Determinantal Point Process

Machine learning research in financial services is limited by the scarcity of representative open-source datasets. Existing resources are often narrowly focused on a single modality or task and fail to reflect the structured, multimodal, and dynamic nature inherent to many problems in financial services. In this paper, we introduce FINESSE, a Financial Event Sequence Simulation Environment, an agent-based simulation framework for generating synthetic, structured datasets composed of multiple interdependent event streams. Each stream corresponds to a distinct financial behavior such as transactions, payments, account status changes, and policy interventions, each with unique action spaces, schemas and variable types. These streams are coupled through agents' latent evolving states, enabling the simulation of temporally rich interactions. We also introduce FINESSE-Bench, a benchmark dataset generated by the simulator, supporting four representative tasks: balance forecasting, transaction fraud detection, missed payment prediction, and next event prediction. We report baseline results using methods from time series forecasting, event sequence modeling, temporal graphs, and temporal point processes. We release the FINESSE framework, including the simulator and dataset to accelerate research on structured, multimodal event sequence modeling challenges in financial services.

Practitioners enrich customer-return models with ever more signals (lifetime value, category, recency/frequency, calendar, geography), and the temporal-point-process (TPP) literature follows suit with covariate- and external-covariate-conditioned intensities. But does any of it improve the timing, and how would you know? A null ("feature X doesn't help") is only meaningful if the model could have found a signal. We make two contributions--a method and a measurement--to answer this credibly. (i) A screen-and-confirm protocol that certifies whether a candidate signal improves a TPP's event-timing likelihood: a positive control plants a coupling of known strength and confirms the model recovers it, so a real-data null can be read as "no signal" rather than "weak method." The control is validated for categorical and continuous encodings, and on a real clock-driven dataset (NYC taxi hour-of-day). (ii) A model-free ceiling quantifying how little of customer-return timing is point-predictable at all (a single-digit percentage of gap variance from any covariate; returns are near-memoryless). With these we certify a clean result on three public benchmarks (Amazon, Taobao, RetailRocket) and a real marketplace (Thumbtack): the inter-event clock--continuous-time decay, long known to beat frozen-intensity models--is nearly sufficient, and the conditioning the field keeps adding is redundant or harmful on top of it (statistically null on the public benchmarks, at most 0.06 NLL; null to mildly harmful on the marketplace). We do not claim to discover that decay helps; our contribution is the tools that turn "conditioning doesn't help" into a checkable, certified statement--plus an honest-evaluation account of the read-out/leakage pitfalls we hit and retracted.

Many of the series that generative time-series models are benchmarked on place a large probability mass on a single value --- it does not rain, no ride is requested, no part is ordered. We report what happens when such data is evaluated carefully. First, the standard rolling-origin protocol can score a model on a window whose atom structure bears no resemblance to the dataset: on one benchmark the dataset is $42\%$ zeros and the evaluation windows are $13\%$, on another $47\%$ against $5\%$. This is not a cosmetic problem --- it reversed one of our own conclusions, turning the strongest occurrence model in our study into what looked like a cautionary tale. Second, we give a control in which CRPS is invariant \emph{by construction} while the temporal coupling is destroyed, which measures exactly how much that coupling contributes to a chosen statistic. Third, benchmarking seven models on a matched protocol over five seeds, an autoregressive hurdle beats a conditional flow on five of six datasets, by up to a factor of $153$, while the flow's own occurrence statistics vary by up to $62\%$ across training seeds and every baseline is deterministic. Finally, the model ordering is not the same under five different occurrence statistics, and the two that do not share a construction agree with each other least.

Recent advances in Passive Acoustic Monitoring (PAM) offer an opportunity to obtain ecological spatial point-process data at unprecedented scale. However, realizing this opportunity necessitates the development of accurate and scalable localization methods. In real-world outdoor soundscapes, however, the assumptions underlying classical localization methods such as hyperbolic and score-based localization are routinely violated by multipath dominance, near-field effects, and complex propagation. Under these conditions, classical localization methods become brittle, with extreme errors possible even in small detection arrays. Rather than statistically replacing the underlying physics, we propose a method to refine it and increase robustness outside of ideal operating conditions: a learned model operating on physics-informed acoustic features corrects a fast hyperbolic solver where it produces implausible solutions, substantially reducing catastrophic worst-case errors while matching its median accuracy on field data. We further provide calibrated, geometry-aware uncertainty estimates suitable for propagation into downstream spatial models. Evaluating on distributed microphone arrays in real and simulated outdoor environments, we demonstrate that the proposed method yields robust, uncertainty-aware localization, providing a step toward scalable automated wildlife monitoring in complex acoustic environments.

