The Future of Tractable Deep Generative Models

Table of Links

Abstract and 1. Introduction

1. Preliminaries and Related Work

2. Key Bottlenecks in PC Parallelization

3. Harnessing Block-Based PC Parallelization

   4.1. Fully Connected Sum Layers

   4.2. Generalizing To Practical Sum Layers

   4.3. Efficient Implementations by Compiling PC Layers

   4.4. Analysis: IO and Computation Overhead

4. Optimizing Backpropagation with PC Flows

5. Experiments

   6.1. Faster Models with PyJuice

   6.2. Better PCs At Scale

   6.3. Benchmarking Existing PCs

6. Conclusion, Acknowledgements, Impact Statement, and References

A. Algorithm Details

B. Additional Technical Details

C. Experimental Details

D. Additional Experiments

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6.3. Benchmarking Existing PCs

\ \

\ \ \ We adopt two PD structures (i.e., PD-mid with 107M edges and PD-large with 405M edges) as well as two HCLT structures (i.e., HCLT-mid with 40M edges and HCLT-large with 174M edges). Details of the adopted models are described in Appendix C.4. We experiment with different optimization strategies and adopt full-batch EM as it yields consistently better performance across models and datasets. Specifically, the computed PC flows are accumulated across all samples in the training set before doing one EM step.

\ Results are shown in Table 3. Notably, we achieve better results compared to previous papers. For example, Liu et al. (2023a) reports 4.82 bits-per-dimension (bpd) for HCLT on ImageNet32, while we achieved 4.33 bpd. The performance improvements stem from more training epochs and the ability to do more hyperparameter search thanks to the speedup. We highlight that the goal of this section is not to set new records for tractable deep generative models, but to establish a set of baselines that can be easily reproduced to track the progress of developments in PC modeling and learning. In Appendix C.4, we include additional benchmark results on the WikiText dataset (Merity et al., 2016).

7. Conclusion

We proposed PyJuice, a novel system that supports training and inference of probabilistic circuits. PyJuice is orders of magnitude faster and much more memory efficient than even very recent baselines. We hope PyJuice can boost future research on tractable deep generative models by allowing for efficient training of large-scale architectures.

Acknowledgements

This work was funded in part by the DARPA PTG Program under award HR00112220005, the DARPA ANSR program under award FA8750-23-2-0004, and the NSF grant #IIS1943641. We thank Honghua Zhang, Pasha Khosravi, and Poorva Garg for providing valuable feedback during the development of PyJuice.

Impact Statement

This paper presents work whose goal is to advance the field of Machine Learning. There are many potential societal consequences of our work, none which we feel must be specifically highlighted here.

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:::info Authors:

(1) Anji Liu, Department of Computer Science, University of California, Los Angeles, USA ([email protected]);

(2) Kareem Ahmed, Department of Computer Science, University of California, Los Angeles, USA;

(3) Guy Van den Broeck, Department of Computer Science, University of California, Los Angeles, USA;

:::

:::info This paper is available on arxiv under CC BY 4.0 DEED license.

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