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Diffusion Language Models (dLLMs) have garnered significant attention for their potential in highly parallel processing. The parallel capabilities of existing dLLMs stem from the assumption of conditional independence at high confidence levels, which ensures negligible discrepancy between the marginal and joint distributions. However, the stringent confidence thresholds required to preserve accuracy severely constrain the scalability of parallelism. Through systematic token-level statistical analysis, we reveal that a substantial proportion of tokens converge to their correct predictions early in the denoising process yet fail to reach standard confidence thresholds, confirming that current confidence-based criteria are overly conservative. In response, we introduce LEAP (Lookahead Early-Convergence Token Detection for Accelerated Parallel Decoding). LEAP is a training-free, plug-and-play method that leverages future context filtering and multi-sequence superposition to detect early-converging tokens. By validating the alignment between early convergence and correctness, we enable reliable early decoding of these tokens. Benchmarking across diverse domains demonstrates that LEAP si

Civilization maintains an elaborate infrastructure devoted to the maintenance of synchronized time. Governments mandate daylight saving time. Standards bodies insert leap seconds into Coordinated Universal Time. Engineers debate leap milliseconds and leap nanoseconds. The Global Positioning System applies relativistic corrections at the nanosecond level. All of these adjustments attempt to preserve an assumption: that a single global time exists and that clocks can be made to agree upon it. This paper argues that this assumption constitutes a category mistake in the sense of Ryle (1949). We show that special and general relativity prohibit absolute simultaneity, that the one-way speed of light is conventionally defined rather than measured, and that recent experiments on indefinite causal order demonstrate nature admits correlations with no well-defined temporal sequence. We trace the consequences of this category mistake through distributed computing, where it manifests as the Forward-In-Time-Only (FITO) assumption that underlies Lamport's logical clocks (1978), the impossibility results of Fischer-Lynch-Paterson (1985), and the CAP theorem (2000). From this perspective, daylight

Leap generators have been introduced in [Duchon et al.'04] for exact-size random generation of structures in a class of the form $\mathcal{C}=\mathrm{Seq}(\mathcal{B})$ (sequence construction), in the supercritical case. We extend these generators to supercritical composition schemes $\mathcal{C}=\mathcal{A}\circ\mathcal{B}$. Compared to the sequence construction, the obtained exact-size random generator for $\mathcal{C}$ still has linear time complexity (under conditions on the sampling complexity in $\mathcal{A}$ and $\mathcal{B}$), but perfect uniformity of the distribution is lost in general. However the distribution on $\mathcal{C}_n$, called leap distribution, is asymptotically uniform, the total variation distance from the uniform distribution being $(c+o(1))n^{-1/2}$ for an explicit constant $c$. These generators are simple to implement and can be applied to several classes of walks and trees, in particular Pólya trees. Leap generators can also be given for certain critical composition schemes, those relating planar map families, where this time the total variation distance to the uniform distribution is $\sim c\,n^{-1/3}$ for an explicit constant $c$.

We introduce Leap+Verify, a framework that applies speculative execution -- predicting future model weights and validating predictions before acceptance -- to accelerate neural network training. Inspired by speculative decoding in language model inference and by the Automatically Scalable Computation (ASC) architecture for program execution, Leap+Verify decomposes training into three dynamically detected regimes (chaotic, transition, stable) using activation-space cosine similarity as a real-time Lyapunov proxy signal. Within each regime, analytic weight predictors (momentum, linear, quadratic extrapolation) attempt to forecast model parameters K training steps ahead; predictions are accepted only when validated against a held-out loss criterion. We evaluate Leap+Verify on GPT-2 124M and Qwen 2.5-1.5B trained on WikiText-103 across five random seeds, sweeping prediction depth K in {5, 10, 25, 50, 75, 100}. Momentum-based prediction (Adam moment extrapolation) fails catastrophically at both scales, with predicted losses exceeding actuals by 100-10,000x -- a universal norm explosion in optimizer-state extrapolation. Finite-difference predictors (linear, quadratic) succeed where momen

Characterizing Europa's subsurface ocean is a key objective of the Europa Clipper and JUICE missions in the search for life beyond Earth. Although the ocean's induced magnetic field provides key constraints on habitability, interpretation is complicated by perturbations arising from Jupiter's plasma interaction with Europa. Physics-based models (e.g. magnetohydrodynamic, MHD) required to characterize these effects are physically comprehensive, but have a prohibitive computational cost. To address this, we introduce Learning Europa's Atmosphere and Plasma (LEAP), a transformer-based surrogate trained on outputs from a state-of-the-art multi-fluid MHD code to predict magnetic field perturbations along spacecraft trajectories. LEAP evaluates in milliseconds on a laptop, whereas MHD takes 12 hrs on a high-performance computer (~40,000x speed-up). The model has test set errors of -/+ 2.6 nT, and for the Galileo E4 and E14 flybys of Europa it matches the parent MHD model in accuracy. Its enhanced speed enables large-scale parameter surveys and probabilistic estimations of plasma conditions, establishing a new framework for accelerated plasma interaction modeling. LEAP can also inform fut

