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Multimodal Large Language Models (MLLMs) exhibit strong visual understanding, yet the internal features that cause these behaviors remain difficult to identify, audit, or control. While applicable to post-hoc inspection, hidden states that are decomposed into interpretable feature directions using sparse autoencoders (SAEs) neither readily isolate which features are changed by multimodal training, nor are they directly useful for targeted control. We introduce MMDiff, a multimodal model-diffing framework that trains multimodal SAEs and turns them into feature-level interfaces for discovering and controlling multimodal behavior. MMDiff supports three uses: (i) feature isolation, by diffing a base-LM SAE against its multimodal-adapted counterpart to identify features altered by multimodal training; (ii) task-specific feature detection, via per-token contrastive firing analysis that isolates causal features; and (iii) feature-level control, by causally removing or steering the discovered feature directions. We train multimodal SAEs for three MLLM families, LLaVA-MORE, PaliGemma 2, and InternVL3.5, and evaluate on visual-spatial understanding, multimodal safety, and OCR. MMDiff discovers sparse, causally specific features whose removal selectively degrades target behaviors by an average of 12% on spatial tasks and 17% on OCR, and reduces attack success rate by 24% on multimodal safety attacks, with no impact on VQA performance. Steering these features improves spatial and OCR accuracy by +3.6% and +1.8% on average over a standard single-layer steering baseline. These results show that multimodal SAEs can serve not only as interpretability tools, but as mechanisms for auditing, steering, and controlling MLLMs behavior toward safer and more capable generations.

We present TorchCurves, a PyTorch library that treats vector-valued parametric curves as learnable primitives. Its central operation maps batches of scalar inputs to points on curves represented in B-spline or Legendre polynomial bases, with differentiation through both inputs and coefficients. Curve coefficients can be optimized jointly with the surrounding model or produced by another network. The library provides trainable modules, reusable basis modules, and a functional interface, supporting applications ranging from continuous feature embeddings to Kolmogorov-Arnold networks and functional regression. Its implementation combines classical evaluation algorithms with vectorized PyTorch operations, emphasizing readability and maintainability without custom hardware kernels. Timing experiments compare curve evaluation against NumPy and SciPy and KAN training against EfficientKAN across a range of problem sizes. The results illustrate where this generality remains computationally practical and where overhead is substantial. Library is available on GitHub at https://github.com/alexshtf/torchcurves.

Reinforcement learning with verifiable rewards (RLVR) produces rich training experience, yet outcome rewards reduce each attempt to a single number and leave most of this information unused. Training-time scaffolds, such as strategies or hints added to the prompt during training, offer a natural way to turn this information into guidance, but their design and adaptation are largely left to humans and tailored to specific domains. We introduce AutoScaffold, a unified AI-for-AI framework that turns a student's training experience into adaptive scaffolds, with minimal domain-specific information and no human intervention during training. A frozen teacher periodically examines this experience, diagnoses bottlenecks, and designs scaffolds in two forms: (i) strategies shared across a class of tasks and (ii) hints for individual hard tasks, adjusting the content and amount of support as the student learns. The scaffolds are removed at evaluation. We apply the same framework to ALFWorld, search-based QA, mathematical reasoning, and GPU kernel generation. When evaluated without scaffolds, students trained with AutoScaffold outperform those trained with the corresponding RL baselines in all four domains, with gains of 7.2 points in ALFWorld success and 4.0 points in average QA exact match. On GPU kernel generation, AutoScaffold increases the fraction of tasks with a correct kernel that runs faster than the PyTorch reference by up to 5.0 points. On math, our student surpasses QuestA's reported accuracy using approximately one-third as many student training steps. Analyses show that the teacher identifies a different failure in each task class and shifts its scaffolds from step-by-step workflows to targeted fixes as the student improves, and that its revised scaffolds help the student learn more than keeping the previous scaffold or using no scaffold.

LLM agents are increasingly used for open-ended, data-driven scientific discovery, yet most of them evaluate hypotheses pointwise, testing an empirical claim $h$ only against its complement $\neg h$. When evidence rejects $h$, the agent learns that one explanation is unlikely but not which alternative the evidence supports. To recover that alternative, we introduce Contrastive Discovery, which replaces the single hypothesis with a contrast set, a scientific question paired with mutually exclusive and collectively exhaustive competing explanations. Each experiment is scored by how its evidence redistributes belief across the set, and the question is resolved when belief concentrates on one explanation. Because contrast sets change only the unit an agent proposes and scores, an existing agent can use them to re-evaluate evidence it has already collected or to guide its search. Across six domains, $89\%$ of the pointwise candidates with the largest belief shifts are rejections. On the same evidence, contrast sets resolve $73\%$ of these candidates to a specific alternative. When contrast sets guide search, the agent resolves $67\%$ more questions than pointwise surprisal under the same experiment budget. In a blinded study, $38$ human experts chose the same explanation on $78\%$ of resolved questions and on $82\%$ of questions where the pointwise agent rejected its hypothesis and stopped. Together, these results support explicit competing explanations as a way for discovery agents to resolve more scientific questions from the same evidence and validation budget.

