Papers

We address the problem of inferring a directed network from nodal measurements generated by linear diffusion dynamics on the sought graph. Observations are modeled as the outputs of a graph convolutional filter, i.e., a polynomial (with unknown coefficients) of a local diffusion graph-shift operator encoding the latent graph topology, excited with an ensemble of independent graph signals with arbitrarily-correlated nodal components. Unlike prior efforts that considered undirected graphs and white signal excitations, here the graph-shift operator and the observations' covariance matrix are not simultaneously diagonalizable. In this challenging context, we first rely on measurements of the output signals along with prior statistical information on the inputs to identify the diffusion filter. Such system identification problem involves solving a system of quadratic matrix equations, which we show is identifiable under spectral-diversity assumptions on the input covariances. For algorithmic purposes we recast it as a smooth quadratic minimization subject to Stiefel manifold constraints. Subsequent identification of the network topology given the graph filter estimate boils down to finding a sparse and structurally admissible shift that commutes with the given filter, thus, forcing the latter to be a polynomial in the sought graph-shift operator. A joint graph filter and topology identification algorithm is also proposed, which alternates between the aforementioned steps in a mutually reinforcing fashion to offer improved sample complexity. Numerical tests corroborate the effectiveness of the proposed algorithms in recovering synthetic digraphs and real-data case studies, and illustrate their potential utility on urban mobility analyses as well as portfolio optimization.

Multi-head attention conventionally partitions the hidden dimension equally across all heads at every layer, enforcing an identical representational subspace dimension (dh = dmodel/h) throughout the models depth. In this work, we identify this uniform allocation as a fundamental structural bottleneck: due to their restricted dimensional space, early-layer heads are unable to faithfully capture complex, high-dimensional contextual patterns. To resolve this, we introduce the Prism Transformer, a novel architectural paradigm that replaces the static, uniform head configuration with a progressive head schedule. By monotonically increasing the head count across layers, the Prism Transformer naturally establishes a local-to-global representational hierarchy: early layers leverage fewer, exceptionally wide heads to capture complex, local compositional patterns, while deep layers deploy many, narrow heads to decompose these patterns into specialized linguistic features. Crucially, this structural shift is parameter-neutral, compute-neutral, and introduces zero training or inference overhead, preserving identical weight matrices and FLOP budgets as the standard Transformer. Across three model scales (124M, 354M, and 757M), the Prism Transformer consistently outperforms uniform baselines, achieving consistent reductions in validation loss alongside consistent gains on downstream zero-shot benchmarks (including PIQA, HellaSwag, ARC-Easy, and WinoGrande). Our findings demonstrate that non-uniform subspace allocation unlocks latent capacity within the standard Transformer budget, enabling more effective use of model capacity.

This paper studies the problem of regret minimization in Markovian bandits with non-observable states and possibly constrained decision epochs. The focus is restricted to a “pure” regret benchmark, that compares the performance of the learning algorithm to the best pure policy which – akin to optimal policies of stochastic bandits – picks the optimal arm from start to finish without ever switching. We introduce a generalization of rested Markovian bandits, self-degrading Markovian bandits, for which pure policies are always asymptotically optimal.We show that without prior knowledge on the underlying bandit, the regret of algorithms that switch arms rarely necessarily scales super-logarithmically for every bandit, i.e., as $\omega(\log(T))$, where $T$ is the learning horizon. Despite the unreachability of the logarithmic regime, we design UCB-NOM, an optimistic algorithm inspired by UCB, of which the regret is nearly logarithmic. Lastly, we show that given prior knowledge on the Markovian bandit in the form of a bound on the bias functions of its arm, a proper instantiation of UCB-NOM achieves $O(\log(T))$ regret. We further show that this prior knowledge allows for a $O(\sqrt{T \log(T)})$ worst-case regret bound for UCB-NOM. Notably, our regret bounds do not depend on the number of states of the underlying Markov chains. Our findings suggest that the non-observability of states is a mild inconvenience in self-degrading Markovian bandits.