Large language models (LLMs) have achieved notable progress. Despite their success, next-token prediction (NTP), the dominant method for LLM training and inference, is constrained in both contextual coverage and inference efficiency due to its inherently sequential process. To overcome these challenges, we propose leap multi-token prediction~(L-MTP), an innovative token prediction method that extends the capabilities of multi-token prediction (MTP) by introducing a leap-based mechanism. Unlike conventional MTP, which generates multiple tokens at adjacent positions, L-MTP strategically skips over intermediate tokens, predicting non-sequential ones in a single forward pass. This structured leap not only enhances the model's ability to capture long-range dependencies but also enables a decoding strategy specially optimized for non-sequential leap token generation, effectively accelerating inference. We theoretically demonstrate the benefit of L-MTP in improving inference efficiency. Experiments across diverse benchmarks validate its merit in boosting both LLM performance and inference speed. The source code is available at https://github.com/Xiaohao-Liu/L-MTP.

Vision Foundation Models (VFMs) with Vision Transformer (ViT) backbones, such as DINOv2, have become essential for downstream tasks like object recognition and semantic segmentation. The immense computational requirements of backbones often necessitate distillation into smaller architectures for edge deployment. Feature-based knowledge distillation (KD) often suffers from the teacher-student gap; the student struggles to imitate teacher's complex feature map due to its limited capacity. To mitigate this bottleneck, we propose LEAP: Layer-skipping Efficiency via Adaptive Progression, a training curriculum for ViT feature-based knowledge distillation. By utilizing the teacher's intermediate feature maps as a sequence of progressively more difficult targets, our curriculum allows the student to build a foundational representation before tackling higher-level abstractions. Our results demonstrate that this paradigm significantly accelerates convergence through adaptive difficulty selection across various student model sizes and dataset scales. With our curriculum, the LEAP-distilled ViT-S achieves 90.1% accuracy on ImageNet-100, a +12.24% improvement compared with baseline. On ImageNet

Large language models (LLMs) have achieved remarkable progress on mathematical tasks through Chain-of-Thought (CoT) reasoning. However, existing mathematical CoT datasets often suffer from Thought Leaps due to experts omitting intermediate steps, which negatively impacts model learning and generalization. We propose the CoT Thought Leap Bridge Task, which aims to automatically detect leaps and generate missing intermediate reasoning steps to restore the completeness and coherence of CoT. To facilitate this, we constructed a specialized training dataset called ScaleQM+, based on the structured ScaleQuestMath dataset, and trained CoT-Bridge to bridge thought leaps. Through comprehensive experiments on mathematical reasoning benchmarks, we demonstrate that models fine-tuned on bridged datasets consistently outperform those trained on original datasets, with improvements of up to +5.87% on NuminaMath. Our approach effectively enhances distilled data (+3.02%) and provides better starting points for reinforcement learning (+3.1%), functioning as a plug-and-play module compatible with existing optimization techniques. Furthermore, CoT-Bridge demonstrate improved generalization to out-of-d

We propose the $S$-leaping algorithm for the acceleration of Gillespie's stochastic simulation algorithm that combines the advantages of the two main accelerated methods; the $τ$-leaping and $R$-leaping algorithms. These algorithms are known to be efficient under different conditions; the $τ$-leaping is efficient for non-stiff systems or systems with partial equilibrium, while the $R$-leaping performs better in stiff system thanks to an efficient sampling procedure. However, even a small change in a system's set up can critically affect the nature of the simulated system and thus reduce the efficiency of an accelerated algorithm. The proposed algorithm combines the efficient time step selection from the $τ$-leaping with the effective sampling procedure from the $R$-leaping algorithm. The $S$-leaping is shown to maintain its efficiency under different conditions and in the case of large and stiff systems or systems with fast dynamics, the $S$-leaping outperforms both methods. We demonstrate the performance and the accuracy of the $S$-leaping in comparison with the $τ$-leaping and $R$-leaping on a number of benchmark systems involving biological reaction networks.