Connectome-constrained models are often used to argue that a measured wiring diagram outperforms shuffled or rewired wiring, and hence that structure shapes function. Such comparisons can confound wiring with how the models are tuned: a connectome fixes who connects to whom, not the excitability, gains or plasticity rates the model also needs, and modellers often tune these until the real-wiring model works. We separate three estimands: physiology tuned on the real wiring and transferred to nulls (P1), each wiring tuned on its own (P2), and P2 restricted to physiology consistent with independent data (P3). The biases involved are known in machine learning (under-tuned baselines, inherited weights, winner's curse); we measure what they do to biological conclusions, using synthetic ground truth, placebo nulls and three Drosophila circuit models. Some claims survive every protocol we test: segregated reward and punishment dopamine improves learning, and head-direction topography is required for a persistent bump. Others do not. In the mushroom body, the real Kenyon-cell output wiring beats a cross-subtype identity shuffle by 0.09 under P1 and P2 but loses to it by 0.09 under P3 (95% CIs exclude zero; held-out runs confirm). The verdict is set by the share of alpha'beta' cells among active Kenyon cells, which P1 selects low; at the share implied by imaging (about 44%) the real-wiring model fails to learn, exposing a model inadequacy rather than a deficit of the fly's wiring. In flyvis, P1 penalises a mirrored connectome, which has a constructed solution within 0.07 (median) of the real error, more than a spatially shuffled one in 50 of 50 members; the ranking survives ten-fold longer retraining but depends on the checkpoint at fifty-fold. A credible structural claim needs matched optimisation, data-constrained physiology and a model that still works there.

We consider one-hidden layer neural networks trained in the feature-learning regime using gradient descent, and relate the output of the finite-width network $f_{\hatρ_t^m}$ to its infinite-width counterpart $f_{ρ_t^{MF}}$, which evolves in the mean-field dynamics. While constant-time horizon bounds for $\|f_{ρ_t^{MF}} - f_{\hatρ_t^m}\|$ may be obtained via standard Grönwall estimates, the long-time behavior of the fluctuation is a more delicate matter. Uniform-in-time bounds often rely on (local) strong convexity in the landscape or Logarithmic Sobolev inequalities present in noisy gradient dynamics. In this work, we establish non-asymptotic weak propagation-of-chaos that holds uniformly in time, obtained by exploiting instead the convergence rate of the mean-field deterministic Wasserstein-gradient-flow dynamics. Specifically, denoting by $L_t$ the mean-field excess MSE loss at time $t$ and $m$ the number of neurons, under standard regularity assumptions and the condition $\int_0^\infty L_t^{1/2} dt =O(\log d)$, we obtain the uniform in time bound $\|f_{ρ_t^{MF}}- f_{\hatρ_t^m}\|^2 \lesssim \text{poly}(d) m^{-\min(1,c/6)}$ whenever $L_t \lesssim t^{-c}$. Our result holds in a noiseless setting and does not make any assumptions on the geometry of the landscape near the optimum, and extends seamlessly to other forms of discretization, including finite number of samples and time discretization. A key takeaway of our result is that whenever the convergence rate of the mean-field, population-loss dynamics is faster than $t^{-2}$, we can attain a loss of $ε$ with only $\text{poly}(d/ε)$ neurons, training samples, and GD steps.

Time series analytics has been widely applied across various domains. While existing time series foundation models (TSFMs) have demonstrated promising results, they still face two major challenges: 1) Most TSFMs mainly rely on stacking Transformer layers to increase parameter size, lacking the ability to adaptively model complex time series patterns from multi-domain data. 2) Current TSFMs are primarily pre-trained for specific tasks, e.g., forecasting or anomaly detection, and a few models support multiple tasks, but they fail to fully leverage task specificity and commonality, resulting in suboptimal performance. To address these challenges, we propose TimeSeek, a novel generalized time series analytics model that adaptively models time series patterns from multi-domain data and unifies multiple tasks in pre-training. Conceptually, TimeSeek is guided by selective information sharing under domain and task heterogeneity. From the perspective of multi-domain data, we propose a Multi-Domain Feature Extractor that adaptively captures temporal dependencies and channel correlations based on domain-specific characteristics, including progressive multi-scale modeling and adaptive slot channel modeling. From the perspective of the diversity of tasks, we propose multi-task collaborative training, which leverages task specificity and task commonality through task customization and cross-task training, effectively unifying multiple tasks in pre-training and better adapting to diverse downstream scenarios. After pre-training on large-scale time series data, TimeSeek achieves state-of-the-art performance in forecasting, anomaly detection, and classification tasks across both few-shot learning and zero-shot situations, together with favorable inference efficiency.

