Eq. (6) suggests that the SDE drift corresponding to the score may be broken down into 3 steps: 1. However, in practice this modification creates a "discontinuity" between the constrained and unconstrained components, leading to erroneous correlations between them in the generated samples. "learning rate" that is determined empirically such that the loss value reduces adequately close to zero Thus it needs to be tuned empirically. The correction in Eq. (16) is equivalent to imposing a Gaussian likelihood on Remark 2. The post-processing presented in this section is similar to [ In this section, we present the most relevant components for completeness and better reproducibility. B.2 Sampling The reverse SDE in Eq. (5) used for sampling may be rewritten in terms of denoiser D As stated in 4.1 of the main text, for this The energy-based metrics are already defined in Eq. (12) and Eq.

However, it has several unique challenges.

The first three authors contributed equally.

Bayesian networks are among the most prominent graphical models for probability distributions.

Imagine a smart camera trap selectively clicking pictures to understand animal movement patterns within a particular habitat. These snapshots, or pieces of data captured from a data stream at adaptively chosen times, provide a glimpse of different animal movements unfolding through time. Learning a continuous-time process through snapshots, such as smart camera traps, is a central theme governing a wide array of online learning situations. In this paper, we adopt a learning-theoretic perspective in understanding the fundamental nature of learning different classes of functions from both discrete data streams and continuous data streams. In our first framework, the setting, a learning algorithm discretely queries from a process to update a predictor designed to make predictions given as input the data stream.

Trajectory inference aims at recovering the dynamics of a population from snapshots of its temporal marginals. To solve this task, a min-entropy estimator relative to the Wiener measure in path space was introduced in [Lavenant et al., 2021], and shown to consistently recover the dynamics of a large class of drift-diffusion processes from the solution of an infinite dimensional convex optimization problem. In this paper, we introduce a grid-free algorithm to compute this estimator. Our method consists in a family of point clouds (one per snapshot) coupled via Schrödinger bridges which evolve with noisy gradient descent. We study the mean-field limit of the dynamics and prove its global convergence to the desired estimator. Overall, this leads to an inference method with end-to-end theoretical guarantees that solves an interpretable model for trajectory inference. We also present how to adapt the method to deal with mass variations, a useful extension when dealing with single cell RNA-sequencing data where cells can branch and die.

In our continuously evolving world, entities change over time and new, previously non-existing or unknown, entities appear. We study how this evolutionary scenario impacts the performance on a well established entity linking (EL) task. For that study, we introduce TempEL, an entity linking dataset that consists of time-stratified English Wikipedia snapshots from 2013 to 2022, from which we collect both anchor mentions of entities, and these target entities' descriptions. By capturing such temporal aspects, our newly introduced TempEL resource contrasts with currently existing entity linking datasets, which are composed of fixed mentions linked to a single static version of a target Knowledge Base (e.g., Wikipedia 2010 for CoNLL-AIDA). Indeed, for each of our collected temporal snapshots, TempEL contains links to entities that are continual, i.e., occur in all of the years, as well as completely new entities that appear for the first time at some point. Thus, we enable to quantify the performance of current state-of-the-art EL models for: (i) entities that are subject to changes over time in their Knowledge Base descriptions as well as their mentions' contexts, and (ii) newly created entities that were previously non-existing (e.g., at the time the EL model was trained). Our experimental results show that in terms of temporal performance degradation, (i) continual entities suffer a decrease of up to 3.1% EL accuracy, while (ii) for new entities this accuracy drop is up to 17.9%. This highlights the challenge of the introduced TempEL dataset and opens new research prospects in the area of time-evolving entity disambiguation.

Abstract--Global Navigation Satellite Systems (GNSS) face growing disruption from intentional jamming, undermining availability exactly when reliable positioning and timing are essential. We tackle this challenge by recasting jamming mitigation as a dynamic graph regression problem and propose a Jamming Guardian (JaGuard), a new receiver-centric deep temporal graph network-based method that estimates, and thereby corrects, the receiver's latitude and longitude errors. At each 1 Hz epoch, we model the satellite-receiver scene as a heterogeneous star graph with the receiver as the center node and the tracked satellites as leaves. These satellites have time-varying attributes such as SNR, azimuth, elevation, and latitude/longitude. A single-layer Heterogeneous Graph ConvLSTM (HeteroGCLSTM) fuses one-hop spatial context with short-term temporal dynamics to produce a 2D deviation vector for error mitigation. We evaluate our approach on datasets collected from physical hardware (two different commercial receivers), subjected to controlled conducted RF interference. Interference is introduced with three jammer types: Continuous Wave CW, multi-tone 3 CW, and wideband FM. Each jammer type was exercised at six power levels from 45 to 70 dBm, with 50 repetitions per scenario, including pre-jam, jam, and recovery phases. Compared to strong multivariate time series baselines (TSMixer MLP, uniform CNN, and Seq2Point CNN), our model consistently yields the lowest Mean Absolute Error (MAE) in positional deviation. Under severe jamming at 45 dBm, it achieves an MAE of 3.64-7.74 On mixed-mode datasets that pool all power levels, the MAE is 3.78 cm for GP01 and 4.25 cm for U-blox 10, surpassing Seq2Point, TSMixer, and uniform CNN. A data-efficiency split further shows that with only 10% of the training data, our approach remains clearly ahead, achieving an MAE of about 20 cm versus 36-42 cm for the baselines. Global Navigation Satellite Systems (GNSS) underpin nearly every critical infrastructure, from telecommunications [1] and aviation safety [2], power-grid synchronization [3], emerging drone ecosystems where location privacy and integrity are paramount [4], to autonomous driving [5].

This paper introduces KANFormer, a novel deep-learning-based model for predicting the time-to-fill of limit orders by leveraging both market- and agent-level information. KANFormer combines a Dilated Causal Convolutional network with a Transformer encoder, enhanced by Kolmogorov-Arnold Networks (KANs), which improve nonlinear approximation. Unlike existing models that rely solely on a series of snapshots of the limit order book, KANFormer integrates the actions of agents related to LOB dynamics and the position of the order in the queue to more effectively capture patterns related to execution likelihood. We evaluate the model using CAC 40 index futures data with labeled orders. The results show that KANFormer outperforms existing works in both calibration (Right-Censored Log-Likelihood, Integrated Brier Score) and discrimination (C-index, time-dependent AUC). We further analyze feature importance over time using SHAP (SHapley Additive exPlanations). Our results highlight the benefits of combining rich market signals with expressive neural architectures to achieve accurate and interpretabl predictions of fill probabilities.