Papers

The loss landscape of Deep Neural Networks (DNNs) exhibits highly complex and non-convex properties. Recent studies have revealed the phenomenon of mode connectivity, demonstrating that independently trained network modes can be connected via a continuous low-loss path. However, existing mode connectivity research is predominantly confined to classifier-based models, leaving it an open question whether similar geometric properties exist in modern complex models. In this paper, we extend the boundaries of mode connectivity to generative and contrastive domains (specifically DDPM and NanoCLIP). Addressing the unique architecture of DDPM and CLIP, we propose an architecture-aware connection building algorithm. Extensive empirical results demonstrate for the first time that we successfully discover mode connectivity between independently trained DDPM and NanoCLIP modes. Our work provides a novel perspective for understanding the geometric properties of the loss landscapes in modern generative and contrastive models.

Retail banking attrition is usually represented as a terminal binary event, even though client relationships often weaken earlier through partial movements of deposits, investments, and recurring activity to external financial institutions. This paper defines that preceding state as financial fragmentation and presents an end-to-end temporal machine-learning system for predicting it before complete disengagement. Using anonymized multi-source data from a large retail bank, the framework predicts whether a valid external transfer or investment event will occur within 90 days. The study uses 595,220 client-month observations, with 346 engineered features combining monthly client profiles, balances, product relationships, prior flow-of-funds behavior, macroeconomic conditions, and competitor activity. A four-stage XGBoost cascade estimates (1) whether an external outflow will occur within 90 days, (2) the expected amount, (3) the originating product, and (4) the destination financial institution. The primary classifier achieved a test precision-recall area under the curve of 0.823. At the validation-selected threshold, it produced 86.4% precision, 75.1% recall, and an F1 score of 0.803. Ranking test observations in descending Stage 1 fragmentation score, the top 1% of clients yielded 95.3% precision, while the top 5% captured 78.7% of observed outflow cases. The amount model placed 94.9% of predictions within an adjacent amount bucket. Destination prediction reached a macro-F1 of 0.81 across 27 classes; source-product prediction achieved a weighted F1 of 0.92. By moving the analytical focus from terminal churn to earlier fund migration, the proposed approach provides a practical foundation for proactive, explainable, and economically informed client-retention decision support.

Antimicrobial peptides (AMPs) often act against multiple pathogen classes, making multi-label activity prediction a more realistic screening target than binary antimicrobial classification. The ESCAPE benchmark formalizes this setting, but leading approaches typically rely on multimodal, structure-conditioned deep models that are costly to train and tune. We show that a simple, sequence-only pipeline can match and surpass these methods by combining 330 interpretable sequence descriptors with TabPFN, a tabular foundation model that performs in-context prediction in a single forward pass without gradient-based training or hyperparameter search. On ESCAPE (82,359 peptides; five labels), a label-powerset TabPFN model achieves mAP-5 = 77.8%, improving on the previously best reported 72.1%. A probabilistic classifier chain is the first method to match or exceed the best published average precision on each of the five labels simultaneously. The gains persist under the prior state-of-the-art single-fold training protocol, indicating they are not a training-set-size artefact, and are largest for remote homologues (+11.2 points below 30% sequence identity). Ablations further show that predicted structure is unnecessary at inference and that performance is not driven by any single descriptor family: ten global physicochemical scalars recover 91% of full-feature performance. Finally, explicitly modelling label dependence yields targeted benefits for scarce activities and supports ranking which activity to assay next from partial positive evidence.

Classical numerical solvers for partial differential equations (PDEs) are computationally expensive to solve repeatedly across varying initial conditions, motivating the need for learned surrogates. In this paper, we propose a trainable Neural Cellular Automata (NCA) based surrogate model for learning long time PDE dynamics. Rather than mapping an entire initial field to a full trajectory in one shot, our proposed model learns a small, local, homogeneous update rule that is applied identically and repeatedly at every grid cell, mirroring the locality of differential operators. We benchmark this framework against three baselines: PDE - Net, a modified physics-informed neural network (PINN), and a Fourier Neural Operator (FNO), on five canonical PDEs (heat, advection, Burgers, Allen - Cahn, and Fisher - KPP), evaluated at temporal domain two times beyond the training temporal domain. The proposed model achieves the lowest long-horizon relative errors on the majority of the experiments.