Numerical methods and neural networks have transformed our understanding of nonlinear partial differential equations (PDEs), yet discovering mathematical representations that explain their dynamics remains largely an expert task. We introduce Agentic Symbolic Search (ASYS), in which coding agents construct and refine explicit approximations from a known PDE and supplied mathematical knowledge. ASYS couples evolutionary search over differentiable symbolic programs with gradient-based fitting, using the governing equation to evaluate candidates and guide their revision. For a singular generalized Constantin-Lax-Majda profile, ASYS infers a missing decay term that sets how fast the field approaches its singular-time limit, and builds a basis that fits the profile to a median error of $3.90\times10^{-5}\%$. For Fujita blow-up, separating diffusion from reaction and deriving a local response lowers the supplied formula's error from 55.5% to 0.0879%. For Allen-Cahn interfaces, a 14-parameter construction yields a mode-coupling law confirmed by independent simulations. These studies show how agentic search develops mathematical starting points into accurate, analyzable approximations.

We study Bayesian inference of persistence from early observations of a heterogeneous susceptible--infected--susceptible (SIS) reaction--diffusion model with standard incidence. We show that the leading prevalence dynamics depend on the unknown coefficients only through the difference between the transmission and recovery rates and the infected diffusivity. The same pair determines the principal eigenvalue whose sign governs persistence, so early prevalence can inform the threshold even when the individual rates remain uncertain. We prove global weak well-posedness and quantitative parameter stability for the SIS system and use the resulting observation-map estimates to establish Bayesian well-posedness. For an initial infection of size $\varepsilon$, we derive a uniform second-order expansion that describes how the separate rates enter prevalence. Incidence depends explicitly on transmission at leading order. When the noise standard deviation is proportional to $\varepsilon$, we prove $O(\varepsilon)$ convergence in Hellinger distance of the nonlinear posteriors to their low-prevalence limits for both prevalence alone and joint prevalence and incidence data. We bound the principal eigenvalue using the growth rate of the infected $L^2$ norm between two times. This rate gives a lower bound for the full nonlinear system, and the upper bound separates spatial transients from nonlinear saturation. Uniform spectral estimates and bounds on infection size and measurement error give sufficient conditions for persistence and extinction. We also bound the error in posterior persistence probabilities under forward and eigenvalue approximation, accounting for posterior mass near the threshold. Numerical examples illustrate threshold inference and the predicted \(O(\varepsilon)\) convergence of the nonlinear posteriors to their low-prevalence limits in Hellinger distance.

Policy optimization is central to language model post-training, yet principled guidance remains limited. We revisit its theoretical foundations to identify algorithms that learn near-optimal policies using total samples and gradient steps governed by the base model's response coverage, a measure of how readily it generates optimal responses. We call such algorithms coverage-preserving. This guarantee captures the goal of amplifying capabilities accessible through sampling from the base model. (1) Coverage collapse. REINFORCE, the basis for PPO and GRPO, can drive the probability of optimal responses to near zero, even as reward improves. This coverage collapse stalls optimization, and convergence can require exponentially many steps despite good initial coverage. The failure arises even with exact gradients and persists under KL regularization to the base model. (2) Reference resets. We show that repeatedly resetting the KL reference to the most recent policy mitigates coverage collapse. We formalize this intervention in Approximate Policy Mirror Descent (APMD), a meta-algorithm that approximately solves a sequence of KL-regularized RL subproblems. APMD enables stronger regularization, making each subproblem easier to solve, while reference resets allow convergence to global optimality. (3) Coverage-preserving algorithms. For softmax linear policies over pretrained features, we use APMD to establish the first global convergence guarantees showing that widely used families of post-training algorithms are coverage-preserving. These include stylized PPO and GRPO variants with explicit KL regularization and reference resets, and squared-loss algorithms that implement them implicitly, including those used to train the Kimi models. These results clarify how regularization, clipping, and objective choice affect the sampling and optimization costs of post-training.

Graph Neural Networks (GNNs) have emerged as a powerful, differentiable class of learning models for graph-structured systems. Their ability to generalize across topologies opens the prospect of a surrogate for combined structural and parametric optimization, which classical metamodels cannot offer. Supply chains are a natural target, yet the use of GNN surrogates for supply chain problems is largely unexplored. This paper lays the foundation, presents initial steps, and discusses key research directions. As a foundation, we formulate the problem and create a large public training dataset of programmatically generated supply chain graphs with input parameters and steady-state performance metrics obtained using our SupplyNetPy simulation library. As initial steps, we explore GNN architectures that work well as surrogates for node- and network-level predictions, and analyze their accuracy-compute trade-off against simulation. Most importantly, we outline the exciting directions this opens, namely gradient-based optimization over topology, fast design-space exploration, and sensitivity analysis.