Multimodal information can improve the accuracy of click-through rate (CTR) prediction and effectively alleviate item cold-start and long-tail problems. Recent studies commonly discretize pretrained multimodal embeddings into semantic identifiers (SIDs), allowing the model to learn task-specific semantic representations for recommendation. However, existing methods still provide limited gains due to two major limitations. First, codebook assignment fails to preserve semantic relevance and discards fine-grained continuous signals in the original embedding space. Second, the residual code paths are highly dependent on prefix codes, which limits the effective representational scalability of hierarchical identifiers. To address these issues, we propose PaletteID (PID), a prototype-based semantic identifier. Inspired by palette-based color composition, PID uses a compact set of representative prototype items as semantic anchors to bridge pretrained multimodal content space and recommendation models. Specifically, we first construct a prototype palette with Semantic Quality-Aware Determinantal Point Process (SQ-DPP), which jointly considers local content density and global semantic diversity. Then, for each target item, PID retrieves a sequence of semantically related prototypes and aggregates them into an informative PID representation, enabling rich and complementary semantic modeling. Extensive experiments on two public datasets demonstrate that PID consistently improves CTR prediction and yields larger gains for long-tail items. PID also produces more robust identifier assignments and provides more interpretable token semantics than existing residual SID methods.

We study generative modeling of spatial point processes (SPP), where both the number of points and their spatial configuration are governed by a joint distribution. While diffusion models have achieved strong performance in modeling complex distributions, extending them to variable-cardinality SPP remains challenging. Existing approaches either decouple the modeling of cardinality and spatial structure, or rely on discrete trans-dimensional operations to modify the number of points, resulting in inflexible and asymmetric generative dynamics. We propose the existence-field diffusion model (EFDM) for spatial point processes modeling, where each potential point is associated with an existence variable representing its degree of presence. This enables a unified diffusion process that jointly models both spatial locations and cardinality without requiring explicit discrete transitions. We demonstrate that our approach provides a flexible and general framework for generative modeling of spatial point processes, achieving improved modeling capability on datasets with varying cardinality.

We introduce the distributional determinantal point process (dDPP) as a novel repulsive point process whose atoms are probability distributions rather than points in a real space. The dDPP is constructed via an L-ensemble with a sliced Wasserstein (SW) kernel between distributions. We show its validity as a well-defined point process. In the discrete setting, we derive concentration results for plug-in estimators of the L-ensemble, the correlation kernel, and their determinants given i.i.d. samples from the distributional atoms. Leveraging this framework, we propose a distribution-valued random partition model by way of a repulsive generalized Bayesian mixture model. The model places a dDPP prior over the atoms of the mixing measure and defines a generalized likelihood based on SW distance. To summarize posterior inference, we develop a decision-theoretic approach to report a point estimate of the mixing measure as a Bayes rule under a hierarchical optimal transport utility function. The latter is a natural choice given that the mixing measure is itself a distribution over distributions. We use the proposed framework for inference with single-cell gene expression data and human epilepsy data, producing interpretable and well-separated clusters that reflect meaningful structure in the data.

Radar cross-section (RCS) modeling is foundational to advancing the utility and sensitivity of spaceborne radar systems. This study introduces a deep sigma-point process (DSPP) model for predicting RCS in synthetic aperture radar (SAR) imagery using a RADARSAT-2 dataset containing 208,191 verified ships. The DSPP model not only strives for predictive accuracy but also characterizes the uncertainty inherent in the intricate relationships among radar signals, ship parameters, and environmental conditions. Unlike traditional approaches that rely on deterministic equations with static parameters, the DSPP uses a hierarchical Gaussian process framework with Bayesian inference to capture variability and uncertainty in RCS predictions. By generating predictive distributions rather than single estimates, the model accounts for the complex dynamics governing radar returns. Using a Matern kernel with automatic relevance determination, the DSPP identifies and ranks critical features across radar, operational, and environmental domains, thereby supporting transparency and interpretability. Performance evaluations demonstrate the model's superiority over linear regression baselines, with a 20.83 percent reduction in root mean squared error, a 25.89 percent increase in R-squared, and a 44.4 percent reduction in both the residual interquartile range and median absolute deviation on the test data. By providing calibrated uncertainty bounds, the DSPP enhances prediction reliability and supports robust decision-making. This work represents a shift toward probabilistic models that incorporate the inherent uncertainty of complex phenomena. By transitioning from fixed equations to distributions over outcomes, the DSPP fosters a deeper understanding of RCS behavior and enables systems to operate effectively in dynamic environments.