Foundation models for structural biology have achieved remarkable performance in predicting biomolecular structure and show promise for the design of proteins and small molecules. Yet understanding which internal features drive their outputs remains challenging. Standard sparse autoencoders (SAEs), effective on transformer-style sequence embeddings, do not transfer cleanly to pairformer-like architectures: naively operating on pairwise representations yields a quadratic blow-up of features and obscures concepts distributed jointly across sequence and pair representations. We introduce PairSAE, which summarizes pairwise tensors via an N-mode SVD into token-wise interaction roles, then uses a sparse autoencoder to learn a shared set of token-level features that decode into both sequence and pair representations. Evaluated on Boltz-2 activations for PLINDER protein-ligand complexes, PairSAE yields interpretable features that align with UniProt annotations and predict Boltz-2 affinity values. These results indicate that PairSAE links the latent space of foundation models for structural biology to interpretable structural concepts, clarifying what the model "knows" while avoiding pairformer-induced pitfalls that limit conventional SAEs.

Since its initial release in 2020, Darts has become a widely used open-source Python library for time series analysis. A series of foundation models have recently claimed accuracy improvements in zero-shot forecasting, promising a paradigm shift from training custom models to harnessing pre-trained general-purpose forecasters. Foundation models, however, are often released as isolated packages with fragmented interfaces and limited interoperability with common tooling, making joint evaluation and integration within complete pipelines difficult. In Darts, we developed a unified $\texttt{FoundationModel}$ class collection (Chronos-2, TimesFM 2.5, TiRex, PatchTST-FM) that provides standardized, full-cycle forecasting interfaces with minimal external dependencies for integrating foundation models into the ecosystem. Existing Darts pipelines can now use foundation models with only a name change; new pipelines can use them for zero-shot or fine-tuned forecasting, uncertainty estimation, and backtesting, combined with data processing and evaluation tooling, all within a unified framework.

The primary goal of Remote Sensing Image Change Captioning (RSICC) is to automatically generate descriptions of changes between remote sensing images captured at different time points. Existing models still rely on a single autoregressive generation paradigm, which tends to prioritize learning easily generated vocabulary over capturing discriminative differences between images. To address this, we reframe the training paradigm and propose a novel Difference Feature Modeling (DFM) framework. Specifically, we introduce a Text-guided Gated Contrastive Loss (TGCL) to guide the vision encoder to extract critical features from a text-modal perspective. Additionally, we incorporate a pre-trained Change Detection model to transfer stable change detection knowledge. In order to further enhance the representation, we design a Joint Feature Modeling (JFM) module to achieve the fusion of multi-scale difference representations, thereby capturing comprehensive spatiotemporal variations between multi-temporal images. Extensive experiments on multiple datasets demonstrate the effectiveness of our approach.

Multi-agent large language model (LLM) systems often rely on verifier and critic agents to suppress hallucinations, but verification is delayed. During this delay, false claims can propagate through the agent network. We model this process as delayed consensus on a graph with grounded corrector nodes. Spectral decomposition by the grounded Laplacian yields a closed-form stability threshold for the verification dose: correction that is too strong or too delayed can turn consensus into oscillation. The most unstable regime occurs when the communication and verification delays coincide; for delay two, the threshold is the inverse golden ratio. The same framework gives a supermodular placement objective and a greedy (1-1/e)-approximation rule for assigning a limited corrector budget to influential nodes. Experiments across five open models confirm the predicted dose-delay oscillations. By contrast, grounded factual answering makes truth an absorbing boundary and eliminates the effect, suggesting that the instability is specific to signed-belief tasks while grounded verification remains stabilizing

Modern image generation demands a single model that unifies diverse capabilities, including text-to-image (T2I), local editing, and global editing. However, these capabilities are rarely naturally aligned and often conflict. For instance, editing tends to degrade T2I performance, while global and local editing interfere with each other. Consequently, effectively composing these capabilities has become a central challenge for image generation model training. To tackle this, we introduce DanceOPD, an on-policy generative field distillation framework for flow-matching models that routes each sample to one capability field, queries one low-noise student-induced state, and trains with a simple velocity MSE objective. With each capability source defined as a velocity field over the shared flow state space, the student learns from fields queried on its own rollout states to compose expert capabilities. This formulation also absorbs operator-defined fields such as classifier-free guidance. Comprehensive experiments on T2I, editing, realism-field absorption, and CFG absorption show that our approach improves multi-capability composition, strengthening target capabilities while preserving anchor generation quality. We believe this work establishes a practical route for generative field distillation in flow-matching models.