Over the last decade, building human-level artificial general intelligence has moved from far-fetched speculation to being a concrete next-decade target for many of the largest AI organizations. Achieving this goal would have profound and far-reaching impacts on human society, which raises many complex questions for the decade ahead. This report investigates how AI itself might continue to develop in a post-AGI world along the continuum of machine intelligence. The endpoint of this continuum, Universal AI, is theoretically well understood, which provides some formal grounding for the main focus of this report: the transition from human-level AGI to artificial general superintelligence, which can intuitively be understood as a system that is more intelligent and cognitively capable than large organizations of humans. After characterizing ASI, the report discusses four potential pathways from AGI to ASI: scaling AGI, AI paradigm shifts, ASI emerging from large-scale multi-agent collectives, and recursive improvement. The report then discusses possible frictions and bottlenecks along these pathways. Determining whether the impact of these frictions will be negligible or substantial raises a number of concrete open research questions. While large uncertainties for predicting ASI progress remain, it cannot be ruled out that AI progress might continue to accelerate over the next years. This would imply that the image of a single transformative step change, caused by the introduction of human-level AGI into our society, could be inaccurate. More apt might be the prospect of a series of transformative societal changes caused by AI-enabled progress and breakthroughs across many areas of science and technology. Preparing for this prospect requires a massively interdisciplinary endeavor of global scope and interest.

Operator learning for partial differential equations (PDEs) on arbitrary geometries builds fast neural surrogates for large-scale simulation. While recent geometry-adaptive neural operators have made substantial progress, they are mainly designed for forward problems in which inputs and outputs share the same spatial domain. This limits their applicability for boundary value problems (BVPs) and inverse problems, where inputs and outputs may live on different domains. We introduce the Geometry-Adaptive Integral Autoencoder (GAIA), an operator learning model that encodes the domain boundary and the interior field distribution into geometry tokens, and conditions integral transform layers on these tokens via cross-attention, allowing the kernel to adapt locally to geometric features. This yields an architecture capable of learning solution operators for forward and inverse problems on arbitrary domains, solving each in a single pass at inference without per-domain optimization, iterative refinement, or graph construction. We evaluate GAIA on seven 2D and 3D benchmarks, four of which are new or substantially extended benchmarks for inverse problems and BVP: electrical impedance tomography, optical tomography, 3D Darcy flow on varying geometries, and a modified setting of the Poisson BVP on mechanical components benchmark (MCB). GAIA sets new state-of-the-art results on every inverse and BVP task, reducing median relative $L^2$ error by 64% on airfoil flow reconstruction and 22% on EIT relative to the next best amortized method, and outperforming all baselines on every shape category of MCB. On other forward problems, GAIA is competitive with specialized solvers while maintaining stable accuracy across point resolutions on which transformer-based baselines degrade.

Neural Processes (NPs) are flexible meta-learning models capable of uncertainty quantification across diverse applications. However, the standard NP framework assumes access to noise-free inputs. This is unrealistic in many practical settings, where sensor noise or measurement errors are unavoidable. This discrepancy between model assumptions and real-world data can significantly degrade prediction quality and uncertainty estimates. We introduce Denoising Neural Processes (DnNPs), a principled extension of the NP framework that explicitly models input uncertainty. We train DnNPs via variational inference. DnNPs jointly learn to denoise corrupted inputs and perform meta-learning, making them robust to noisy training data. We demonstrate DnNPs' effectiveness on both synthetic and real-world datasets, showing consistent improvements in prediction and uncertainty quantification compared to standard NPs. On PM2.5 spatial interpolation from real-world air quality sensors, DnNP reduces RMSE by up to 30% and NLL by up to 73% relative to standard NPs. We also provide theoretical grounding: we show that the Bayes-optimal predictor under noisy inputs belongs to the DnNP model class, and that plug-in models with fixed observation variance incur an irreducible KL divergence gap that DnNP provably avoids.