Temporal point processes (TPPs) provide a general and flexible framework for modeling sequences of events in continuous time. Neural networks have been successfully employed to model TPPs in a highly expressive and data-driven way. Neural TPPs are typically trained via Maximum Likelihood Estimation (MLE) by minimizing the negative log-likelihood (NLL), which depends on both the conditional intensity function (CIF) and its integral over time, the compensator. Recent neural TPP approaches enable exact evaluation of the NLL without numerical integration. However, these methods typically model the compensator rather than the CIF directly, impose constraints on the neural network architecture, and are computationally expensive during training, as event contributions to the NLL are evaluated sequentially rather than in parallel. In this work, we propose a novel neural TPP model that directly parametrizes the CIF as a non-negative combination of B-spline basis functions, whose coefficients are predicted by a neural network. This formulation enables exact evaluation of the NLL, preserves full flexibility in the neural architecture, allows efficient parallelization during training, and naturally supports CIF smoothness regularization through the integrated squared second derivative. Experiments on both synthetic and real-world datasets show improved computational efficiency and predictive accuracy compared to the reference neural TPP baseline.

In this paper, we propose deep learning based NeuroMem-FHP framework for estimating the parameters of the fractional Hawkes process (FHP), a self-exciting point process that captures long-range dependence through a fractional Mittag-Leffler excitation kernel. Two neural architectures, namely a Long Short-Term Memory (LSTM) network and a Transformer, are developed to estimate the model parameters $(μ,γ,α,β)$ directly from sequences of inter-arrival times without requiring computationally intensive likelihood optimization. Experiments on synthetic data that both neural models significantly outperform the classical Maximum Likelihood Estimation (MLE) method, with the Transformer achieving the highest estimation accuracy (MSE = $0.1634$), followed by the LSTM (MSE = $0.1752$), compared to MLE (MSE = $2.8032$). An ablation study further examines the effects of key hyperparameters on model performance. The proposed framework is also on two real-world high-frequency datasets, namely AAPL NBBO transaction data and Montgomery County 911 emergency call records. Using a predictive validation approach, event sequences simulated from the estimated parameters closely reproduce the empirical distribution, tail behavior, and temporal dependence structure of the observed data. These results demonstrate that Transformer-based parameter estimation provides an accurate and efficient alternative to conventional estimation techniques for FHP and offers a promising framework for modeling event-driven systems with long-memory dynamics.

Rough path signatures are a universal feature map for continuous paths and, via the expected signature, characterise path distributions. These guarantees do not directly extend to cadlag paths of Temporal Point Processes (TPPs), limiting the use of signature methods for event sequences. Furthermore, neural TPP models, including recent generative approaches, optimise per-event objectives with no global sequence-level loss, while evaluation of variable-length event sequences lacks distributional discrepancy measures. This paper proposes a common pathwise framework for addressing these limitations. We introduce the interarrival embedding, a stable, injective lift from jump paths to continuous paths of bounded variation, extending signature methods to discrete event sequences. Our theoretical contributions give rise to sigTPP, the first signature-based generative model for TPPs, trained using a path-level loss on complete trajectories. We further analyse the space of counting paths and derive three distributional discrepancies, providing mathematically justified tools for evaluating generative TPP models. Across synthetic and real-world datasets, sigTPP achieves the best average rank based on eight complementary metrics, outperforms or is within a standard error of the strongest baseline in 64% of the dataset-metric pairs, and according to a relative score, improves against every baseline by at least 19% on average.

Determinantal point processes have recently emerged as a kernel-based alternative to standard independent sampling for constructing efficient minibatches, coresets, and other compact representations of large-scale datasets. In particular, sampling mechanisms based on DPPs are believed to demonstrate better approximation properties compared to classical i.i.d. samplers, even at the scale of the exponent. One of the key strengths of DPP based samplers is that they can be deployed over very general spaces, in contrast to more classical sampling methods beyond i.i.d. which tend to work in very well-structured settings, principally Euclidean spaces. In this work, we establish explicit rate guarantees for determinantal sampling in spaces that extend far beyond known Euclidean setups, focusing on spectral kernels obtained from eigenspaces of naturally associated Laplacian and other Markov diffusion operators. This includes, in particular, Riemannian manifolds and weighted networks. In determinantal sampling from compact Riemannian manifolds, we establish sampling rates that automatically pick up the intrinsic dimensionality $d_{\text{int}}$ of the underlying manifold. In the setting of networks, we investigate DPP-based samplers on the celebrated k-nearest neighbour graphs, as well as weighted random geometric graphs, and demonstrate a similar improved dependence on the intrinsic dimensionality of the data. Overall, our approach achieves guarantees of $\big(\text{sample size}\big)^{-\frac{1}{2}-\frac{1}{2d_{\text{int}}}}$ that match known rates on Euclidean spaces of comparable dimension. In terms of techniques, we connect to the celebrated Weyl's Law for manifold spectra, and leverage tools from the theory of Markov diffusions and Dirichlet forms as well as certain ingredients from the theory of pseudodifferential operators, which could be of independent interest in this area.