Reinforcement learning with verifiable rewards (RLVR) for training LLMs typically rely on ground-truth answers to assign rewards, limiting their applicability to tasks where the ground-truth solution is unknown. We introduce a Ranking-induced VERifiable framework (RiVER) that trains LLMs on score-based optimization tasks without ground-truth solutions, using deterministic execution feedback as continuous-valued supervision. When applying group-relative RL to such continuous rewards, we identify two key challenges: scale dominance, where uncalibrated score magnitudes across test instances distort policy updates, and frequency dominance, where repeatedly sampled suboptimal solutions can outweigh rare but stronger candidates. RiVER addresses these challenges with calibrated reward shaping that uses instance-wise comparisons and emphasizes top-ranked solvers while retaining bounded feedback for other valid solutions. We train on 12 AtCoder Heuristic Contest tasks and evaluate on Algorithm Engineering Benchmark (ALE-Bench), LiveCodeBench, and USACO. RiVER advances Qwen3-8B and GLM-Z1-9B-0414 by 8.9% and 9.4% in ALE rating rank. More importantly, despite training exclusively on score-based tasks without any ground-truth solutions, RiVER also improves the backbones across exact-solution benchmarks such as LiveCodeBench and USACO by an absolute average improvement of 2.4% and 3.5%. By contrast, baselines trained with raw execution scores improve ALE rating but fail to transfer to exact-solution benchmarks. These results suggest that score-based optimization tasks, combined with proper reward calibration, can serve as effective training environments for general coding ability without ground-truth solutions.

Efficient sampling of molecular systems at thermodynamic equilibrium is a hallmark challenge in statistical physics. This challenge has driven the development of Boltzmann Generators (BGs), which allow rapid generation of uncorrelated equilibrium samples by combining a generative model with exact likelihoods and an importance sampling correction. However, modern BGs predominantly rely on normalizing flows (NFs), which either suffer from limited expressivity due to strict invertibility constraints (discrete time) or computationally expensive likelihoods (continuous time). In this paper, we propose Autoregressive Boltzmann Generators (ArBG) – a novel autoregressive modelling framework – that overcomes these limitations by departing from the flow-based BG paradigm. ArBG circumvents the topological constraints of flows and enables sequential inference-time interventions, while offering enhanced scalability by leveraging architectures effective in Large Language Models. We empirically demonstrate that ArBG leads to significant improvements over flow-based models across all benchmarks, but particularly in larger peptide systems such as the 10-residue Chignolin. Furthermore, we introduce Robin, a 132 million parameter transferable model trained with the ArBG framework which improves over the previous state-of-the-art, reducing the zero-shot energy error, E-W$_2$, on 8-residue systems by over 60$\%$. The code can be found at the following link: https://github.com/danyalrehman/autobg.

Many decoding methods for large language models can be understood as shifting probability mass toward outputs that are more likely under the model, either locally at the token level or globally at the sequence level. Therefore, their success depends on a fundamental question: when does sequence probability, that is, the conditional probability of a continuation given a prompt, actually align with correctness? In this paper, we set out to quantify this relationship across decoding methods, models, and benchmarks at four levels: across decoding methods, across hyperparameters within a method, across prompt-answer pairs within a dataset, and across repeated responses to the same prompt. We find that higher sequence probability is often predictive of correctness across prompt-answer pairs within a fixed dataset. However, this relationship does not generally transfer to decoding decisions: increasing sequence probability by changing hyperparameters or methods does not reliably improve accuracy. Further, sequence probability is not a good indicator of correctness for responses to the same prompt. These findings clarify when decoding can and cannot be expected to improve correctness, and provide practical guidance for decoding, self-consistency, and verifier-free self-improvement.