Concept-based explanations in neural models are important for the development, certification, and adoption of autonomous systems. Yet, interpretability remains correlational. Without methods to guide and quantify causal relationships between explanations, a concept explanation can be provided without being necessary or sufficient for the observed output thereby appearing correct while misleading. We introduce Causal Concept Wrapper Network (CCW-Net), the first use of interventional mediation analysis from fields such as economics, medicine, and epidemiology as a training objective to align causal effects of concept-based explanations with a model's output. We further apply mediation analysis as an evaluation tool to quantify, per concept label combination, how much of any model's output is causally attributable to each concept explanation. As a training objective, CCW-Net shapes a model's concept representations such that they are both necessary and sufficient for the outputs they are credited with and independent of other concepts' contributions. Counterfactual concept representations anchor a set of causal alignment criteria: necessity, sufficiency, and independence. Necessity drives irrelevant concept effects toward zero, sufficiency ensures relevant concept representations fully reconstruct a model's output, and independence enforces the total effect decomposes linearly across concepts. We evaluate CCW-Net across aircraft control, driving, and image classification. CCW-Net provides a step toward concept-based explanations that are not merely interpretable, but quantifiably causal, supporting safer evaluation, certification, and deployment of transparent and trustworthy neural models.

South Asian monsoon precipitation depends on the thermodynamic structure of the lower troposphere, but how its ingredients combine to shape precipitation remains unclear, partly because this dependence is nonlocal in the vertical. We use symbolic distillation, which combines neural networks and symbolic regression, to discover interpretable precipitation equations from 21 years of June-August reanalysis data. Neural networks first learn the vertical thermodynamic structure most relevant to precipitation, condensing each variable into a single interpretable feature not tied to a particular vertical grid. Then, symbolic regression derives closed-form equations from these features and the surface state. Our best equation explains 1.5 times as much precipitation variance as a widely used buoyancy-based diagnostic and recovers about 85% of neural network skill while using about a thousand times fewer parameters. Unlike the buoyancy diagnostic, which adds moisture and instability, the equations treat them as competing controls, with the heaviest precipitation occurring when the lower free troposphere is humid. Over ocean, sensible heating is associated with additional precipitation mainly when near-surface air is warm and moist, improving predicted precipitation and its diurnal cycle. Although the learned features were optimized only for precipitation prediction, the equations largely respond to each feature as expected from convective physics, consistent with the reanalysis. These responses reduce the dependence of monsoon precipitation on the entire vertical column to a few simple, testable constraints that could guide data-driven precipitation models to make them more physically consistent.

Speculative decoding accelerates LLM inference by having a draft model propose multiple tokens for the target model to verify in one pass. The speedup is governed by the expected acceptance length (EAL), yet standard training objectives such as cross-entropy, KL divergence, and total variation focus only on distribution matching or single-step overlap. Recent studies instead propose block-level training objectives, aiming to optimize EAL directly. However, these objectives remain surrogates rather than exact formulations of EAL. For example, some average later acceptance over target-distributed continuations rather than the verification branches selected by accepted tokens, introducing a covariance gap that can reverse the gradient direction. We analyze this gap and derive REAL, a real EAL training loss that uses path weights for unbiased estimation and Rao-Blackwellization for variance reduction. In a controlled loss-level comparison with a Qwen3.6-35B-A3B target and a Domino drafter, REAL outperforms WTV, VSD, DBLast, and the static LK baseline on probabilistic serving acceptance length across 9 task subsets and 5 evaluation seeds. These gains require only a change to the training loss, with no modification to the drafter architecture or inference procedure, demonstrating the practicality of real EAL training. A reference implementation of the REAL loss is available at https://github.com/King-ty/speculators/tree/real-loss.

Low-rank adaptation (LoRA) is the de facto method for parameter-efficient fine-tuning of large neural networks, achieving strong task adaptation with minimal trainable parameters and low optimization cost. Beyond this efficiency, practitioners have observed two striking properties: \textit{robustness to catastrophic forgetting} and the ability to \textit{merge independently trained adapters} into a single model that performs competitively across multiple tasks. These properties are central to continual and multi-task learning, yet remain poorly understood. In this work, we provide a theoretical explanation through a unified \textit{margin-based perspective}. We analyze LoRA in multiclass linear classification under a near-orthogonal task regime with $\ell_2$-regularization, and characterize the optimal LoRA adapter across regularization regimes. Our analysis shows that, in an intermediate regime of regularization parameters, the optimal adapter aligns with the \emph{max-margin solution} on the fine-tuning data. Building on this characterization, we derive two key consequences. First, we obtain closed-form expressions for the margins on pre-training and fine-tuning data, revealing a precise margin trade-off: the regularization parameter controls the balance between retention and adaptation. Second, we analyze adapter merging, proving that merged models achieve positive margin on each task and deriving optimal mixing coefficients that balance margins across tasks and maximize the margin over their union. These results lead to a simple, training-free merging rule, which we term \textit{margin-based LoRA merging} (MaLoRA). Experiments on modern architectures and real datasets validate our theoretical predictions, showing that MaLoRA matches or outperforms several adapter-merging baselines across a range of vision and language classification tasks.

