely the recommendation structure least likely to be attempted. We propose POROS (Peer-Grounded Optimal Routes Over States), a domain-agnostic framework rooted in Bandura's self-efficacy theory and Festinger's social comparison theory that constructs a Behavioral Progression Graph – a directed acyclic graph over observed patient states in which every edge requires both peer-grounded behavioral proximity and strict health outcome improvement. Every edge is therefore a behavioral change that individuals in the cohort have demonstrated is achievable within a single period. Minimum-cost paths through this graph decompose otherwise inactionable behavioral gaps into incremental, peer-grounded steps. We evaluate POROS on two independent longitudinal cohorts of patients with diabetes. For patients below the 70% clinical threshold for time in range (TIR, blood glucose within 70-180 mg/dL), it reduces the mean gain required per step from 26.3 percentage points (pp) to 5.5 pp on one cohort and from 31.1 pp to 5.7 pp on the other, decomposing large behavioral jumps into the incremental steps that self-efficacy requires. Across both cohorts, 97-98% of multi-hop paths cross patient boundaries, embedding social comparison by construction.

Multi-teacher on-policy distillation (MOPD) integrates specialized capabilities into a single student, but existing practice typically hard-routes each prompt to a domain-matched teacher for the entire rollout. This dependence on prompt-level domain labels restricts using unlabeled training mixtures and leaves complementary signals from other teachers unused. We introduce MOPD-Router, a framework that routes supervision over the full teacher pool at each token, without domain labels or training a separate routing model. Its plug-in interface supports different metrics for selecting and weighting teacher-specific OPD signals. Within this interface, we propose ExpertAlign, which scores each teacher by whether its correction to the student at the current token expresses the specialization that teacher acquired during post-training, and compare it against two reference metrics built on teacher confidence (Entropy) and teacher-student discrepancy (Novelty). Experiments on unlabeled and domain-labeled training mixtures under strong-to-weak and same-size distillation scenarios show that ExpertAlign achieves the strongest overall performance in all four settings. On unlabeled data, it improves the overall score by 5.88 (+12.3%) points over Mean aggregation; on domain-labeled data, it outperforms standard MOPD by 3.95 (+7.8%) points without using available domain labels. These results demonstrate token-level routing can exploit cross-domain complementary supervision, and reduce exclusive reliance on prompt-level domain assignment. Code is available at: https://github.com/TURLEing/MOPD-Router.

Learned particle simulators based on graph neural networks achieve strong one-step accuracy, but errors compound over long horizons. An underexplored variable is the interaction graph: existing methods fix its topology via k-nearest neighbors or a static radius rule, regardless of local model confidence. We propose making this graph adaptive: a per-particle variance head, trained jointly with the acceleration head under a heteroscedastic Gaussian NLL loss, drives a trajectory in which high-uncertainty particles receive an expanded neighborhood. This is done at little extra inference cost by using the previous step's uncertainty estimate. A key discovery is that the variance head learns a meaningful notion of uncertainty: high-variance particles concentrate near complex regions, such as splash zones or free surfaces. When this signal drives graph topology, the resulting AdaptGNS simulator achieves a strict Pareto improvement on WaterDrop and a modest gain on Sand. Given the model's stronger performance on WaterDrop, we hypothesize that adaptive graphs are most useful when complexity is concentrated in space. Our code can be found at https://github.com/aidenzhou8/AdaptGNS.

Looped transformers reuse weights across recurrence steps, making low-bit quantization especially attractive. We identify two distinct failure modes of standard post-training quantization. On Huginn-3.5B, per-channel INT4 fails primarily at the non-residual loop-entry adapter, while quantizing the residual core is much less damaging. We call this feedback exposure: a quantized layer perturbs the recurrent state without an identity path, and the resulting error is fed back at later steps. Controlled experiments on linear filters and Mamba state-space models show that feedback exposure also occurs outside transformers. Grouped INT4 reveals a separate failure, calibration blindness: our one-step GPTQ baseline builds its Hessian from step-0 activations, leaving input directions used later in the recurrence nearly unweighted. Across nine checkpoints from seven looped architectures, one-step GPTQ is worse than round-to-nearest (RTN) on the primary task metric for five checkpoints. Accumulating the GPTQ Hessian across recurrence steps outperforms both one-step GPTQ and RTN on all nine checkpoints and recovers bf16-level accuracy on Huginn. These results separate two questions for PTQ on looped models: where quantization error enters the recurrence, and which states calibration sees.