Neural surrogate models offer fast approximate mappings from PDE parameters to solutions, but they typically treat solving as a purely statistical task: once trained, they struggle to correct their own constraint violations and extrapolate beyond the training distribution. Recent hybrid methods promote physical correctness by targeting the PDE residual via gradient descent or Gauss–Newton steps, but inherit the compute cost and instability of the underlying classical optimizers. We show, theoretically and empirically, that numerically minimizing the PDE residual can be an unreliable proxy for reconstruction accuracy in ill-conditioned systems, explaining why these methods often do not make accurate predictions despite achieving low residuals. We propose error-conditioned Neural Solvers (ENS), built on a different principle: rather than an optimization target, the PDE residual field is passed as a direct input to the network at each iteration, enabling it to read the spatial structure of its own errors and learn an update policy to iteratively correct its predictions. Across four PDE families, ENS attains the highest prediction accuracy in the large majority of settings, with gains reaching $10\times$ on turbulent Kolmogorov flow, while avoiding the expensive compute cost of hybrid methods. ENS's learned correction policy generalizes under distribution shift, including zero-shot parameter changes and cross-equation transfer, where its relative advantage is largest in the ill-conditioned regimes where residual minimization is least reliable. Project website: https://neuralsolver.github.io/.

Entity Matching (EM) is a core operation in the data integration pipeline, where records from different sources are compared to determine whether they refer to the same real-world entity. Recent work has incorporated domain information and low-resource learning techniques to better adapt EM systems to realistic settings. While these approaches have demonstrated strong performance, it remains unclear how they behave under varying data constraints and levels of supervision in practice. In this paper, we investigate a state-of-the-art method for low-resource, domain-aware EM–BEACON–and study how its performance is affected by different algorithmic choices and data availability conditions. We conduct a series of targeted experiments to evaluate these variations, providing deeper insight into the role of distribution alignment and the behavior of the BEACON framework.

Multimodal web agents can assist humans in operating repetitive GUI tasks, where effective task planning is essential for decomposing complex tasks into executable actions. While small open source MLLMs are cost efficient and privacy preserving compared with commercial large models, they suffer from weak planning and limited cross website generalization. To address these limitations, we introduce the planning experience exploration and utilization (PEEU) method, which autonomously explores environments to discover experiences and utilizes hindsight experience to synthesize strictly aligned, high level training data. To quantitatively analyze the generalization behaviors driving this performance, we propose the task decomposition hierarchical analysis framework (TDHAF) to systematically study compositional generalization across three task granularities: low, middle and high levels. Our analysis reveals that mastering low level atomic skills does not guarantee high level planning competence, while high level task training yields stronger OOD generalization. Experiments on real world benchmarks demonstrate PEEU's superior effectiveness: our 7B model achieves 30.6% accuracy, outperforming the much larger Qwen2.5-VL-32B model. These demonstrate constructing hindsight high level tasks and leveraging experiences is crucial for OOD planning abilities of small MLLMs.

Modern generative world models render increasingly realistic action-controllable futures, yet they frequently hallucinate: rollouts remain visually fluent while drifting from the ground-truth dynamics. We hypothesize that hallucination concentrates in low-coverage regions of the state-action space, where lightweight data-centric signals can both detect it and guide mitigation. To test this, we introduce MMBench2, a 427-hour, 210-task dataset for visual world modeling with ground-truth actions, rewards, and live simulators, and train a 350M-parameter world model on it. We identify three distinct hallucination modes: perceptual, action-marginalized, and scene-diverging – each anchored to a different stage of the pipeline, and develop three signals that accurately predict where the model will fail. To close coverage gaps at training time, we develop a coverage-aware sampling technique; to close them online, our hallucination predictors serve as curiosity rewards for targeted data collection, yielding a data-efficient finetuning recipe that adapts the pretrained world model to entirely unseen environments with as few as 50 real environment trajectories. Overall, our findings reveal that hallucination in world models is inherently a data coverage issue, and that the same signals used to detect it can also be used for mitigation. An interactive web version of our paper is available at https://www.nicklashansen.com/mmbench2