Normal behavior models have shown promise for reliable fault detection in wind turbines. However, these unsupervised anomaly detection models require sufficient fault-free training data to learn the normal operation behavior of turbines. Under data scarcity, for example in newly deployed wind turbines, these models may result in poor fault detection performance. In this work, we propose a multi-domain generative domain mapping approach based on Star Generative Adversarial Networks (StarGAN) to improve fault detection on data-scarce wind turbines. Our model maps SCADA measurements from a data-scarce turbine to resemble those of several data-rich turbines. By preserving the operational state during translation, faults occurring in a data-scarce domain can be mapped and detected by reliable pre-trained normal behavior models of data-rich domains. Highlighting the benefits of an ensemble fusion strategy, we show that under severe data scarcity our method can produce anomaly scores comparable to models trained on large representative datasets. Our approach can consistently outperform models trained on scarce data when less than 2 weeks of training data are available. With just 2 weeks of accumulated training data, we achieve an anomaly score similarity that is, on average, +16% higher than conventional fine-tuning, and +10% higher than single-source domain mapping. As a step towards unsupervised model selection, we propose a proxy metric that detects poor performance at training time, despite an absence of anomalies. Our study presents the potential and challenges of multi-domain mapping for wind turbine fault detection under unrepresentative training data.

Large language models (LLMs) finetuned for specialized domains represent crucial high-impact applications. Inference-time alignment improves safety degraded from specialization finetuning without requiring substantial computational resources, complementing finetuning-based methods with an easy-to-use, plug-and-play solution. However, existing inference-time methods fail to reliably improve safety without disrupting domain capability. We identify the root cause as complementary expertise orthogonality: specialized base models and general-domain guidance models have orthogonal competencies, making the guidance signal unreliable for specialized generation. This primarily manifests as stop token interference, where the guidance model's tendency toward continuation overrides the base model's decision to stop, burying correct answers under guidance-induced continuation. To address this problem, we propose CREST, an inference-time alignment method that steers base model hidden representations using safety directions extracted from a guidance model of any family, avoiding token-level structural limitations entirely. CREST improves safety where specialization has weakened it while preserving both domain-specific capability and the safety of already well-aligned models, outperforming baselines by up to 22.2% on safety benchmarks. Our code is available at: https://github.com/DecayingSeart/CREST.

Dynamic origin-destination (OD) matrix estimation calibrates time-dependent input demand for simulations to reproduce observed link flows. Reinforcement learning is well suited to online estimation because a trained policy estimates demand in a single evaluation, but varying target flows complicate learning from aggregate rewards. We propose reinforcement learning with link-flow propagation guidance (LFPG-RL), combining simulated vehicle propagation records with downstream errors to guide individual OD components. Using 250 weekday link-flow trajectories from a Melbourne arterial network, LFPG-RL achieves a mean test root mean squared error (RMSE) of 7.41 vehicles per 15-minute interval, mean absolute percentage error of 31.24%, and Pearson correlation of 0.987. Comparisons with optimisation, filtering and reinforcement learning without guidance show a 40.1% RMSE reduction over the strongest baseline, gradient descent with propagation guidance. LFPG-RL enables rapid demand updates that keep traffic simulations consistent with observed conditions, supporting the evaluation of traffic management strategies.

Token embeddings are the basic representational units that connect discrete tokens with continuous computation in language models. Although modern language models learn embeddings from random initialization through gradient-based training, the dynamical mechanism by which meaningful embedding structures emerge remains unclear. In this work, we identify that the evolving embedding structures are closely related to token-conditioned label and contextual distributions, which we formalize as probability signatures. We observe a progressive learning process, which we term Context Staircase: embeddings learn the low-order statistic signatures of the data before the high-order ones. More specifically, we observe that early in training they align with the simplest, context-free signature linking a token to its label, and as training proceeds, they progressively reflect signatures involving more and more context tokens. We then analyze the gradient flow of embeddings under small initialization to explain this phenomenon, deriving embedding evolution equations for feed-forward and self-attention architectures. We further extend these observations to real language-model training. Finally, we show that these embedding structures play an important role in both task learning and the incorporation of semantic structure into the embedding space. Overall, our results provide a dynamic explanation of how data statistics and architecture jointly shape token embeddings in language models, and reveal an implicit bias in the space of data statistics: training proceeds from simpler, low-order statistical relations toward increasingly complex, context-dependent ones.