Eco-acoustic monitoring generates vast volumes of audio data, making active learning a promising approach for reducing annotation effort while efficiently training reliable biodiversity classifiers. This report presents CARE-DPP, a batch active-learning acquisition method submitted to BioDCASE Active Learning for Bioacoustics 2026 challenge. The method combines class-balanced predictive uncertainty with embedding-space novelty, while a determinantal point process (DPP) objective selects a high-quality and non-redundant acquisition batch. The uncertainty-novelty balance is annealed over the annotation budget: early cycles emphasize geometric coverage, whereas later cycles increasingly exploit classifier uncertainty. To mitigate unreliable early scores, the DPP candidate pool mixes top-quality candidates with a decreasing proportion of random exploration. An adaptive acquisition schedule uses smaller batches early and larger batches later. Evaluated over five repeats on the BirdSet HSN, POW and UHH subsets and on ATBFL, CARE-DPP obtains a mean development AULC of 0.50 for macro mAP, compared with 0.46 for the official CoreSet baseline. Ablations identify DPP batch diversification and the adaptive acquisition schedule as the largest contributors.

Temporal point processes (TPPs) have widespread applications across various domains. Compared to modeling the conditional intensity of a TPP, modeling its cumulative conditional intensity function (CCIF) improves computational efficiency and eliminates numerical approximation errors. However, current CCIF parameterizations uniformly rely on Monotone Neural Networks (MNNs), which we identify as suffering from three structural deadlocks--convexity restrictions, saturation limits, and violations of CCIF modeling requirements--that fundamentally restrict their representational capacity for complex temporal dynamics. To resolve these bottlenecks, this paper proposes a novel framework called Monotone Alternating Splines (MAS). By leveraging distinct interpolation and extrapolation components, MAS provides a flexible and efficient framework for modeling CCIFs. Theoretically, MAS's interpolation provides strong fitting accuracy, while its extrapolation supports robust generalization, reducing the irreducible approximation gaps of MNNs. Extensive experiments show that MAS achieves superior performance on both synthetic and real-world datasets.

Spatio-temporal point-process models must often generalise across space when local event histories are sparse. We study whether exogenous spatial context can compensate in such regimes. Using a fixed log-Gaussian Cox process backbone, we compare an event-only model with the same model augmented by AlphaEarth embeddings as linear spatial context. We evaluate spatial transfer on emergency medical services (EMS) forecasting across eight held-out regions, fixed forecast anchors, and a sweep over history length $w$, using only AlphaEarth (AE) embeddings available strictly before each anchor. AE improves out-of-region predictive performance across all history regimes, with the largest gains under scarce histories: approximately $2$--$6\times$ multiplicative improvements at $1-2$ weeks, tapering to roughly $10$--$20\%$ at $w=20$--$104$ weeks. These results show that contextual information can substantially stabilise spatially transferred point-process forecasts when event history is limited.

Spatiotemporal point processes (STPPs) model event data in continuous time and space, with applications in mobility, epidemiology, and public safety. Recent neural STPPs span expressive intensity models, conditional density models, continuous-time latent dynamics, normalizing-flow spatial decoders, and score-based generative mechanisms. Yet comparison remains fragile because implementations differ in preprocessing, coordinate normalization, splits, likelihood conventions, and evaluation protocols. We present SEAHORSE, a unified framework for reproducible STPP experimentation. SEAHORSE formalizes neural STPPs through a common encode-evolve-decode interface and trains, tunes, and evaluates every model family under a single executable benchmark protocol with raw-coordinate likelihood reporting. This enables fair comparisons but, more importantly, controlled diagnostic studies. We pair SEAHORSE with HawkesNest, a synthetic stress-test suite, and show that increasing event-pattern complexity exposes each family's inductive bias, degrading some models sharply and leaving others stable. Code: https://github.com/YahyaAalaila/seahorse.