Sparse autoencoders (SAEs) have become a leading tool for interpreting the representations of vision foundation models, decomposing their polysemantic activations into a larger set of sparse, more monosemantic features. The Top-$k$ SAE, a now-standard variant, enforces sparsity architecturally through its activation function, retaining only the $k$ most active latents per input. Because it was designed precisely to avoid the $\ell_1$ penalty used by earlier SAEs and its known drawbacks, it has not been combined with an explicit sparsity regularizer. Yet the Top-$k$ SAE retains limitations of its own, and we hypothesize that a sparsity penalty acting before the selection could sharpen each latent's selectivity and make the code more interpretable, without reintroducing the drawbacks of the $\ell_1$ penalty. We introduce two sparsity regularizers compatible with the Top-$k$ architecture, both acting on the activations before the Top-$k$ selection: an $\ell_1$ penalty on the unselected (off-support) units, and a scale-invariant $\ell_1/\ell_2$-ratio penalty that concentrates the code onto fewer effective units. Both penalties are applied only to the batch-active units, those selected by the Top-$k$ operator at least once within the batch. Across two datasets, three vision foundation models, and a range of $k$, both regularizers consistently improve monosemanticity at no cost to reconstruction quality. The $\ell_1/\ell_2$ penalty further concentrates information into fewer latents, making reconstruction more robust to the inference-time choice of $k$ and improving small-budget linear probing. Our central finding is that hard architectural sparsity and soft sparsity regularization are complementary rather than mutually exclusive.

Neural audio autoencoders have become a core component of compression, feature extraction, and generation. However, while existing systems support variable bitrate, the vast majority of models still operate at a fixed latent frame-rate, allocating equal temporal budget to regions with very different information density, which can result in unnecessarily long sequences. We introduce Elastic Time, a dynamic frame-rate bottleneck that converts fixed-frame-rate autoencoders to dynamic ones. Our method learns a lightweight latent predictor used to decide which frames can be skipped and later reconstructed, enabling efficient greedy boundary selection at inference. Experiments show our method enables deployment-time rate control while improving efficiency-quality tradeoffs relative to baselines. Overall, we provide a flexible mechanism for adjusting temporal resolution in audio autoencoders, potentially facilitating more efficient downstream modeling for generation and long-context tasks.

Gradient equilibrium (GEQ) is a recently introduced online optimization framework that generalizes first-order stationarity from offline optimization and abstracts problems like online conformal prediction. While GEQ has curious similarities with known online learning frameworks, namely regret minimization, prior work has shown that GEQ error and regret are incomparable objectives, leaving open a precise understanding of how GEQ fits into the broader online learning landscape. In this work, we show that GEQ is equivalent to Blackwell approachability in the algorithmic sense. That is, a Blackwell approachability problem can always be solved using queries to a black-box GEQ oracle, with no asymptotic loss in the oracle's error rate, and vice versa. Taken together with known equivalences between approachability, regret minimization, and calibration, these results imply that GEQ is equivalent to these frameworks, as well. Our reductions are efficient and can be used to transfer refined guarantees, such as optimism and strong adaptivity, from regret minimization to GEQ. Along the way, we also identify necessary and sufficient conditions for GEQ, and establish reductions between different notions of GEQ with unconstrained and constrained decision sets.

Guided wave-based structural health monitoring (GWSHM) with onboard transducers offers significant potential for the early diagnosis of damage in engineering structures. However, the practical deployment of deep learning models is often hindered by the limited availability of labelled experimental data and the high computational cost of generating large-scale high-fidelity simulation datasets. This study presents a multifidelity transfer learning framework that integrates lightweight physics-based simulations, convolutional autoencoder (CAE)-based deep feature learning, a feed-forward neural network, and limited experimental measurements for accurate damage localisation and sizing in plate-like structures instrumented with piezoelectric transducers. A computationally efficient one-dimensional time-domain spectral element model is employed to generate a large synthetic dataset for pretraining, while transfer learning adapts the model to experimental domains using only a small amount of labelled data. The CAE-based transfer learning framework significantly outperforms its CNN-based counterpart in damage localisation accuracy. The model achieves excellent predictive performance with $R^2$ scores exceeding 0.93 for damage localisation and 0.99 for damage sizing. Its generalisation capability is demonstrated on previously unseen data, showing high prediction accuracy for damage scenarios not represented during pretraining or fine-tuning. The results establish the proposed framework as an accurate, computationally efficient, and practically viable solution for real-world GWSHM applications.

