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Researcher profile

Anji Liu

Anji Liu contributes to research discovery and scholarly infrastructure.

ResearcherAffiliation not importedOpen to collaborate
Machine LearningArtificial IntelligenceData Structures and AlgorithmsInformation Theorymath.IT

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Published work

5 published item(s)

preprint2026arXiv

The Expressivity Boundary of Probabilistic Circuits: A Comparison with Large Language Models

Probabilistic Circuits (PCs) are deep generative models that support exact and efficient probabilistic inference. Yet in autoregressive language modeling, PCs still lag behind Transformer-based large language models (LLMs), suggesting an important expressivity gap. In this work, we compare PCs and LLMs under a unified autoregressive formulation. First, an output bottleneck: PCs parameterize predictions as convex combinations in probability space, which struggles to represent the sharp distributions typical of language; adopting a logit-space parameterization substantially narrows this gap. Second, a context-encoding bottleneck: we prove that structured-decomposable PCs can match Transformer separation rank on vtree-aligned partitions, but show, both theoretically and empirically, that this capacity is limited to partitions aligned with the fixed routing structure, leading to severe degradation when the data exhibits heterogeneous dependency topologies. We further prove that decomposable PCs are strictly more expressive than structured-decomposable ones, though effectively optimizing them remains an open challenge.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Lossless Compression with Probabilistic Circuits

Despite extensive progress on image generation, common deep generative model architectures are not easily applied to lossless compression. For example, VAEs suffer from a compression cost overhead due to their latent variables. This overhead can only be partially eliminated with elaborate schemes such as bits-back coding, often resulting in poor single-sample compression rates. To overcome such problems, we establish a new class of tractable lossless compression models that permit efficient encoding and decoding: Probabilistic Circuits (PCs). These are a class of neural networks involving $|p|$ computational units that support efficient marginalization over arbitrary subsets of the $D$ feature dimensions, enabling efficient arithmetic coding. We derive efficient encoding and decoding schemes that both have time complexity $\mathcal{O} (\log(D) \cdot |p|)$, where a naive scheme would have linear costs in $D$ and $|p|$, making the approach highly scalable. Empirically, our PC-based (de)compression algorithm runs 5-40 times faster than neural compression algorithms that achieve similar bitrates. By scaling up the traditional PC structure learning pipeline, we achieve state-of-the-art results on image datasets such as MNIST. Furthermore, PCs can be naturally integrated with existing neural compression algorithms to improve the performance of these base models on natural image datasets. Our results highlight the potential impact that non-standard learning architectures may have on neural data compression.

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preprint2021arXiv

A Compositional Atlas of Tractable Circuit Operations: From Simple Transformations to Complex Information-Theoretic Queries

Circuit representations are becoming the lingua franca to express and reason about tractable generative and discriminative models. In this paper, we show how complex inference scenarios for these models that commonly arise in machine learning -- from computing the expectations of decision tree ensembles to information-theoretic divergences of deep mixture models -- can be represented in terms of tractable modular operations over circuits. Specifically, we characterize the tractability of a vocabulary of simple transformations -- sums, products, quotients, powers, logarithms, and exponentials -- in terms of sufficient structural constraints of the circuits they operate on, and present novel hardness results for the cases in which these properties are not satisfied. Building on these operations, we derive a unified framework for reasoning about tractable models that generalizes several results in the literature and opens up novel tractable inference scenarios.

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preprint2020arXiv

Off-Policy Deep Reinforcement Learning with Analogous Disentangled Exploration

Off-policy reinforcement learning (RL) is concerned with learning a rewarding policy by executing another policy that gathers samples of experience. While the former policy (i.e. target policy) is rewarding but in-expressive (in most cases, deterministic), doing well in the latter task, in contrast, requires an expressive policy (i.e. behavior policy) that offers guided and effective exploration. Contrary to most methods that make a trade-off between optimality and expressiveness, disentangled frameworks explicitly decouple the two objectives, which each is dealt with by a distinct separate policy. Although being able to freely design and optimize the two policies with respect to their own objectives, naively disentangling them can lead to inefficient learning or stability issues. To mitigate this problem, our proposed method Analogous Disentangled Actor-Critic (ADAC) designs analogous pairs of actors and critics. Specifically, ADAC leverages a key property about Stein variational gradient descent (SVGD) to constraint the expressive energy-based behavior policy with respect to the target one for effective exploration. Additionally, an analogous critic pair is introduced to incorporate intrinsic rewards in a principled manner, with theoretical guarantees on the overall learning stability and effectiveness. We empirically evaluate environment-reward-only ADAC on 14 continuous-control tasks and report the state-of-the-art on 10 of them. We further demonstrate ADAC, when paired with intrinsic rewards, outperform alternatives in exploration-challenging tasks.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Watch the Unobserved: A Simple Approach to Parallelizing Monte Carlo Tree Search

Monte Carlo Tree Search (MCTS) algorithms have achieved great success on many challenging benchmarks (e.g., Computer Go). However, they generally require a large number of rollouts, making their applications costly. Furthermore, it is also extremely challenging to parallelize MCTS due to its inherent sequential nature: each rollout heavily relies on the statistics (e.g., node visitation counts) estimated from previous simulations to achieve an effective exploration-exploitation tradeoff. In spite of these difficulties, we develop an algorithm, WU-UCT, to effectively parallelize MCTS, which achieves linear speedup and exhibits only limited performance loss with an increasing number of workers. The key idea in WU-UCT is a set of statistics that we introduce to track the number of on-going yet incomplete simulation queries (named as unobserved samples). These statistics are used to modify the UCT tree policy in the selection steps in a principled manner to retain effective exploration-exploitation tradeoff when we parallelize the most time-consuming expansion and simulation steps. Experiments on a proprietary benchmark and the Atari Game benchmark demonstrate the linear speedup and the superior performance of WU-UCT comparing to existing techniques.

0 citations0 reviewsNo code linkedOpen access