In many safety-critical applications, control of uncertain dynamical systems relies on observers that estimate states and external disturbances. Neural network observers can improve estimation accuracy, but certifying their Lyapunov stability via Linear Matrix Inequality (LMI) constraints leads to large-scale semidefinite programs (SDPs) that are difficult to solve for large networks. To overcome this scalability bottleneck, we propose a novel two-stage training framework for provably stable neural network observers. Our approach decouples the optimization into a point-guided Lyapunov pre-training phase, which rapidly achieves high estimation accuracy and local stability over sampled states, followed by an LMI fine-tuning phase that efficiently satisfies a strict global Lyapunov stability certificate. We provide formal theoretical guarantees for local stability radii and probabilistic coverage over a prescribed compact error-state domain under specified regularity and sampling assumptions. Experiments on nonlinear control benchmarks and X-29 aircraft ablations show that our LMI-certified neural network observers train significantly faster than direct LMI-based methods and generalize robustly across diverse systems, achieving improved tracking accuracy over a range of observer baselines. The code is available at https://github.com/Berry-Myon/LearningNeuralNetworkObserver.

Online conformal prediction can fail when predictions shape actions and actions determine which outcomes enter calibration. Standard adaptive methods may retain marginal coverage while systematically miscovering the counterfactual outcomes of rarely selected actions. This paper formalizes the failure through counterfactual coverage and introduces Propensity-Weighted Online Conformal Prediction, an inverse-propensity-weighted recursion that debiases calibration. A doubly robust variant further reduces nuisance bias to the product of outcome-model and propensity errors. Under positivity, the resulting coverage rate matches an information-theoretic lower bound up to logarithmic factors. Experiments on synthetic decision tasks, open bandit data, and financial rebalancing show that PW-OCP and DR-OCP improve counterfactual coverage and downstream regret without sacrificing prediction-set sharpness.

We investigate the use of neural network solvers for infinity and $p$-Laplace problems, which are fundamental in nonlinear analysis and have practical applications. Our approach employs Physics-Informed Neural Networks (PINNs) and Deep Operator Networks (DeepONets) to address computational challenges associated with large $p$ values, ranging from $2$ to $1000$, on various 2D and 3D domains. Our method offers advantages over traditional physics-based solvers, especially in three dimensions where mesh-based solvers become very costly for these problems. We also establish conditional convergence results for PINN approximations of both problems and a universal approximation result for DeepONet on the parametric $p$-Poisson problem. We demonstrate the effectiveness of these neural network solvers through numerical experiments and compare their performance with conventional methods.

Many temporal process learning and monitoring pipelines operate in local windows, making window-level decisions unavoidable in practice. In such settings, classical statistical tests can be applied to individual windows, but they typically evaluate predefined parametric hypotheses-such as unit-root or moment-based conditions-thereby limiting flexibility when reference behavior is defined empirically from task- or domain-specific data. In this work, we view window-level monitoring as a process control problem and reformulate it as reference-based hypothesis testing, where the null hypothesis is specified by an empirical reference distribution rather than a fixed parametric model. We operationalize this perspective through a representation-based, nonparametric framework that combines pretrained time series encoders, kernel density estimation, and conformal calibration, yielding finite-sample valid inference in learned representation space. Classical notions such as stationarity and cyclostationarity arise as natural instantiations of empirical reference sets within this framework. Through experiments, we demonstrate sensitivity to window-level distributional deviations while maintaining well-calibrated inference under stable reference regimes, highlighting the applicability of the proposed approach to a broad class of time series process control and monitoring tasks.