Hybrid large language models interleave full-attention layers with linear-attention layers to reduce the cost of long-context inference. This structure complicates prefix caching: full-attention key-value caches are token-addressable, whereas linear-attention layers maintain recurrent states that cannot be rolled back to arbitrary prefix boundaries. Existing hybrid prefix caching methods address this mismatch by storing recurrent-state checkpoints. As a result, token-level matches are directly usable only at positions aligned with stored checkpoints, constraining prefix reuse to a discrete set of boundaries. We present Tail-Replay, a prefix caching mechanism that enables unconstrained token-level prefix reuse in hybrid large language models. The key insight is that linear-attention mechanisms such as Gated DeltaNet can be viewed as a structured, lossy compression of the input prefix: gated recurrent updates progressively attenuate the contributions of earlier inputs. Consequently, the recurrent state of a matched prefix can be well approximated by replaying only a short, recent suffix of that prefix. Tail-Replay exploits this property by caching the exact full-attention key-value cache while omitting recurrent-state checkpoints. On a cache hit, it reconstructs the linear-attention states by replaying a short, recent suffix of the matched prefix. As a result, the reuse boundary is determined by the shared tokens rather than by recurrent-state checkpoints. We evaluate Tail-Replay on three Gated DeltaNet-based hybrid models using the LongBench and RULER benchmarks. With only a 5–10% replay budget, it retains 92.8–99.9% of full-prefill quality on LongBench and RULER. For serving efficiency, we evaluate time-to-first-token speedups across multiple matched-prefix lengths—8K, 16K, and 32K. The speedup grows with prefix length, reaching $9.1$–$14.3\times$ over full prefill at 32K.

Large language models (LLMs) have demonstrated strong capabilities in handling long-context tasks, but processing such long contexts remains challenging due to the substantial memory requirements and inference latency. In this work, we discover that certain attention heads exhibit sequential consistency in their attention patterns, which can be persistently identified using a coefficient-of-variation-based algorithm. Inspired by this observation, we propose CateKV, a hybrid KV cache method that retains only critical token information for consistent heads, thereby reducing KV cache size and computational overhead, while preserving the majority of KV pairs in adaptive heads to ensure high accuracy. We show the unique characteristics of our algorithm and its extension with existing acceleration methods. Comprehensive evaluations on long-context benchmarks show that, while maintaining accuracy comparable to full attention, CateKV reduces memory usage by up to $2.72\times$ and accelerates decoding by $2.18\times$ in single-sample inputs, and boosts throughput by $3.96\times$ in batch scenarios.

Expected-cost constraints can still permit rare, high-cost events. Monte Carlo conditional value at risk (CVaR) gradients can be noisy at high confidence, whereas critics that model an outcome distribution add complexity. We propose BCPPO (Bachelier-Inspired Constrained Proximal Policy Optimization), a proximal policy optimization (PPO) method. Separately initialized cost-prediction networks (critics), trained with random sample masks, produce disagreement that marks predictions sensitive to which state-action regions occur in the training data and to critic training. A Bachelier formula for the expected amount above a reference level converts this disagreement into a smooth policy-update penalty. Gradients from this penalty do not alter the critics, so temporal-difference (TD) critic learning is unchanged. A saturation-aware controller adjusts the mean-cost penalty and stops accumulated error from growing while that penalty is clipped. Deployment retains only the policy network. The disagreement penalty is neither a tail-event probability nor a guaranteed error bound, and it provides no safety guarantee. Across 175 runs with shared tasks, costs, budgets, training steps, and evaluation seeds, no comparator attains both higher mean return and lower mean CVaR than BCPPO in any task. On Push1, BCPPO has no lower return and no higher CVaR than every comparator, with at least one strict gain. These results support a practical balance among reward, caution around cost predictions that vary across trained critics, and policy-only deployment.