We study the fundamental problem of learning a high-dimensional Gaussian truncated to an unknown halfspace. Lee, Mehrotra and Zampetakis (FOCS'24) recently obtained the first polynomial time algorithm for this problem, but their resulting sample and time complexity bounds are not optimal. Under non-trivial truncation, for any target accuracy $\varepsilon > 0$ and dimension $d$ we give an efficient algorithm that uses $n = \tilde{O}(d^2/\varepsilon^2)$ samples and learns the underlying Gaussian to error $\varepsilon$ in total variation distance. Our algorithm is also fast: its runtime is dominated by the cost of computing the empirical covariance matrix. Both our sample and time complexity are optimal in terms of $d$ and $\varepsilon$ even without truncation: in this regard, we can learn a Gaussian under halfspace truncation for free. The key ingredient behind our result is a novel reinterpretation of the low-degree moments of the truncated Gaussian in terms of a relative truncation parameter. This relative truncation parameter uniquely determines the parameters of the untruncated Gaussian and enables direct parameter recovery. This reinterpretation allows us to circumvent the time intensive projected stochastic gradient descent procedure that is widely used in learning under truncation.

Analog hardware platforms such as coupled oscillators and Analog Ising Machines naturally solve differential equations at a fraction of the energy cost of digital computation, making them attractive for low-power generative modeling, yet a fundamental mismatch exists: modern generative models assume flexible, software-defined dynamics, whereas analog hardware imposes fixed, physics-determined differential equations with limited approximation capacity. This paper introduces Analog Interaction Systems (AIS), a unified framework for hardware-implementable dynamical systems, and empirically characterizes their expressivity gap relative to neural network baselines. Two hardware-compatible mechanisms are proposed to narrow this gap - time-varying piecewise parameters and hidden physical states - and a Wasserstein GAN training procedure is developed to enable training of these models without requiring them to follow a specific trajectory. We characterize how area and power scale with connection density and precision, showing that sparse connectivity and low-bit-width quantized parameters are necessary for practical implementation, and estimate an energy cost of 23uJ per generated image for the chosen architecture, representing a 2-orders-of-magnitude improvement over digital baselines. On MNIST and Fashion-MNIST, our oscillator-based AIS achieves FID scores of 27.6 and 80.8, outperforming the best prior hardware-implementable analog generative models by 3-4x with a 4-bit sparse architecture.

Job-search platforms rely on low-bandwidth query interfaces that often fail to capture the high-dimensional complexity of candidate profiles. We present an end-to-end RLAIF (Reinforcement Learning from AI Feedback) framework to generate portable job search queries, terms that abstract away seeker-specific identifiers while preserving generalizable qualifications. This task introduces a highly adversarial reward surface where policy optimization frequently exploits flaws in LLM-as-judge rubrics, resulting in degenerate verbatim-copying behaviors. We conducted comprehensive empirical experiments to isolate the impact of optimization mechanics against structured reward engineering. Our results demonstrate that for critic-free optimizers, performance is overwhelmingly dictated by robust reward shaping, rendering the specific choice of algorithm largely immaterial. While critic-free per-rollout baseline methods (RLOO and REINFORCE++) natively resist reward-hacking, the group-relative advantage normalization in GRPO appears uniquely sensitive to spurious reward signals, making it disproportionately susceptible to exploitation. We show that introducing a deterministic, rule-based reward floor to correct for rewards assigned to verbatim copying mitigates this failure mode, resulting in a substantial $+0.147$ quality improvement on a cross-family evaluation judge. Ultimately, we show that the training-time reward model inflates performance gains by $2.4\times$, confirming that the training success is fundamentally dependent on enforcing reward-shaping disciplines rather than selecting alternative optimizers.