Modeling and sampling from the underlying distribution of asynchronous event sequences are crucial in various real-world applications, including social networks, medical diagnosis, and financial transactions. Existing autoregressive methods suffer from error accumulation during multi-step generation, while non-autoregressive diffusion methods are typically limited to fixed-length output sequences. In this paper, we propose Latent Block-Diffusion Temporal Point Processes (LBDTPP), a novel semi-autoregressive TPP framework that introduces a latent block diffusion mechanism for high-quality and variable-length event sequence generation. The core idea is to define an autoregressive probability distribution over event blocks in latent space and perform Gaussian diffusion within each block. By sequentially generating blocks while simultaneously sampling events in each block, LBDTPP preserves the length flexibility of autoregressive TPPs and inherits the parallel high-quality generation capability of diffusion models. Theoretically, we derive Wasserstein error bounds showing that, under suitable local approximation and prefix-stability assumptions, block-wise generation can reduce error accumulation compared with event-wise autoregressive generation. Extensive experiments on six real-world benchmark datasets demonstrate that LBDTPP outperforms state-of-the-art TPP baselines in both unconditional and conditional generation tasks. Further empirical analyses verify the benefits of latent-space diffusion and block-wise generation, and reveal the trade-off between generation quality and block size. Our code is available at https://github.com/Zh-Shuai/LBDTPP.

Selecting a small, diverse, high-quality subset from a massive pool of candidates is a recurring primitive in modern machine learning -- data curation and coreset selection for training and fine-tuning large models, active-learning batch acquisition, prompt and exemplar selection for in-context learning, retrieval diversification, and experimental design. Determinantal Point Processes (\DPP s) give a principled, well-calibrated notion of diversity for this task, but their \emph{MAP} objective -- pick a size-$k$ subset $S$ maximizing $\logdet(L_S)$ -- is NP-hard, and the standard greedy and sampling algorithms scale superlinearly in the ground-set size $n$. This cost is prohibitive precisely in the data-centric regime where diversity matters most, where $n$ ranges over millions to billions of candidate examples, features, or embeddings. We recast \DPP-MAP as a continuous optimization problem over the Stiefel manifold, and show that its first-order optimality conditions form a \emph{Nonlinear Eigenvalue Problem with eigenvector dependency} (\NEPv) of a previously unstudied form. This \NEPv\ admits a self-consistent field (\SCF) iteration with a spectral-gap-based local contraction guarantee, giving a principled iterative solver where the diversity objective drives an eigenvector-dependent operator. The resulting algorithm, \OurMethod, requires only matrix-vector products with the kernel and runs in time $O\!\big((ndk+nk^2)\,t\big)$ for a small number of iterations $t$, scaling near-linearly in $n$ and integrating directly with low-rank and feature-map kernels common in ML. This paper focuses on the relaxation, solver, and scaling analysis; full real-data benchmarking is left to a planned empirical study.

Evaluation of spatiotemporal point process (STPP) models relies heavily on opaque real-world datasets, where latent generative structure is unknown and model failures are difficult to attribute. We introduce HawkesNest, a generator-aligned benchmark for controlled spatiotemporal pattern complexity built on a multivariate Hawkes backbone. HawkesNest defines four complexity axes: space--time entanglement, background heterogeneity, cross-type interaction, and domain topology. Each axis is associated with a deterministic index computed from the latent data-generating mechanism. By varying these axes while holding global rate, stability, and simulation budget fixed, HawkesNest enables diagnostic stress tests of STPP models under known structural difficulty. We verify that the indices are monotone and nearly orthogonal under controlled sweeps. We illustrate its use by showing that Hawkes-family baselines degrade under joint heterogeneity--entanglement complexity, even though they are structurally aligned with the Hawkes data-generating backbone. We further show that HawkesNest exposes neural-model sensitivity: AutoSTPP remains vulnerable under isolated increases in space--time entanglement. Code. Available at https://github.com/YahyaAalaila/HawkesNest

Continuous-time event data, in which entities emit instantaneous events over time, arises naturally across many domains such as neuroscience, seismology, and social networks. Non-negative matrix factorization (NMF) is a natural tool to uncover interpretable structure in such data, but it has so far only been applied after binning or smoothing the entity-level counting measures. This preprocessing step comes with the risk of erasing entity-level heterogeneities and fine-grained temporal features. In this paper, we introduce EventNMF, a continuous-time non-negative factorization model that operates directly on event times: each entity's events are modeled as a Poisson process whose intensity factorizes through a non-negative B-spline basis, and a simple estimation procedure recovers interpretable temporal templates shared across entities. The resulting method is mathematically principled, easy to implement, and computationally efficient. We further show that standard binned-count approaches arise as the special case of degree-zero splines, explore bias-variance tradeoffs and compare against existing methods on a synthetic latent factor model, and demonstrate the effectiveness of EventNMF on several real-world applications.

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 next-event prediction, with the largest gains appearing on the spatial side. The results also indicate that prior-guided leap inference substantially reduces reverse-sampling cost while preserving the stochastic generation capability of diffusion models.