The exact Shannon capacity is unknown for every odd cycle beyond the five-cycle $C_5$, making odd cycles a central open problem in zero-error information theory. Improving the known lower bounds requires constructing large independent sets in strong powers of these graphs. Recent AI-assisted work has produced a rapid sequence of improvements: building on the construction of Itty et al., Gao developed a recursive product construction for combining structured independent sets, and Buys, Polak, and Zuiddam (BPZ) subsequently strengthened this through a richer recursion framework. We continue this line of AI-assisted exploration and introduce a heterogeneous refinement of these constructions. The central observation is that the usefulness of an intermediate construction depends not only on the size of its current main independent set, but also on the auxiliary structure it carries into subsequent recursion. Consequently, different parts of that auxiliary structure need not use the same independent set, and different occurrences in a recursion need not use the same intermediate representation. We formalize this for Gao's binary product and derive explicit propagation rules showing how heterogeneous choices strengthen the resulting gadget while leaving its current code size unchanged, then extend the principle to the more general BPZ framework, tailoring constructions to the distinct roles they play within the recursion. Applying these refinements to the seven-cycle $C_7$, we obtain an independent set in $C_7^{\boxtimes 500}$ yielding $\Theta(C_7)\ge 3.25883262\ldots$, improving the best known lower bound. Beyond the numerical gain, the results illustrate a general principle for recursive zero-error constructions: intermediate structures with the same dimension and current code size can have different downstream value depending on where and how they are used in the recursion.

We study decentralized online optimization of upper-linearizable payoffs over an action set under efficient separation access, with applications to online continuous diminishing-return (DR) submodular maximization. We propose Decentralized Barrier Follow-the-Regularized-Leader (Dec-BFTRL), and evaluate each agent's played action against the average of all local objectives. Each agent maps an internal iterate to a feasible action through an approximate gauge projection, communicates only a cumulative surrogate-gradient dual state, and invokes the local HybridNewton procedure to approximately minimize its post-communication BFTRL potential. For every agent, we achieve expected network-aggregate regret of $\widetilde O(\sqrt{T})$. Over $T$ rounds, each agent uses $T$ neighbor-mixing steps and $\widetilde O(T)$ separation-oracle calls. We give wrapper instantiations covering four up-concave or DR-submodular maximization problems.

Scientific simulations generate collections of physical fields with heterogeneous statistics and dependencies, yet learned compressors often encode those fields independently or rely on a shared encoder without explicitly modeling the structure that remains in latent space. We present CAESAR-LDAR, an error-controlled multivariate learned compressor that augments a shared CAESAR-V backbone with two complementary mechanisms: a trainable orthogonal transform that reorganizes dependence across aligned latent channels, and a causal autoregressive hierarchical prior that captures local spatial structure left after transformation. Orthogonality is maintained through a matrix-exponential parameterization, making the transform exactly invertible without an additional penalty. A common residual-correction stage is applied uniformly to all variants to enforce the requested reconstruction tolerance. Experiments across combustion, climate, and turbulence data show that the two mechanisms are useful in different regimes. Latent decorrelation helps most when substantial linear cross-channel dependence survives the nonlinear encoder, whereas autoregressive modeling remains effective when the remaining structure is primarily local or spatial. Their combination provides the strongest or near-strongest rate-distortion performance across the evaluated datasets. The global transform adds little computational overhead, while autoregressive coding introduces a larger throughput tradeoff. More broadly, the results suggest a practical design principle for multivariate scientific compression: exploit global cross-channel dependence when it is measurably present in latent space, and use local probabilistic context as a complementary mechanism across a wider range of data regimes.

We estimate the conditional population-risk curve of a realized smooth nonconvex gradient flow from the training sample. Flow approximate leave-one-out (Flow-ALO) propagates a deletion response and evaluates omitted observations at approximate deleted paths. The risk-curve error decomposes into response approximation, exact-LOO fluctuation, and deletion-to-full risk transfer. On each fixed finite horizon, bounded centered training-loss gradients, a one-sided Hessian lower bound, locally Lipschitz Hessians, and a strict tube-closure condition yield an explicit $(n-1)^{-2}$ bound for the deletion-response error. Bounded evaluation-loss gradients transfer the deletion-response bound to the score without requiring the Hessian to be invertible. Direct first-order jackknife cancellation and exact-LOO concentration control deletion-to-full risk transfer and fluctuation, respectively, completing recovery of the conditional population-risk curve. For bounded smooth two-layer mean-field networks training both layers, the score-error bound is uniform in width.