Multi-model LLM systems such as routing, voting, cascades, fusion, and mixture-of-agents are used to beat single-model accuracy. We show that their gain is capped by a quantity the field rarely reports. For any policy whose output is one member model answer, accuracy cannot exceed one minus beta, where beta is the rate at which every model is wrong on the same query. In contrast, the usual diagnostic, average pairwise error correlation rho, cannot identify beta: error laws with identical marginals and pairwise correlations can have different all-wrong rates. A Clopper-Pearson bound on beta gives a finite-sample certificate on the largest gain any router, vote, or cascade could deliver before training a router. Across 67 models from 21 providers, a tetrachoric-calibrated single-factor model still underprices the all-wrong tail: on open-ended mathematics, observed beta is 0.052 versus 0.023 under the full 67-model Gaussian copula, about 2.5 times underpricing, with 90 percent CI 1.7 to 3.4 and k equals 17. The effect recurs on execution-graded code, where beta is 0.079. Re-asking the same GPQA-Diamond questions in free-response rather than multiple-choice form reopens the tail, with beta 0.127 and a five-judge panel with kappa 0.73 to 0.92, locating co-failure in answer format rather than subject. At matched quality, low-rho heterogeneous ensembles beat high-rho Self-MoA, but on checkable tasks in our pool, combining models rarely beats the single best model without a strong query-level routing signal. Gains come from models failing on different questions, not from adding more models.

Learning governing equations from observed solution data is a fundamental challenge in scientific machine learning, yet the theoretical conditions under which a ground-truth ODE can be uniquely and stably identified from multiple solution observations remain largely undeveloped, and no quantitative analysis of the sample complexity of such learning tasks exists in the literature. To address this gap, we introduce the Hausdorff distance on solution sets as the natural metric for comparing differential equations, since it captures the worst-case separation between two equations over all admissible initial conditions and thus encodes the minimax structure of the identification problem. We establish identifiability bounds for governing ODEs across a wide class of structure equations–ranging from linear ODEs to nonlinear classes with Lipschitz (Hölder)-continuous vector fields–characterizing precisely when two distinct equations can be distinguished from solution data. Using this metric, we derive metric entropy estimates for the relevant ODE classes and analyze sample complexity bounds, quantifying how many solution observations are needed to reliably recover the governing equation.

Time-series forecasting research has been moving steadily toward larger architectures, from specialized transformers to general-purpose foundation models, on the assumption that capacity is what unlocks accuracy. We take the opposite position: most of the gap can be closed at far lower cost by tuning preprocessing rather than scaling models. We use Ridge regression as the testbed, since it has a closed-form solution and interpretable weights, which let the optimal hyperparameters be read off the search directly. We search over context length, local normalization, regularization, and augmentation on eight standard benchmarks and find three patterns. (1) Optimal lookback is strongly series-specific and often non-monotonic in forecast horizon, with fitted power-law exponents ranging from $+0.46$ on ETTm2 to $-0.19$ on Exchange and Traffic, challenging the convention that longer horizons need longer history. (2) Normalizing over a learned trailing fraction of the context, rather than its entirety, is almost universally preferred. (3) Series within the same dataset often disagree on hyperparameters; the optimal degree of cross-series sharing varies from fully shared to fully per-series. The resulting models beat prior linear forecasters on most dataset-horizon entries and exceed Transformer, MLP, and CNN baselines on six of eight benchmarks. The optimized hyperparameters also serve as a diagnostic on the data itself, revealing structures that larger models absorb silently into their learned parameters. We provide an accompanying interactive online demonstration and the code at https://sakanaai.github.io/SearchCast/.

The promotion of betting applications on social media platforms has increased significantly in recent years. Many of these advertisements use persuasive techniques that may mislead users, encourage risky behavior, and potentially influence users' mental well-being. However, research on the automated detection of manipulative and deceptive betting advertisements remains limited due to the lack of publicly available annotated datasets. In this work, we introduce a new dataset of betting-related advertisements collected from two widely used social media platforms, Instagram and Reddit. The advertisements were manually annotated for manipulative and deceptive advertising practices. In addition to classification labels, the dataset includes human-provided explanations that describe the reasoning behind each annotation, enabling research into explainable approaches to detecting manipulative advertising. Furthermore, we analyze the strategies commonly used in betting advertisements and examine how these persuasive tactics may impact users' mental health. The proposed framework can also enable practical applications such as browser plugins that warn users about manipulative betting advertisements and automated web crawlers that help regulatory authorities monitor and detect such promotions online.