Spatio-temporal point processes (STPPs) provide a principled framework for modeling asynchronous events in continuous time and space. Recent diffusion-based approaches offer a flexible alternative to deterministic prediction by modeling complex conditional distributions, but their application to STPPs remains challenging: reverse sampling from pure noise is costly, and weak structural constraints in sparse spatial domains can lead to poorly localized probability mass. We propose \textbf{GLIDE} (Graph-guided Leap Inference for Diffusion Estimation), a conditional diffusion framework for next-event modeling in STPPs. GLIDE organizes historical events into a multi-scale historical graph and encodes temporal evolution and spatial topology through a dual-stream architecture, yielding a structured conditioning context for a dual-branch diffusion denoiser. It further introduces a prior-guided leap inference mechanism, in which a lightweight mean predictor provides a deterministic anchor and the reverse process starts from an intermediate diffusion step instead of from pure Gaussian noise. Experiments on multiple real-world datasets show that GLIDE improves both distribution fitting and ne

Layer-aligned distillation and convergence-based early exit represent two predominant computational efficiency paradigms for transformer inference; yet we establish that they exhibit systematic incompatibility under standard deployment conditions for convergence-based early exit. Distillation objectives that align intermediate student layers to teacher representations suppress the representational convergence that early-exit mechanisms exploit, rendering such mechanisms ineffective on distilled models. We introduce LEAP (Layer-wise Exit-Aware Pretraining), an auxiliary training objective that reconciles this incompatibility. LEAP requires no architectural modifications; it augments standard distillation with a single constraint ensuring intermediate layers approximate final-layer representations. LEAP-MiniLM achieves 1.61$\times$ measured wall-clock speedup (batch=1, NVIDIA L4) at $θ$=0.95, with 91.9% of samples exiting by layer 7 and 1.80$\times$ theoretical layer reduction, where standard distilled models achieve zero effective speedup. We validate across sentence similarity (STS-B: 0.760 $\pm$ 0.006) and retrieval benchmarks (BEIR), providing operational guidance including laten

Unstructured sparsity is now natively accelerated by recent GPU kernels and dataflow hardware, shifting the bottleneck from inference execution to the pruning algorithm. State-of-the-art methods for unstructured LLM pruning are layer-wise surrogates derived from the Optimal Brain Surgeon principle, and they sacrifice end-to-end accuracy, especially under aggressive sparsity. End-to-end alternatives such as MaskLLM and PATCH show that learnable masks can close this gap, but their categorical-over-patterns parameterization scales with the number of valid masks per row and does not port to the unstructured setting. We introduce LEAP, which replaces this intractable parameterization with a per-weight Bernoulli-via-Gumbel-sigmoid relaxation that makes end-to-end unstructured mask learning tractable. Across five LLM families from 0.5B to 8B parameters at 50% and 60% sparsity, LEAP improves six-task average zero-shot accuracy by +2.59 points on average over ADMM, the best layer-wise baseline in our sweep.

Modern industrial recommender systems rely on thousands of heterogeneous features -- ranging from low-dimensional scalars (e.g., statistical value) to high-dimensional embeddings (e.g., user-id embeddings, MLP representations) -- to achieve high-precision predictions. Given the immense computational costs associated with training, efficient feature selection is critical. However, existing methods encounter three primary bottlenecks: (1) they typically assume uniform feature dimensions or require costly mapping to a fixed size; (2) they struggle with extreme sparsity, where the majority of features (e.g., 99%+) remain at default values; and (3) traditional permutation-based approaches are computationally prohibitive in large-scale settings. To address these challenges, we propose LeAP (Learnable Adaptive Permutation), a novel, model-agnostic plug-in module for feature selection. LeAP transforms the inefficient random permutation process into a learnable mechanism, significantly accelerating the evaluation of feature importance. In addition, we introduce an adaptive regularization strategy tailored for heterogeneous dimensions and extreme sparsity, enabling superior feature importanc

Hallucination in large language models (LLMs) remains a critical barrier to their safe deployment. For hallucination detection to be practical in real-world scenarios, the use of efficient small models is essential to ensure low latency and minimal resource consumption. However, existing methods rely on fixed verification strategies, where simply tuning small models to mimic fixed verification trajectories fails to capture the adaptability required for diverse hallucination patterns, thereby inducing planning instability. To address this limitation, we propose a ``Learning to Evaluate and Adaptively Plan'' (LEAP) framework, which shifts hallucination detection from fixed execution to dynamic strategy learning. Specifically, LEAP first employs a powerful teacher model to iteratively explore and refine verification strategies through a failure-driven loop. This dynamic planning capability is then distilled into an efficient student model, augmented by a novel proactive correction mechanism that enables the model to evaluate and optimize its verification strategy before execution. Experiments on three benchmarks demonstrate that LEAP outperforms state-of-the-art methods, offering an e