While it is well-established that prosody carries crucial cues for syntactic structure, the degree and nature of correspondence between these two domains remains contested. We investigate the syntax-prosody interface through an information-theoretic lens, quantifying the interaction between prosodic features and syntactic representations as their mutual information. We provide a general-purpose framework for estimating this quantity over large speech-text corpora using multimodal language models. Our framework is structure-agnostic and modular, insofar as it can be used to measure the contributions of individual prosodic features or components of structure. We evaluate the syntax-prosody relationship for two features (word duration and inter-word pauses) across two domains–read audiobooks and spontaneous conversations–both in English. Our results demonstrate that prosody contains measurable syntactic information, with prosodic features reducing syntactic uncertainty in spontaneous conversations by up to 10.2%. Our findings offer new empirical support for several theoretical accounts of the syntax-prosody interface.

We resolve the threshold part of Question 4 of the COLT 2025 open problem "Data Selection for Regression Tasks" of Hanneke, Moran, Shlimovich and Yehudayoff. We study vector-valued linear regression with square loss $\ell_{(x,y)}(W)=\lVert Wx-y\rVert_2^2$, where $x\in\mathbb{R}^d$ and $y\in\mathbb{R}^m$. The learner returns the minimum-Frobenius-norm empirical risk minimizer. We prove that the minimal budget of weighted examples for recovering the full-data loss on every finite dataset is exactly $n^{\star}(d,m)=(m+1)d$. We determine the weighted selection profile $F_{\mathrm{weighted}}(d,m,n)$ at the near-threshold budget: $F_{\mathrm{weighted}}(d,m,(m+1)d-1)=1+1/(dm^2)$. We recover the known spanning-budget value $F_{\mathrm{weighted}}(d,m,d)=d+1$ for every $m$, and $F_{\mathrm{weighted}}(d,m,n)=\infty$ for $n<d$. For the smallest open intermediate cell $(d,m)=(2,2)$ we prove $F_{\mathrm{weighted}}(2,2,3)\in[13/8,15/8]$ and $F_{\mathrm{weighted}}(2,2,4)\in[5/4,3/2]$. We reduce the conjectured exact values $13/8$ and $5/4$ to a finite moment problem on the circle with at most seven atoms and assemble structural evidence for it. The upper bounds use a fixed-basis conic compression lemma, a determinant–facet rigidity theorem for maximal certificates, and sharp sparsification lemmas for zero-mean weighted point systems. These tools may be of independent interest. We also exhibit an explicit six-point integer dataset with $d=m=2$ on which no weighted selection of $2d$ points recovers the optimal loss. Thus the scalar sufficient budget $2d$ does not extend to vector-valued outputs. Our new regression-profile results for $m\ge2$ extend the scalar theory for $m=1$.

Long-context LLM applications such as document summarization and multi-turn agents require generation from prefixes spanning tens of thousands of tokens, making decoding latency a major bottleneck. Speculative decoding (SD) reduces latency without changing model outputs, but its speedup depends on both accepted draft tokens and draft-step latency: Lightweight drafts are fast but lack the capacity to capture long-range dependencies, whereas strong independent drafts recover acceptance but incur growing KV-access cost at long prefixes. We introduce memory-augmented drafting for long-context SD, equipping a strong independent draft with compressed draft-side KV memory: A lightweight adaptor constructs and incrementally updates this memory to retain distant information and exact recent context. The target verifier retains its full KV cache and applies the standard accept/reject rule, preserving SD's lossless guarantee. Experiments on Llama~3.1-8B and 70B targets at prefix lengths up to 32K show that our method reduces draft-side memory by over 70%. It achieves speedups of up to 2.08x and 3.33x , respectively, over autoregressive decoding.