Extreme events in chaotic systems are difficult to learn from short trajectories because they are controlled by finite-time instabilities rather than by frequently observed bulk dynamics. We propose a mechanism-aware conditioning plug-in framework that turns a nudged ensemble of an imperfect model into a non-intrusive sensor of the local instability geometry. In the small-noise regime, the ensemble covariance has the same finite-time deformation kernels that govern local instability, providing a Jacobian-free proxy for local amplifications around a trajectory. A small Feature-Wise Linear Modulation (FiLM) network injects the ensemble geometry into an otherwise unchanged backbone without modifying the low-fidelity model simulator. We demonstrate this interface in two settings: a Transformer-style residual-attention corrector for a controlled low-dimensional chaotic system and a probabilistic recurrent STORN corrector for topographic two-layer quasi-geostrophic (QG) flow. In the low-dimensional benchmark, leading ensemble-covariance directions identify transient instabilities that are also detected by Optimally Time-Dependent (OTD) modes. FiLM conditioning improves 99th-percentile exceedance-frequency errors over an otherwise identical unconditioned Transformer. In QG, an ensemble-conditioned FiLM-STORN model substantially improves long-horizon rare-event statistics in the data-limited regime, including density-tail errors, exceedance frequencies, and spatial exceedance-area distributions relative to an unconditioned STORN trained on the same data. On averaged high-threshold exceedance diagnostics, it also outperforms the unconditioned baseline STORN trained with 20 times more expensive trajectory data. These results show that local instability geometry is not merely interpretable post hoc, but an actionable conditioning signal for data-efficient rare-event emulation.

Masked Diffusion Models (MDMs) are well known for fast text generation via parallel decoding. However, independent parallel sampling can commit to inconsistent predictions, and less is known about how to selectively revise these early token commitments. In this work, we introduce $\underline{\mathrm{P}}$lanned $\underline{\mathrm{U}}$nmasking-and-$\underline{\mathrm{R}}$evision Joint $\underline{\mathrm{L}}$earning (PURL) for MDMs, a training-based framework that seamlessly unifies parallel generation with selective token revision. We derive a normalized joint transition whose likelihood factorizes into edit selection, unmask selection, and token prediction. These components are trained jointly on partially masked sequences constructed according to the model's own unmasking policy. During inference, all three decisions are supported by a single shared forward pass, enabling the model to decode masked tokens and revise noisy tokens. Across logic puzzles, mathematical reasoning, and code generation, PURL improves accuracy at matched unmask budgets, with relative gains up to 47.4% accuracy improvement and up to an $8\times$ reduction in scheduled decoding rounds. Beyond these gains, our analysis further reveals general principles of revisable decoding: token edits become more effective as context accumulates; early edits can steer unfinished trajectories, whereas later edits tend to remain localized; and effective edits therefore depend on both calibrating when to intervene and learning where and how to revise. Together, these suggest that effective parallel generation depends not on revising more tokens, but on making the right commitments revisable at the right time.

Weight binarization has emerged as a promising strategy to reduce the complexity of large language models (LLMs). Existing approaches fall into post-training binarization, which is simple but causes severe performance loss, and training-aware methods, which depend on full-precision latent weights, adding complexity and limiting efficiency. We propose a novel framework that represents LLMs with multi-kernel Boolean parameters and, for the first time, enables direct finetuning LMMs in the Boolean domain, eliminating the need for latent weights. This enhances representational capacity and dramatically reduces complexity during both finetuning and inference. Extensive experiments across diverse LLMs show our method outperforms recent ultra low-bit quantization and binarization techniques.

Probabilistic linear solvers (PLSs) return probability distributions that quantify uncertainty due to limited computation in the solution of linear systems. The literature has traditionally distinguished between Bayesian PLSs, which condition a prior on information obtained from projections of the linear system, and probabilistic iterative methods (PIMs), which lift classical iterative solvers to probability space. In this work we show this dichotomy to be false: Bayesian PLSs are a special case of non-stationary affine PIMs. In addition, we prove that any realistic affine PIM is calibrated. These results motivate a focus on (non-stationary) affine PIMs, but their practical adoption has been limited by the significant manual effort required to implement them. To address this, we introduce affine tracing, an algorithmic framework that automatically constructs a PIM from a standard implementation of an affine iterative method by passing symbolic tracers through the computation to build an affine computational graph. We show how this graph can be transformed to compute posterior covariances, and how equality saturation can be used to perform algebraic simplifications required for computation under specific prior choices. We demonstrate the framework by automatically generating a probabilistic multigrid solver and evaluate its performance in the context of Gaussian process approximation.