Choosing features is difficult with few labeled molecules, even for a tabular foundation model that learns in context. We study this problem with TabPFN for low-data molecular property prediction, separating input width, feature meaning, and predictive usefulness while keeping contexts, query molecules, and predictor settings matched. On ADME/Tox assays from Therapeutics Data Commons, endpoint-matched assay predictions improve a compact RDKit descriptor baseline, and a provenance audit shows that most audited query molecules already occur in the predictors' training sources. Across 77 FS-Mol development tasks and 157 held-out test assays drawn from ChEMBL, broad RDKit descriptor and fingerprint families provide a strong default, rank-averaging TabPFN with support-fitted fingerprint forests improves upon both models, and learned weighting of family predictions adds further gains at a larger prediction budget. A utility-trained selector builds a traceable 16-column input from 238 sourceassay predictors, improving upon the baseline while trailing wider representations and equalwidth structural SVD coordinates. Named outputs identify what each feature predicts and where it comes from. Their usefulness for a new assay is assessed alongside the other input features, and paired removal and replacement tests measure what each selected output contributes. Together, these studies offer a protocol for evaluating feature selection, representation choice, and data provenance with a fixed tabular foundation model for few-shot molecular property prediction.

Clinical measurements are recorded for some patients but not others, at rates that differ across hospitals, and marginal conformal coverage does not ensure coverage within groups defined by missingness. We propose a missingness-aware conformal calibration procedure for mortality prediction under cross-hospital distribution shift. It selects a measurement on an independent sample, groups patients by whether that measurement is recorded, and applies Mondrian calibration within each group, so no calibration outcome is reused. We evaluate the procedure across hospitals in eICU and across care units within one MIMIC-IV hospital, using three predictors. Relative to pooled calibration, it reduces the average worst-group coverage gap on its selected groups in all six settings, with a median reduction of 1.9 percentage points; paired site-bootstrap intervals exclude zero in five. These gains do not extend uniformly. Calibration by predicted risk achieves smaller gaps on a broader panel of missingness groups, and when eICU hospitals are evaluated separately, the gain shrinks for all three predictors and reverses in sign for one. We explain this discrepancy with a hospital-level decomposition. Pooling reweights hospitals through a covariance between group shares and coverage errors, and lets errors of opposite sign cancel: weighting explains the reversal, and cancellation accounts for most of the attenuation for the other two predictors. Constructed population distributions show that pooled and within-hospital evaluations can rank calibration methods oppositely even without sampling noise. Pooled improvement alone therefore cannot establish better coverage within hospitals, even when the calibration groups are fixed.

Cross-domain few-shot learning requires adapting a classifier to a new visual domain from very few labelled examples without target-time parameter updates. We isolate one question: under a fixed global representation, what does joint query-support adaptation contribute to prototype construction? The Within-Instance Prototypical Transformer (WIPT) implements single-query test-time prototype adaptation by jointly transforming one unlabelled query and the labelled support embeddings, then forming query-specific class means. Using a shared frozen ViT-S/16 encoder, miniImageNet source training, and CUB, EuroSAT and ISIC targets, we replicate the key comparisons across five independent training seeds. In 1-shot evaluation, WIPT improves frozen ProtoNet in every run on CUB (+0.21 percentage points) and EuroSAT (+2.07), but decreases ISIC (-0.22). In 5-shot evaluation, ProtoNet remains strongest overall, while WIPT consistently improves a capacity-matched support-only Transformer on ISIC (+0.99). Joint processing of up to five queries yields no reliable accuracy gain; in a head-only 5-shot benchmark, g = 5 reduces analytical attention-token pairs by 73% and peak allocated memory by 29% relative to g = 1, although latency is non-monotonic. Across all target/shot conditions, WIPT changes uncertain ProtoNet decisions far more than confident ones, and rescue/break decomposition accounts for the observed gains and losses. Source-shift and scorer controls further show that the benefit is not universal. Overall, WIPT provides a streaming-compatible form of test-time prototype adaptation that can improve difficult low-shot cross-domain decisions without target-time optimization.