The fundamental theorem of statistical learning states that, under suitable measurability assumptions, finite Vapnik–Chervonenkis (VC) dimension guarantees that every proper consistent learning rule is probably approximately correct (PAC). Blumer, Ehrenfeucht, Haussler, and Warmuth showed, assuming the Continuum Hypothesis, that the "well-behavedness" condition of the concept class cannot be omitted: they constructed a concept class of Borel sets of VC dimension one admitting a consistent learning rule that is not PAC. We show that the Continuum Hypothesis is unnecessary. Working in Zermelo–Fraenkel set theory with the Axiom of Choice (ZFC) alone, we construct a concept class of Borel sets on $[0,1]$ of VC dimension one and a proper consistent learning rule that is not PAC. More precisely, for a suitable Borel probability measure and target concept, the rule has true risk one at every sample size on a set of samples of outer probability one. Consequently, finite VC dimension and Borel measurability of the individual concepts do not suffice to guarantee that every proper consistent learning rule is PAC. The result shows, with no need of extra set-theoretical assumptions, that the additional regularity assumption in the fundamental theorem cannot in general be omitted.

General embodied agents should perceive, predict, act, evaluate, and improve within a unified system. World models have shown great promise in building such agents, yet existing models typically append an action output head to a world simulator, without coupling them into a closed decision-and-learning loop for policy improvement. We present Motus2, a self-evolving general world model for dexterous manipulation. Motus2 advances world modeling through model scaling and data scaling. For model scaling, a single model with shared weights exposes three control interfaces: a policy (world-action model), a simulator (action-conditioned world model), and an evaluator (value model). The policy proposes candidate action chunks, the simulator predicts their visual consequences, and the evaluator assesses the predicted outcomes. Their coupling forms a closed decision-and-learning loop for policy improvement. This formulation uses curated expert demonstrations for action learning, while failed and suboptimal interactions provide valuable evidence for dynamics modeling and value learning. For data scaling, Motus2 progresses from large-scale monocular egocentric data to synchronized stereo egocentric data, followed by robot-domain adaptation with robot trajectories and supplementary human-robot alignment data. Motus2 further studies global-autoregressive and hybrid-memory extensions of its sliding-window context, adds tactile feedback for contact-aware control, and is instantiated on a fully biomimetic platform with stereo vision, dual arms, dual dexterous hands, and tactile sensing. Together, egocentric data scaling and closed-loop general world model scaling provide a general path toward self-evolving dexterous manipulation.

We propose a new design of fair classifiers for multi-class classification problems in the presence of vector-valued sensitive attributes. In that scenario each sensitive attribute has multiple values and forms several groups relevant to the fairness consideration. Naturally those groups are overlapping and one should also analyze the interaction of factors. Additionally, the decision makers aided by the classification should not violate individual rights at the expense of satisfying fairness metrics at the group level. We propose an approach using the theory and methods of coherent measures of risk aiming at resolving the fairness challenges. Further, we propose a specialized numerical method for solving the resulting optimization problem. The method scales well with the increase of the number of observations. Additionally, we note that the obtained classifier is robust with respect to corrupted data or to situation when data is scarce. We demonstrate the advantages of the proposed framework in comparison to the support-vector machine framework and other methods handling fairness.

Localized extreme precipitation is a major trigger of urban flash floods and landslides, yet producing nowcasts that combine fine spatial detail with probabilistic uncertainty remains challenging. Here we introduce exPreCast-ENS, a conditional residual diffusion framework that transforms the deterministic 4 km radar nowcaster exPreCast into a 1 km probabilistic ensemble while correcting systematic forecast errors. Conditioning on both the forecast and preceding radar observations lets the ensemble-mean correct the baseline rather than perturb it, while members represent unresolved fine-scale variability. Over the Korean Peninsula, skill improves with ensemble size. In two high-impact events in 2023, a 30-member ensemble recovers 38-47% of heavy-rain pixels missed by exPreCast while retaining approximately 95% of its correct detections and alarming on under 1% of the pixels it correctly left clear. The method generates a 1-h forecast in 3.4 s on a single GPU and yields consistent improvements on the French regional MeteoNet radar dataset.