Gradient-boosted decision trees are among the strongest off-the-shelf predictors for tabular regression, but point predictions alone do not quantify uncertainty. Conformal prediction provides distribution-free marginal coverage, yet standard split conformal uses a single global residual quantile and can adapt poorly to heteroscedasticity. We propose LoBoost, a model-native local conformal method that reuses the fitted ensemble's leaf structure to define a multiscale partition of the feature space. Each input is represented by the sequence of leaves it visits along the boosting path, and matching leaf prefixes define nested groups in which residual quantiles are estimated locally. By reusing the predictive structure already learned by the model, LoBoost requires no auxiliary partition or nuisance model, no retraining, and no additional data split beyond standard conformal calibration. Our theory connects the stability of the fitted ensemble and the geometry of its induced cells to local residual-score homogeneity, providing finite-sample coverage-error control and asymptotic pointwise validity as the local calibration size grows and the cells become sufficiently homogeneous. Experiments show a transparent quality-cost trade-off: LoBoost improves over global split conformal on several heterogeneous datasets, but it is not uniformly superior to the adaptive baselines and is not uniformly Pareto-optimal.

Data spaces like the European Health Data Space (EHDS) require the protection of sensitive data in studies during the data's processing and the study's release alike. In this work, we investigate how to implement this mandate using established trusted execution environments (TEEs) and timing side-channel hardening to protect the processing even under a compromised server, and the state-of-the-art differential privacy (DP) notion to protect the release of studies on tabular data. This combined setup could seem to complete the picture, but in fact raises unexpected security challenges that we mitigate by introducing MammothDP: a significant milestone towards a holistic machine learning system based on the recent gradient boosted decision tree learner S-BDT that is provably DP if used within a privacy filter, timing side-channel hardened, and deployed on a TEE. To achieve a strong privacy-utility tradeoff, we introduce two novel components: an early stopping criterion that adaptively selects the number of trees without any privacy overhead, and an improved rollback protection that is no longer vulnerable under timing side-channel attacks.

Concept vectors aim to enhance model interpretability by linking learned internal representations with human-understandable semantics, but their practical utility is often limited by noisy and inconsistent activations. In this work, we discover the SuperActivator Mechanism: a transformer dynamic that amplifies concept activation gaps, concentrating the most reliable concept evidence into a small set of highly activated tokens, which we call SuperActivators. We theoretically characterize this mechanism, proving that concept-aligned attention produces two competing effects: a tail amplification effect, where gaps among already-high activations grow disproportionately fast, and an equalization effect that eventually dominates as attention concentrates on extreme tokens. We validate the predicted tail amplification empirically, finding that in-concept activation distributions develop well-separated upper tails consistently across models, image and text modalities, and concept types. Moreover, we demonstrate the practical implications of SuperActivators for concept detection and localization. First, using only high-activation tokens as concept indicators improves detection by up to 14 F1 points over competing baselines. Second, restricting detection to the extreme activation tail is not merely sufficient but essential: including activations beyond the top 5-10% of the in-concept distribution introduces noise that degrades performance. Finally, using SuperActivators as instance-specific attribution targets yields more accurate and faithful concept localization heatmaps than using global concept vectors.

The escalating complexity of deep neural networks hinders the deployment of federated learning (FL) on resource-constrained devices, especially for multimedia applications such as on-device image classification and speech recognition. Parallel split learning (PSL) has emerged as a promising solution by offloading a substantial portion of the computational workload to the server through layer-wise model partitioning, making it particularly suitable for resource-limited visual and speech intelligence scenarios. However, the absence of client-side aggregation renders PSL sus ceptible to severe training divergence and potential convergence failure under heterogeneous data distributions. To address this challenge, we propose PSL-RGHA, a gradient-aligned PSL framework that employs reference gradient half-space alignment mechanism to mitigate training divergence among client devices. PSL-RGHA comprises two novel components: reference gradient progressive construction (RGPC) and gradient half-space alignment (GHA). Specifically, RGPC evaluates the directional consistency of client gradients and progressively synthesizes a robust reference gradient via Weiszfeld updates, effectively approximating the global descent direction. Then, GHA constrains client gradients within the reference half-space defined by RGPC to mitigate gradient conflicts and rectify local updates. Extensive experiments demonstrate that our PSL-RGHA framework outperforms existing baselines in various settings.