We study the geometry of determinantal point processes (DPPs) through the spectral decomposition $L=UΛU^{\top}$. The spectrum $Λ$ governs the cardinality distribution via elementary symmetric polynomials, while the eigenspace orientation $U$ governs the conditional law within each fixed-cardinality stratum. Conditioning on cardinality $k$ yields the $k$-DPP, for which the identifiability structure changes fundamentally: the spectral parameter becomes identifiable only up to a common scale, and the eigenspace rotation parameter is identifiable only through squared minors of the eigenvector matrix. We characterize the identifiability gap precisely, via three explicit invariances (scale, sign similarity, and eigenspace rotation) and a dimension-counting theorem showing the existence of additional continuous non-identifiability whenever $\binom{N}{k}<N(N+1)/2$. In contrast, for the full DPP the non-identifiability comes only from the discrete sign similarity.

Survival analysis aims to estimate a time-to-event distribution from data with censored observations. Many existing methods either impose structural assumptions on the hazard function or discretize the time axis, which may limit flexibility and introduce approximation errors. We propose the Survival Diffusion Probabilistic Model (SDPM), a generative approach to continuous-time survival analysis. SDPM models the conditional distribution of the survival outcome, represented by the pair of observed time and censoring indicator, $\mathbb{P}(T,δ\mid \mathbf{x})$, using a denoising diffusion model. Under the assumption of conditionally independent censoring, conditional samples generated by the model can be transformed into survival function estimates using the Kaplan-Meier estimator. This formulation avoids parametric assumptions on the event-time distribution and does not require a discretization of the output time space. The model operates in a transformed target space, using standardized log-times and a continuous Gaussian-mixture representation of the censoring indicator. We evaluate SDPM on ten real survival datasets and compare it with five strong baselines, including tree-based, boosting-based, and neural survival models. Results show that SDPM achieves competitive predictive performance across C-index, integrated time-dependent AUC, and integrated Brier score. A study on synthetic Cox-Weibull data demonstrates that SDPM can recover the shape of an underlying continuous survival distribution more accurately than a strong nonparametric baseline when sufficiently many samples are generated. An ablation study confirms the importance of the proposed target-space transformations, which improve event-rate calibration, reduce invalid generated times, and provide consistent gains in predictive discrimination. Codes implementing the proposed model are publicly available.

Multi-class event streams arise in numerous real-world applications, where uncovering structured, interpretable inter-event relationships, together with accurate prediction, remains a central challenge. Existing neural point process models are highly expressive but encode event interactions in a black-box manner, preventing explicit discovery of structured dependencies. In this paper, we propose a structured neural marked point process (SNMPP) that achieves high modeling flexibility while enabling explicit event-wise and class-wise relationship discovery from data. Our model constructs a product-form neural influence kernel composed of a signed interaction network over event types and a delay-aware monotonic temporal network. This design enables explicit characterization of inter-class influence topology -- including excitation, inhibition, and neutrality -- while flexibly capturing diverse temporal decay patterns and potential influence delays. For efficient learning, we develop a stratified Monte Carlo estimator for stochastic training. Extensive experiments on synthetic and real-world benchmark datasets validate the ability of our approach to uncover structured relationships and deliver strong predictive performance.

Irregularly sampled multivariate event streams remain a difficult modality for generative modeling: tokenization-based approaches break down when inter-event intervals vary by orders of magnitude. We (i) propose \textbf{SurF}, a generative model that uses the Time Rescaling Theorem (TRT) as a learnable bijection between event sequences and i.i.d.\ unit-rate exponential noise, enabling a single model to be trained across heterogeneous event-stream datasets; (ii) three efficient parameterizations of the cumulative intensity that scale to long sequences; and (iii) a Transformer-based encoder for multi-dataset pretraining. On six real-world benchmarks, SurF achieves the best reported time RMSE on Earthquake, Retweet, and Taobao, and is within trial-level noise of the strongest specialist on the remaining three. Under a strict leave-one-out protocol, the held-out checkpoint beats every classical and neural-autoregressive baseline on $5/6$ datasets and beats every baseline on Amazon and Earthquake, an initial step toward foundation models over asynchronous event streams (Code is available at https://github.com/MrRezaeiUofT/SurF).