Directly robustifying small-signal stability in AC optimal power flow is challenging since the stability boundary in the original uncertainty space is implicit, highly nonconvex, and changes with the operating decision. This paper exploits an alternative geometry. For a fixed model-specific stability certificate admitting suitable physical lifts, the small-signal stability requirement becomes an affine positive semidefinite constraint in the lifted variables, thereby defining a convex certified safe region. Instead of approximating the nonlinear instability boundary itself, we optimize a sample-wise safe radius in the original uncertainty space and certify, in the lifted space, that the entire power-flow image of the corresponding uncertainty ball is contained in the convex stability region. To this end, a componentwise Perron certificate guarantees existence, uniqueness, and Jacobian regularity of the target AC power-flow branch throughout each ball. An adjoint elimination then provides an exact affine-quadratic representation of the stability-relevant quantities, while rigorous matrix remainder bounds convert their nonlinear variation into finite robust PSD constraints. The resulting radii are certified lower bounds on the distances from empirical samples to failure and can therefore be coupled directly to the distance-based reformulation of a Wasserstein distributionally robust chance constraint, without directly approximating the instability boundary. Numerical studies demonstrate the effectiveness of the proposed framework.

Digital twin technologies have the potential to improve operational flexibility and responsiveness capabilities of nuclear systems. To provide decision support, cyber event characterization, state estimation, predictive control, and real-time dynamic processing of operational data, however, an efficient digital twin needs to integrate multiple models (data-driven as well as physics-based) with explainability while at the same time maintain two-way synchronization with the physical facility at a time constant less than its operational cycle. In this work, we present the Purdue University Reactor One Digital Twin (PUR-1 DT), a cyber-physical digital twin with a complete high-fidelity physics-based and AI-driven virtual model stack (neutronics, thermal-hydraulics, point kinetics) which provides closed-loop explainable diagnostics, forecasting, predictive control, and action recommendation back to the reactor via two-way communications and a cyber-physical testbed. We demonstrate real-time synchronized state estimation and short-term forecasting over a full reactor operational cycle and conduct a series of benchmarking experiments to validate accuracy and latency. Our results show good agreement with experimental results and lay the groundwork for further development and experimental demonstration of DT-enabled functionalities in real-world facilities.

Peptide-protein affinity models are often evaluated with a single data split, obscuring whether they interpolate among measurements for observed targets or generalize across peptide or target shifts. We integrated three sources of quantitative peptide-protein binding data to obtain 11,349 deduplicated pairs and benchmarked ten peptide representations, ESM-2 protein embeddings, and six regressors under peptide-similarity, within-target, and leave-target-out partitions. Across 60 matched representation-regressor configurations, mean test Spearman correlations were 0.462, 0.669, and 0.530, respectively. The top configuration shifted from ECFP-16 count fingerprints with random forest in the first two settings to HELM-BERT with Extra Trees when exact target sequences were excluded. Representation-rank correlations ranged from -0.042 to 0.624 across partitions, whereas regressor-rank correlations ranged from 0.771 to 0.943. Learning curves showed that representation differences were largest with limited supervision and narrowed as training data increased. PeptideCLM-2 adaptation and simple element-wise interaction features provided no consistent gain over a frozen encoder and direct concatenation under the tested protocols. These conclusions are specific to a dataset that pools transformed Kd, Ki, and IC50 measurements and to target exclusion at the exact-sequence level. Peptide-protein affinity benchmarks should therefore align data partitions with the intended use and jointly assess the effects of data scale, molecular representation, and downstream learner.

We present a reinforcement-learning agent that solves symbolic equations step by step, covering both nonlinear closed equations (radicals, exponentials, trigonometric) and a controlled class of restricted-open families requiring a change of variables (CoV) such as completing the square. We cast algebra as an MDP with a dynamic action space and a tree-structured policy (TreeMLP). The main policy learns from reward alone with no supervised solution traces; the CoV substitution comes from a supervised generator interchangeable with a CAS call. On closed equations the agent matches the prior best on CommonCore (0.93 greedy vs. ConPoLe's 0.925) under a single policy. On four hand-designed restricted-open families (quadratic, cubic, quartic, exponential) it reaches 0.79 beam / 0.67 greedy, exceeding the strongest non-learned search (A-star, 0.64). Learned CoV timing has content only on the exponential family, the one requiring a nested CoV, where a natural rule solves none of the held-out equations while the policy solves 75% from reward alone. At 10x scale a sharp seed-level bimodality emerges; a UCB learning-progress curriculum shows a non-significant positive trend toward mitigating it. We do not claim general open-equation solving: every open-equation result is confined to these four controlled families.