Interactive computational environments can help students explore algorithmic concepts through collaborative hands-on experimentation. However, static and instructor controlled demos in lectures limit engagement. Even when interactive visualizations are used, interactions are solely controlled by the instructor, leaving students as passive observers. In addition, the tools used for demonstration often vary significantly, as they are typically developed by individual instructors. Consequently, the visualizations remain confined to a single classroom, rather than being shared and adapted across courses or reused by other instructors. To address this gap and foster active engagement in live classrooms, we present a lightweight and seamless software framework named LEAP for developing interactive computational lab exercises using a simple idea: remotely callable instructor-defined functions. Using API endpoints and a provided client, students can discover and then call instructor defined functions remotely from their coding environment using scripts or interactive notebooks. Each function call is time-stamped and persistently logged in a database, allowing real-time visualization of par

Link prediction is a crucial task in many downstream applications of graph machine learning. To this end, Graph Neural Network (GNN) is a widely used technique for link prediction, mainly in transductive settings, where the goal is to predict missing links between existing nodes. However, many real-life applications require an inductive setting that accommodates for new nodes, coming into an existing graph. Thus, recently inductive link prediction has attracted considerable attention, and a multi-layer perceptron (MLP) is the popular choice of most studies to learn node representations. However, these approaches have limited expressivity and do not fully capture the graph's structural signal. Therefore, in this work we propose LEAP, an inductive link prediction method based on LEArnable toPology augmentation. Unlike previous methods, LEAP models the inductive bias from both the structure and node features, and hence is more expressive. To the best of our knowledge, this is the first attempt to provide structural contexts for new nodes via learnable augmentation in inductive settings. Extensive experiments on seven real-world homogeneous and heterogeneous graphs demonstrates that LE

Social scientists are increasingly interested in analyzing the semantic information (e.g., emotion) of unstructured data (e.g., Tweets), where the semantic information is not natively present. Performing this analysis in a cost-efficient manner requires using machine learning (ML) models to extract the semantic information and subsequently analyze the now structured data. However, this process remains challenging for domain experts. To demonstrate the challenges in social science analytics, we collect a dataset, QUIET-ML, of 120 real-world social science queries in natural language and their ground truth answers. Existing systems struggle with these queries since (1) they require selecting and applying ML models, and (2) more than a quarter of these queries are vague, making standard tools like natural language to SQL systems unsuited. To address these issues, we develop LEAP, an end-to-end library that answers social science queries in natural language with ML. LEAP filters vague queries to ensure that the answers are deterministic and selects from internally supported and user-defined ML functions to extend the unstructured data to structured tables with necessary annotations. LE

Visual odometry estimates the motion of a moving camera based on visual input. Existing methods, mostly focusing on two-view point tracking, often ignore the rich temporal context in the image sequence, thereby overlooking the global motion patterns and providing no assessment of the full trajectory reliability. These shortcomings hinder performance in scenarios with occlusion, dynamic objects, and low-texture areas. To address these challenges, we present the Long-term Effective Any Point Tracking (LEAP) module. LEAP innovatively combines visual, inter-track, and temporal cues with mindfully selected anchors for dynamic track estimation. Moreover, LEAP's temporal probabilistic formulation integrates distribution updates into a learnable iterative refinement module to reason about point-wise uncertainty. Based on these traits, we develop LEAP-VO, a robust visual odometry system adept at handling occlusions and dynamic scenes. Our mindful integration showcases a novel practice by employing long-term point tracking as the front-end. Extensive experiments demonstrate that the proposed pipeline significantly outperforms existing baselines across various visual odometry benchmarks.

Graph neural networks (GNNs) largely rely on the message-passing paradigm, where nodes iteratively aggregate information from their neighbors. Yet, standard message passing neural networks (MPNNs) face well-documented theoretical and practical limitations. Graph positional encoding (PE) has emerged as a promising direction to address these limitations. The Euler Characteristic Transform (ECT) is an efficiently computable geometric-topological invariant that characterizes shapes and graphs. In this work, we combine the differentiable approximation of the ECT (DECT) and its local variant ($\ell$-ECT) to propose LEAP, a new end-to-end trainable local structural PE for graphs. We evaluate our approach on multiple real-world datasets as well as on a synthetic task designed to test its ability to extract topological features. Our results underline the potential of LEAP-based encodings as a powerful component for graph representation learning pipelines.