Determinantal point processes (DPPs) have emerged as a kernelized alternative to vanilla independent sampling for generating efficient minibatches, coresets and other parsimonious representations of large-scale datasets. While theoretical foundations and promising empirical performance have been demonstrated, there are two challenges for current proposals for DPP-based coresets or minibatches. The first is the need for families of DPPs with certain key variance reduction properties, usually constructed in a continuous setting, of which there are few known examples. The second is the need for an ad-hoc construction of a discrete DPP defined on a given dataset, that inherits such variance reduction. In this work, we contribute to the programme of establishing DPPs as a subsampling toolbox for ML by advancing on these two fronts. First, we propose new DPPs on the Euclidean space based on wavelets, with provably better accuracy guarantees than the best known rates. Second, we introduce a general method to convert such continuous DPPs, which are more amenable to proving analytical statements, into discrete kernels, which are pertinent for subsampling tasks such as minibatch and coreset constructions. This conversion mechanism simultaneously preserves the desired variance decay and reveals a low-rank decomposition of the discrete kernel, which makes sampling the corresponding DPP computationally inexpensive. En route, we enlarge the class of ML tasks amenable to improvements via DPP-based minibatches and coresets to include objective functions with arbitrarily low regularity, and rate guarantees that explicitly adapt to this regularity.

Video understanding in multimodal large language models requires selecting informative frames from long, redundant videos under limited visual-token budgets. Existing methods often rely on uniform sampling, point-wise relevance scoring, chunk-wise selection, or agentic exploration, which either miss global dependencies or introduce substantial overhead. We propose LDDR (Linear DPP-Based Dynamic Resolution), a training-free, plug-and-play, and budget-aware video frame sampling framework. LDDR performs query-aware Determinantal Point Process (DPP) frame selection in a task-conditioned feature space, achieving a 3x runtime speedup over standard DPP baselines. It further introduces a Group DPP importance metric to guide frame retention and dynamic resolution allocation, assigning more tokens to informative, non-redundant frames while downscaling or pruning less useful ones. Across four video benchmarks spanning short-, medium-, and long-range videos, LDDR consistently outperforms the next-best baselines, achieving gains of 2.5 points under budget-constrained settings and 1.6 points in high-budget scenarios. These improvements are consistently observed across multiple MLLM backbones, including both open- and closed-source models. Qualitative analysis confirms that relevant frames are selected and allocated a higher budget, facilitating improved video understanding.

Electronic design automation (EDA) addresses placement, routing, timing analysis, and power-integrity verification for integrated circuits. Learning methods -- attention (Transformer) and reinforcement learning (RL) -- have recently emerged on EDA tasks, yet face two common bottlenecks: vanilla attention's quadratic complexity limits scaling, and data-scarce models overfit statistical noise and amplify weak long-range correlations against the underlying physics. We observe that EDA tasks share a physical prior -- pairwise electrical and routing interactions decay exponentially along Manhattan distance -- and integrate it as a unified inductive bias into both architecture and training. We propose PhysEDA, comprising two components Physics-Structured Linear Attention (PSLA) folds the separable Manhattan decay into the linear-attention kernel as a multiplicative bias, reducing complexity from quadratic to linear; Potential-Based Reward Shaping (PBRS) constructs a physical potential from the same kernel, providing dense reward signal under sparse RL while preserving the optimal policy via the policy-invariance theorem. Across three EDA scenarios -- decoupling-capacitor placement, macro placement, and IR-drop prediction -- PhysEDA improves zero-shot cross-scale transfer by 56.8% and achieves 14x inference speedup with 98.5% memory savings on 100x100 grids; PBRS adds another 10.8% in sparse-reward DPP.

Dynamics of interacting systems in engineering, society, and nature often evolve over latent networks that govern which entities can interact. We study the problem of inferring these networks from event-based observations, which arise naturally in finance, seismology, and neuroscience. While there is substantial algorithmic work addressing this important problem, theoretical results are scarce. In this paper we ask the following fundamental question: what is the minimum time that one must observe the dynamics in order to exactly recover the underlying network, as a function of the number $d$ of interacting entities? For a class of stationary Hawkes processes with sparse, weak interactions, we prove that an observation time of order $\log d$ is sufficient and necessary. For the upper bound we construct a two-stage estimator that uses clipped and binned event data for screening, followed by a least-squares refinement, and apply concentration bounds derived from the Poisson cluster representation. For the lower bound we combine Fano's inequality with Jacod's Girsanov formula for point processes on a suitable subclass of networks.

Events in spatiotemporal systems are ubiquitous, yet modeling their complex distributions remains challenging. Existing point process models often rely on strong structural assumptions and are typically limited to autoregressive, event-by-event prediction. As a result, they struggle to support broader inference tasks such as inverse inference, trajectory reconstruction, and recovery of missing event locations. We introduce Arbitrarily Conditioned Hierarchical Flows (ARCH), a hierarchical flow matching framework for spatiotemporal event modeling. ARCH is expressive enough to capture complex event distributions while enabling tractable and accurate computation of conditional intensities, which quantify instantaneous event risk. Built on a history-encoder-generative-decoder architecture, ARCH introduces a hybrid masking strategy for flexible conditioning on arbitrary observed events. This enables a unified treatment of forecasting, inverse inference, and partial trajectory recovery within a single framework. Experiments on synthetic and real-world datasets show that ARCH consistently outperforms existing baselines across both prediction and conditional inference tasks.