Reliably quantifying predictive uncertainty is difficult for complex, high-dimensional, or misspecified models. Both fully Bayesian and bootstrap resampling methods provide principled uncertainty estimates but are often too expensive for modern machine-learning models because they require posterior sampling or repeated model refitting. We introduce Ribbon, a scalable approximation to Dirichlet-reweighted bootstrap uncertainty. Ribbon replaces repeated refitting with an influence-function linearization around a single fitted model, preserving the first-order data-reweighting structure of the Bayesian bootstrap while requiring only post-hoc linear algebra. Ribbon approximates the Bayesian-bootstrap or weighted-likelihood-bootstrap refitting target. With a general concentration parameter, Ribbon gives a calibrated Dirichlet-reweighting family whose uncertainty scale can be tuned on validation data. We show that Ribbon is asymptotically equivalent to a flat-prior Laplace approximation under correct likelihood specification and recovers the robust sandwich covariance under misspecification. Across synthetic regression, MNIST classification, and California Housing benchmarks, Ribbon provides competitive predictive performance and improved calibration in several settings while avoiding repeated model retraining.

In NLP, mental health conditions are often modeled as isolated phenomena, without interpersonal context. We use Reddit posts about long-distance relationships to capture both mental health distress and associated relational triggers. We introduce the Relational Stress and Psychiatry Corpus (RSPC) containing 1,799 Reddit posts annotated by psychiatrists for diagnostic categories, including the most prevalent mood disorders (anxiety and depression), relational stressor triggers, and indications of relationship phase. We benchmark seven fine-tuned transformer models and five large language models across multi-label disorder classification, relational trigger detection, and temporal phase prediction tasks. We find clear task-dependent differences between model families, with Claude-3-Haiku achieving the best disorder classification performance (Macro-F1 = 0.538) and GPT-4o obtaining the strongest relational trigger detection performance (Macro-F1 = 0.519), suggesting distinct model capabilities. We further find strong associations between anxiety disorders and chronic relational uncertainty. Overall, RSPC establishes a benchmark for NLP tasks that consider relational context and supports a shift from individual-centric to context-aware mental health modeling that captures the social and temporal dynamics of distress.

We study a solvable high-dimensional model of generative adversarial network (GAN) training in which a linear generator learns a low-dimensional subspace from data with structured latent covariance. Prior solvable GAN analyses assume unconditional signals with diagonal latent covariance; we extend the multi-feature discriminator setting to class-dependent, correlated, and non-zero-mean latent structure. For the quadratic energy discriminator, all such heterogeneity enters the dynamics through a probability-weighted effective second moment. We prove that the stochastic microscopic training process converges, in the high-dimensional limit, to deterministic ordinary differential equations governed by this effective covariance. In the matched-covariance specialization, the stability analysis yields a mode-wise solvable interval determined by the learning rates and noise level: learning begins when the leading effective eigenvalue crosses the lower threshold, while full recovery requires all relevant effective modes to remain within the interval. This reveals a signal-boosting mechanism: low-rank correlations can lift weak directions above the learnability threshold, whereas overly strong correlations destabilize recovery. Numerical simulations validate the ODE, phase boundary, and boosting mechanism. Experiments on MNIST, FashionMNIST, and CIFAR-10 further show that informed generator covariance improves alignment with the data-driven reference subspace.

Training-free source selection for LLM families with shared vocabularies arises in scientific string domains such as SMILES, protein, and genomic sequences, where candidate corpora share a tokenizer but differ in prediction targets. This creates an activation-dark regime: representation-similarity metrics can be uninformative without assumptions about label-conditioned error geometry, while classical update-geometry metrics are computationally prohibitive at vocabulary scale. We show that, in a shared-output head setting, representation metrics (e.g., CKA) are non-identifiable for transfer; models can share identical representations yet have orthogonal head updates. The key identity is that head Fisher alignment is exactly a cosine between kernel mean embeddings in the joint activation-error space, exposing activation, error, and coupling factors rather than requiring a materialized Fisher matrix. FisherSketch estimates this cosine directly in a single streaming pass, making K=128,256 head Fisher alignment practical with a 16 KB task signature (m=4096) and a 192 KB per-task streaming state, small enough to store next to a model hash, but encoding transfer-relevant update structure. Beyond source selection, the same signatures and marginals provide a diagnostic instrument for studying whether LLM task similarity is driven by activations, errors, or their coupling; shared-parameter and internal-layer validations, together with Llama-3.1-8B verbalizer-shift experiments, show that FisherSketch remains informative when activation similarity cannot distinguish tasks.