Neural Information Processing Systems http://nips.cc/

First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. In reply to the author's feedback Our description of uniformization might be misleading, because the problems we describe do not occur in all of its applications. For the SGCP model discussed in our paper, however, the uniformization really is over the rate, which is lambda in our model. There is no MJP in the SGCP model, because the rate is continuous. After rereading the relevant sections of the paper, I am sure that this is incorrect.

We study masked discrete diffusion -- a flexible paradigm for text generation in which tokens are progressively corrupted by special mask symbols before being denoised. Although this approach has demonstrated strong empirical performance, its theoretical complexity in high-dimensional settings remains insufficiently understood. Existing analyses largely focus on uniform discrete diffusion, and more recent attempts addressing masked diffusion either (1) overlook widely used Euler samplers, (2) impose restrictive bounded-score assumptions, or (3) fail to showcase the advantages of masked discrete diffusion over its uniform counterpart. To address this gap, we show that Euler samplers can achieve $ε$-accuracy in total variation (TV) with $\tilde{O}(d^{2}ε^{-3/2})$ discrete score evaluations, thereby providing the first rigorous analysis of typical Euler sampler in masked discrete diffusion. We then propose a Mask-Aware Truncated Uniformization (MATU) approach that both removes bounded-score assumptions and preserves unbiased discrete score approximation. By exploiting the property that each token can be unmasked at most once, MATU attains a nearly $ε$-free complexity of $O(d\,\ln d\cdot (1-ε^2))$. This result surpasses existing uniformization methods under uniform discrete diffusion, eliminating the $\ln(1/ε)$ factor and substantially speeding up convergence. Our findings not only provide a rigorous theoretical foundation for masked discrete diffusion, showcasing its practical advantages over uniform diffusion for text generation, but also pave the way for future efforts to analyze diffusion-based language models developed under masking paradigm.

The authors present a variational inference algorithm for continuous time Markov jump processes. Following previous work, they use "uniformization" to produce a discrete time skeleton at which they infer the latent states. Unlike previous work, however, the authors propose to learn this skeleton (a point estimate, via random search) and to integrate out, or collapse, the transition matrix during latent state inference. They compare their algorithm to existing MCMC schemes, which also use uniformization, but which do not collapse out the transition matrix. While this work is well motivated, I found it difficult to tease out which elements of the inference algorithm led to the observed improvement.

Markov jump processes are continuous-time stochastic processes widely used in statistical applications in the natural sciences, and more recently in machine learning. Inference for these models typically proceeds via Markov chain Monte Carlo, and can suffer from various computational challenges. In this work, we propose a novel collapsed variational inference algorithm to address this issue. Our work leverages ideas from discrete-time Markov chains, and exploits a connection between these two through an idea called uniformization.

Renewal processes are generalizations of the Poisson process on the real line whose intervals are drawn i.i.d.

We propose a simple and novel framework for MCMC inference in continuoustime discrete-state systems with pure jump trajectories. We construct an exact MCMC sampler for such systems by alternately sampling a random discretization of time given a trajectory of the system, and then a new trajectory given the discretization. The first step can be performed efficiently using properties of the Poisson process, while the second step can avail of discrete-time MCMC techniques based on the forward-backward algorithm. We show the advantage of our approach compared to particle MCMC and a uniformization-based sampler.

The multi-modal entity alignment (MMEA) aims to find all equivalent entity pairs between multi-modal knowledge graphs (MMKGs). Rich attributes and neighboring entities are valuable for the alignment task, but existing works ignore contextual gap problems that the aligned entities have different numbers of attributes on specific modality when learning entity representations. In this paper, we propose a novel attribute-consistent knowledge graph representation learning framework for MMEA (ACK-MMEA) to compensate the contextual gaps through incorporating consistent alignment knowledge. Attribute-consistent KGs (ACKGs) are first constructed via multi-modal attribute uniformization with merge and generate operators so that each entity has one and only one uniform feature in each modality. The ACKGs are then fed into a relation-aware graph neural network with random dropouts, to obtain aggregated relation representations and robust entity representations. In order to evaluate the ACK-MMEA facilitated for entity alignment, we specially design a joint alignment loss for both entity and attribute evaluation. Extensive experiments conducted on two benchmark datasets show that our approach achieves excellent performance compared to its competitors.

Motivation: We consider continuous-time Markov chains that describe the stochastic evolution of a dynamical system by a transition-rate matrix $Q$ which depends on a parameter $\theta$. Computing the probability distribution over states at time $t$ requires the matrix exponential $\exp(tQ)$, and inferring $\theta$ from data requires its derivative $\partial\exp\!(tQ)/\partial\theta$. Both are challenging to compute when the state space and hence the size of $Q$ is huge. This can happen when the state space consists of all combinations of the values of several interacting discrete variables. Often it is even impossible to store $Q$. However, when $Q$ can be written as a sum of tensor products, computing $\exp(tQ)$ becomes feasible by the uniformization method, which does not require explicit storage of $Q$. Results: Here we provide an analogous algorithm for computing $\partial\exp\!(tQ)/\partial\theta$, the differentiated uniformization method. We demonstrate our algorithm for the stochastic SIR model of epidemic spread, for which we show that $Q$ can be written as a sum of tensor products. We estimate monthly infection and recovery rates during the first wave of the COVID-19 pandemic in Austria and quantify their uncertainty in a full Bayesian analysis. Availability: Implementation and data are available at https://github.com/spang-lab/TenSIR.

Markov jump processes are continuous-time stochastic processes widely used in statistical applications in the natural sciences, and more recently in machine learning. Inference for these models typically proceeds via Markov chain Monte Carlo, and can suffer from various computational challenges. In this work, we propose a novel collapsed variational inference algorithm to address this issue. Our work leverages ideas from discrete-time Markov chains, and exploits a connection between these two through an idea called uniformization. Our algorithm proceeds by marginalizing out the parameters of the Markov jump process, and then approximating the distribution over the trajectory with a factored distribution over segments of a piecewise-constant function. Unlike MCMC schemes that marginalize out transition times of a piecewise-constant process, our scheme optimizes the discretization of time, resulting in significant computational savings. We apply our ideas to synthetic data as well as a dataset of check-in recordings, where we demonstrate superior performance over state-of-the-art MCMC methods.