Michalis K. Titsias

Xiangming Gu, Soham De, Michalis Titsias et al.

In this work, we demonstrate that reliable stochastic sampling is a fundamental yet unfulfilled requirement for Large Language Models (LLMs) operating as agents. Agentic systems are frequently required to sample from distributions, often inferred from observed data, a process which needs to be emulated by the LLM. This leads to a distinct failure point: while standard RL agents rely on external sampling mechanisms, LLMs fail to map their internal probability estimates to their stochastic outputs. Through rigorous empirical analysis across multiple model families, model sizes, prompting styles, and distributions, we demonstrate the extent of this failure. Crucially, we show that while powerful frontier models can convert provided random seeds to target distributions, their ability to sample directly from specific distributions is fundamentally flawed.

Jiaxin Shi, Kehang Han, Zhe Wang et al.

Masked (or absorbing) diffusion is actively explored as an alternative to autoregressive models for generative modeling of discrete data. However, existing work in this area has been hindered by unnecessarily complex model formulations and unclear relationships between different perspectives, leading to suboptimal parameterization, training objectives, and ad hoc adjustments to counteract these issues. In this work, we aim to provide a simple and general framework that unlocks the full potential of masked diffusion models. We show that the continuous-time variational objective of masked diffusion models is a simple weighted integral of cross-entropy losses. Our framework also enables training generalized masked diffusion models with state-dependent masking schedules. When evaluated by perplexity, our models trained on OpenWebText surpass prior diffusion language models at GPT-2 scale and demonstrate superior performance on 4 out of 5 zero-shot language modeling tasks. Furthermore, our models vastly outperform previous discrete diffusion models on pixel-level image modeling, achieving 2.75 (CIFAR-10) and 3.40 (ImageNet 64x64) bits per dimension that are better than autoregressive models of similar sizes. Our code is available at https://github.com/google-deepmind/md4.

Tammo Rukat, Chris C. Holmes, Michalis K. Titsias et al.

Boolean matrix factorisation aims to decompose a binary data matrix into an approximate Boolean product of two low rank, binary matrices: one containing meaningful patterns, the other quantifying how the observations can be expressed as a combination of these patterns. We introduce the OrMachine, a probabilistic generative model for Boolean matrix factorisation and derive a Metropolised Gibbs sampler that facilitates efficient parallel posterior inference. On real world and simulated data, our method outperforms all currently existing approaches for Boolean matrix factorisation and completion. This is the first method to provide full posterior inference for Boolean Matrix factorisation which is relevant in applications, e.g. for controlling false positive rates in collaborative filtering and, crucially, improves the interpretability of the inferred patterns. The proposed algorithm scales to large datasets as we demonstrate by analysing single cell gene expression data in 1.3 million mouse brain cells across 11 thousand genes on commodity hardware.

Michalis K. Titsias, Omiros Papaspiliopoulos

We introduce a new family of MCMC samplers that combine auxiliary variables, Gibbs sampling and Taylor expansions of the target density. Our approach permits the marginalisation over the auxiliary variables yielding marginal samplers, or the augmentation of the auxiliary variables, yielding auxiliary samplers. The well-known Metropolis-adjusted Langevin algorithm (MALA) and preconditioned Crank-Nicolson Langevin (pCNL) algorithm are shown to be special cases. We prove that marginal samplers are superior in terms of asymptotic variance and demonstrate cases where they are slower in computing time compared to auxiliary samplers. In the context of latent Gaussian models we propose new auxiliary and marginal samplers whose implementation requires a single tuning parameter, which can be found automatically during the transient phase. Extensive experimentation shows that the increase in efficiency (measured as effective sample size per unit of computing time) relative to (optimised implementations of) pCNL, elliptical slice sampling and MALA ranges from 10-fold in binary classification problems to 25-fold in log-Gaussian Cox processes to 100-fold in Gaussian process regression, and it is on par with Riemann manifold Hamiltonian Monte Carlo in an example where the latter has the same complexity as the aforementioned algorithms. We explain this remarkable improvement in terms of the way alternative samplers try to approximate the eigenvalues of the target. We introduce a novel MCMC sampling scheme for hyperparameter learning that builds upon the auxiliary samplers. The MATLAB code for reproducing the experiments in the article is publicly available and a Supplement to this article contains additional experiments and implementation details.