Adding abstention to a task-adapted multimodal model can discard correct answers, including capabilities acquired during adaptation. We formulate abstention repair as maximizing correct abstention on unanswerable questions under a budget on newly lost correct answers. We propose ReFrain (Regression-Free Abstention), which combines a linear probe on first-token logits, threshold calibration on held-out image clusters, and a deterministic veto that replaces rejected outputs with the displayed "none of the above" option while preserving all other responses. "Regression-free" denotes zero loss on the calibration set at the zero-budget target. All abstention methods in our main comparison start from the same answering-SFT checkpoint; we separately track lost correct answers, repaired errors, and retained SFT gains. On Qwen2.5-VL-3B, ReFrain at zero budget retains all 57 SFT-gained answers with no losses and improves correct abstention by 7.30 percentage points. At a 0.5% calibration budget, it reaches 74.05% correct abstention with 8 losses and retains 55 gains; CLIP-UP EmbLoRA reaches 64.65% with 62 losses, 41 repairs, and 40 retained gains. The same probe at its default threshold loses 298 correct answers. With models and thresholds frozen, confirmation on 228 independent question clusters yields 66.05% correct abstention and no losses at the 0.5% point, exceeding EmbLoRA by 32.72 percentage points. Ordinary refusal SFT achieves higher correct abstention at greater regression cost. Code and reproduction materials: https://github.com/ModeLiberaL/ReFrain.

System-1 Decision Models directly make structured probabilistic decisions over query-specified options given a state in a single forward pass, without autoregressively generating reasoning trajectories or textual responses. Recent evaluations cover diverse tasks but often rely on existing benchmarks, where prior exposure to test material can obscure generalization. Moreover, real-world decision making often involves long contexts, large option spaces, and complex logical dependencies, challenges that existing benchmarks do not adequately capture together. Thus, we introduce MMDM (Massive Multitask Decision Making), a benchmark of 5,448 high-quality questions across 16 task categories, combining newly constructed tasks with source-grounded recompositions and rewrites for single-select, multi-select, and soft-label decision making in fresh contexts. It covers realistic scenarios such as agent state tracking, tool and skill selection, preference judgments, and rubric scoring, with option spaces ranging from 2 to 1,024 and inputs extending to 64,817 tokens. With MMDM, we conduct a comprehensive quantitative evaluation of 28 decision models, showing that many perform well on common knowledge yet struggle with interdependent options, constrained decisions, and multi-select tasks. For example, Perplexity Decider-V1.2 reaches 78.75% Hard Single-select Accuracy on world knowledge, but only 53.95% on option logic and 47.95% on constraint planning, while the best Hard Multi-select Accuracy across all models is 36.81%. These results highlight joint reasoning, constraint-aware selection, and complete multi-select recovery as key priorities for decision model development, with MMDM providing a testbed for measuring this progress.

Many open mixture-of-experts (MoE) language models train with Muon instead of AdamW. Most balance the load with a bias on each expert's routing score, adjusted after every step. Their recipes disagree on whether Muon should also train the router. In models with 55M and 108M active parameters, we measure how the optimizer changes the span of these biases, the largest minus the smallest in a layer. The span grows when all tokens favor the same experts, so it shows how hard a layer is to balance. At learning rates tuned on shorter runs, Muon raised the span of the first MoE layer at every seed, roughly doubling it on average, while the other layers changed much less. The rise came from Muon on the rest of the network, whichever optimizer trained the router. In those runs, the inputs to the first router shared a direction, and soon after the warmup its busiest expert averaged four to seven times its fair share. Over the first 3,000 steps, subtracting the batch mean from these inputs removed this overload while barely changing the loss. On the smaller model, halving Muon's learning rate removed most of the rise and slightly improved the loss. Moving only the router to AdamW made the loads shift more during the warmup and slightly raised the loss, so at this scale the results favor keeping the router on Muon.

Objective: Epidemic outbreaks are often asynchronous across regions, yet collaborative forecasting is hampered by privacy laws and heterogeneous public health interventions. We developed and evaluated, as a proof of concept, a federated learning (FL) framework for cross-regional COVID-19 forecasting under asynchronous outbreaks among Guangdong, Macau, and Portugal, while maintaining data sovereignty. Methods: Using daily case data from WHO and China CDC for the three regions, whose outbreaks were asynchronous and interventions heterogeneous, we trained Long Short-Term Memory networks via FL for short-term forecasting, benchmarked against localized and centralized training using Root Mean Square Error, Mean Absolute Error, and Symmetric Mean Absolute Percentage Error. All experiments used the Flower FL framework with consistent hyperparameters across sites. Publicly available, aggregated case-count data were used so that the centralized benchmark could be computed as a reference. Results: The dataset comprised 1,233 daily observations (411 days) of new confirmed COVID-19 cases from November 24, 2021, to January 8, 2023. The earlier Omicron wave in Portugal supplied transmission dynamics that improved forecasts in the later-onset regions of Macau and Guangdong. The FL model achieved a normalized Root Mean Square Error of 0.028, an 88.3% improvement over the local model (0.240) and comparable to the centralized model, with network overhead mainly determined by model size and aggregation rounds. Conclusion: FL achieved short-term forecasting accuracy close to centralized training while maintaining data residency, with acceptable overhead. Leveraging asynchronous outbreaks across regions may offer a practical path to privacy-preserving collaborative forecasting, though prospective validation is required.