115 research outputs found
From random walks to distances on unweighted graphs
Large unweighted directed graphs are commonly used to capture relations
between entities. A fundamental problem in the analysis of such networks is to
properly define the similarity or dissimilarity between any two vertices.
Despite the significance of this problem, statistical characterization of the
proposed metrics has been limited. We introduce and develop a class of
techniques for analyzing random walks on graphs using stochastic calculus.
Using these techniques we generalize results on the degeneracy of hitting times
and analyze a metric based on the Laplace transformed hitting time (LTHT). The
metric serves as a natural, provably well-behaved alternative to the expected
hitting time. We establish a general correspondence between hitting times of
the Brownian motion and analogous hitting times on the graph. We show that the
LTHT is consistent with respect to the underlying metric of a geometric graph,
preserves clustering tendency, and remains robust against random addition of
non-geometric edges. Tests on simulated and real-world data show that the LTHT
matches theoretical predictions and outperforms alternatives.Comment: To appear in NIPS 201
Likelihood-Based Diffusion Language Models
Despite a growing interest in diffusion-based language models, existing work
has not shown that these models can attain nontrivial likelihoods on standard
language modeling benchmarks. In this work, we take the first steps towards
closing the likelihood gap between autoregressive and diffusion-based language
models, with the goal of building and releasing a diffusion model which
outperforms a small but widely-known autoregressive model. We pursue this goal
through algorithmic improvements, scaling laws, and increased compute. On the
algorithmic front, we introduce several methodological improvements for the
maximum-likelihood training of diffusion language models. We then study scaling
laws for our diffusion models and find compute-optimal training regimes which
differ substantially from autoregressive models. Using our methods and scaling
analysis, we train and release Plaid 1B, a large diffusion language model which
outperforms GPT-2 124M in likelihood on benchmark datasets and generates fluent
samples in unconditional and zero-shot control settings
- …