Graph positional encodings are widely used in graph neural networks and graph Transformers, yet it remains unclear when the code itself can identify nodes. We study a hybrid distance-spectral encoding that combines anchor-distance profiles with quantized low-frequency Laplacian-energy coordinates. Treating the encoding as an observation map yields a simplex-refined converse, an exact collision factorization \(\kappa_H=\kappa_D\kappa_{S|D}\), and the collision information \(I_H=-\log\kappa_D-\log\kappa_{S|D}\). On random regular graphs, the criterion is made explicit through a bounded-correlation Gaussian-wave surrogate; for actual Laplacian-energy coordinates, we give the distance-conditioned spectral collision condition sufficient for conditional actual-coordinate achievability. Experiments show that \(I_H/\log n\) calibrates localization success, and PE-only structural task probes on Universal Dependencies trees show that hybrid encodings better recover syntactic-tree geometry than distance-only or spectral-only baselines.

Preference optimization is widely used to align large language models with human preferences, but preference-data composition may also influence privacy-relevant memorization. We examine whether adding synthetic privacy-preference pairs to Direct Preference Optimization (DPO) is associated with lower canary-based memorization signals without modifying the objective or introducing a formal privacy mechanism. We propose Privacy-Pressure Preference Mixing (P3M), a data-composition protocol that varies the amount of privacy-preference data while keeping helpfulness and harmlessness preference data fixed. We evaluate a non-privacy Baseline and privacy-mixing ratios of 0.5, 1.0, and 2.0 using Gemma 3 270M-IT across five random seeds and validate the same four conditions using 4-bit-quantized Gemma 2 2B-IT across three seeds. Overall, under the tested conditions, privacy-preference mixing is associated with lower mean canary suffix log-likelihood proxy values across both model settings and lower aggregate membership-inference attack performance relative to the Baseline in the mixed-source 2B evaluation. Specifically, across the privacy-aware 2B configurations, the mean area under the receiver operating characteristic curve (AUROC) ranges from 0.596 to 0.629, and the mean area under the precision-recall curve (AUPRC) ranges from 0.541 to 0.575, compared with 0.804 and 0.790, respectively, for the Baseline. However, the reduction in membership distinguishability does not hold uniformly across data sources. Moreover, the relationship between the privacy ratio and harmlessness preference accuracy varies by model setting, whereas helpfulness preference accuracy remains broadly stable. These findings suggest that P3M should be viewed as a lightweight empirical protocol for examining privacy-utility-safety trade-offs rather than as a formal privacy guarantee or a defense against extraction attacks.

Current video-to-music (V2M) models lack semantic control and fail to penalize instruction violations, largely due to their reliance on reconstruction objectives and the representational bottleneck of static cross-modal conditioning in Diffusion Autoregressive (DAR) architectures. To resolve this, we introduce VIBE, a novel text-and-video-to-music (T+V2M) generation model that leverages: (1) Conditioning Connection, a depth-wise cross-layer conditioning mechanism that dynamically bridges the planning and diffusion refinement heads and (2) a comprehensive reward modeling taxonomy, optimizing for both hard, verifiable constraints (e.g., tempo, key) and soft, subjective qualities (e.g., musicality, multimodal alignment) with a structured 5-stage training curriculum. Upon evaluation using audio-visual alignment, instruction following, and audio quality metrics, along with a subjective human evaluation study, we observe that VIBE demonstrates enhanced controllability and instruction adherence while performing comparably to most evaluated baselines on generation fidelity and multimodal alignment.

Systematic generalization remains a significant challenge in deep learning. In particular, combinatorial generalization - generalizing to new configurations of known factors of variation - is effortless for humans but difficult for standard neural architectures that rely on statistical correlations rather than explicit structural representations. We introduce a new architectural component that embeds structured inductive bias into deep learning: an attention mechanism operating over tensor-product representations (TPRs). Through controlled experiments on compositional tasks, we show that this TPR-attention mechanism outperforms existing architectural components in combinatorial generalization. These results highlight the value of integrating explicit compositional structure into neural attention and point toward a promising path for models capable of systematic generalization.