Automated Market Makers (AMMs), as a core infrastructure of decentralized finance (DeFi), uniquely drive on-chain asset pricing through a deterministic reserve ratio mechanism. Unlike traditional markets, AMM price dynamics is triggered largely by on-chain events (e.g., swap) that change the reserve ratio, rather than by continuous responses to off-chain information. This makes event-level analysis crucial for understanding price formation mechanisms in AMMs. However, existing research generally neglects the micro-structural dynamics at the AMMs level, lacking both a comprehensive dataset covering multiple protocols with fine-grained event classification and an effective framework for event-aware modeling. To fill this gap, we construct a dataset containing 8.9 million on-chain event records from four representative AMMs protocols: Pendle, Uniswap v3, Aave and Morpho, with precise annotations of transaction type and block height timestamps. Furthermore, we propose an Uncertainty Weighted Mean Squared Error (UWM) loss function, which incorporates the block interval regression term into the traditional Time-Point Process (TPP) objective function by weighting the uncertainty with homoscedasticity. Extensive experiments on eight advanced TPP architectures demonstrate that this loss function reduces the time prediction error by an average of 56.41% while maintaining the accuracy of event type prediction, establishing a robust benchmark for event-aware prediction in the AMMs ecosystem. This work provides the necessary data foundation and methodological framework for modeling the discreteness and event-driven characteristics of on-chain price discovery. All datasets and source code are publicly available. https://github.com/yosen-king/Deep-AMM-Events

The standard Monte Carlo estimator $\widehat{I}_N^{\mathrm{MC}}$ of $\int fdω$ relies on independent samples from $ω$ and has variance of order $1/N$. Replacing the samples with a determinantal point process (DPP), a repulsive distribution, makes the estimator consistent, with variance rates that depend on how the DPP is adapted to $f$ and $ω$. We examine two existing DPP-based estimators: one by Bardenet & Hardy (2020) with a rate of $\mathcal{O}(N^{-(1+1/d)})$ for smooth $f$, but relying on a fixed DPP. The other, by Ermakov & Zolotukhin (1960), is unbiased with rate of order $1/N$, like Monte Carlo, but its DPP is tailored to $f$. We revisit these estimators, generalize them to continuous settings, and provide sampling algorithms.

Across many scientific fields, measurements often represent the number of times an event occurs. For example, a document can be represented by word occurrence counts, neural activity by spike counts per time window, or online communication by daily email counts. These measurements yield high-dimensional count data that often approximate a Poisson distribution, frequently with low rates that produce substantial sparsity and complicate downstream analysis. A useful approach is to embed the data into a low-dimensional space that preserves meaningful structure, commonly termed dimensionality reduction. Yet existing dimensionality reduction methods, including both linear (e.g., PCA) and nonlinear approaches (e.g., t-SNE), often assume continuous Euclidean geometry, thereby misaligning with the discrete, sparse nature of low-rate count data. Here, we propose p-SNE (Poisson Stochastic Neighbor Embedding), a nonlinear neighbor embedding method designed around the Poisson structure of count data, using KL divergence between Poisson distributions to measure pairwise dissimilarity and Hellinger distance to optimize the embedding. We test p-SNE on synthetic Poisson data and demonstrate its ability to recover meaningful structure in real-world count datasets, including weekday patterns in email communication, research area clusters in OpenReview papers, and temporal drift and stimulus gradients in neural spike recordings.

Experience replay is widely used to improve learning efficiency in reinforcement learning by leveraging past experiences. However, existing experience replay methods, whether based on uniform or prioritized sampling, often suffer from low efficiency, particularly in real-world scenarios with high-dimensional state spaces. To address this limitation, we propose a novel approach, Efficient Diversity-based Experience Replay (EDER). EDER employs a determinantal point process to model the diversity between samples and prioritizes replay based on the diversity between samples. To further enhance learning efficiency, we incorporate Cholesky decomposition for handling large state spaces in realistic environments. Additionally, rejection sampling is applied to select samples with higher diversity, thereby improving overall learning efficacy. Extensive experiments are conducted on robotic manipulation tasks in MuJoCo, Atari games, and realistic indoor environments in Habitat. The results demonstrate that our approach not only significantly improves learning efficiency but also achieves superior performance in high-dimensional, realistic environments.