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GFlowNet Foundations (2111.09266v4)

Published 17 Nov 2021 in cs.LG, cs.AI, and stat.ML

Abstract: Generative Flow Networks (GFlowNets) have been introduced as a method to sample a diverse set of candidates in an active learning context, with a training objective that makes them approximately sample in proportion to a given reward function. In this paper, we show a number of additional theoretical properties of GFlowNets. They can be used to estimate joint probability distributions and the corresponding marginal distributions where some variables are unspecified and, of particular interest, can represent distributions over composite objects like sets and graphs. GFlowNets amortize the work typically done by computationally expensive MCMC methods in a single but trained generative pass. They could also be used to estimate partition functions and free energies, conditional probabilities of supersets (supergraphs) given a subset (subgraph), as well as marginal distributions over all supersets (supergraphs) of a given set (graph). We introduce variations enabling the estimation of entropy and mutual information, sampling from a Pareto frontier, connections to reward-maximizing policies, and extensions to stochastic environments, continuous actions and modular energy functions.

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Citations (169)
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Summary

  • The paper introduces detailed balance as a novel local training objective, offering an efficient alternative to traditional flow-matching losses in sampling tasks.
  • The authors demonstrate that GFlowNets can represent joint and marginal distributions, enabling effective amortized inference and partition function estimation.
  • The paper extends GFlowNets to stochastic environments and continuous action spaces, broadening their applicability to complex domains like molecular generation and combinatorial optimization.

Overview of GFlowNet Foundations

The paper "GFlowNet Foundations" primarily elaborates on the theoretical underpinnings and extensions of Generative Flow Networks (GFlowNets). Introduced by Bengio et al. in a prior work, GFlowNets provide a novel framework for generating samples proportionally to a given reward function within a large state space. This approach can be particularly advantageous in scenarios such as active learning, where the aim is to sample diverse candidates efficiently.

Key Contributions

The paper presents a range of important theoretical results and developments concerning GFlowNets:

  1. Detailed Balance as a Training Objective: The authors introduce a new local and efficient training objective known as detailed balance. This concept draws an analogy with Markov Chain Monte Carlo (MCMC) methodologies and provides an alternative to flow-matching loss, which requires explicit sums.
  2. Representation of Joint Distributions: GFlowNets are demonstrated to represent joint and marginal distributions in scenarios where some variables are unspecified. Notably, they can model distributions over composite objects like graphs and sets, thus broadening their applicability to complex structures.
  3. Amortized Inference and Partition Function Estimation: The work explores the potential of GFlowNets to perform amortized probabilistic inference and estimations of partition functions. This capability allows the approximation of intractable sums over states and offers a computationally efficient alternative to MCMC by generating each sample in a single forward pass.
  4. Estimation of Information-Theoretic Quantities: New methodologies for estimating entropies and mutual information within the GFlowNet framework are proposed, leveraging conditional GFlowNets.
  5. Handling Stochastic Environments and Continuous Actions: The paper discusses extending GFlowNets to stochastic scenarios and continuous action spaces, broadening their utility in uncertain or high-dimensional spaces.
  6. Unsupervised and Multi-objective Sampling: The authors delve into methodologies that allow unsupervised learning in GFlowNets. Moreover, a framework for sampling along a Pareto frontier is introduced, providing a mechanism to handle multi-objective optimization problems.

Implications and Future Directions

The implications of the developments in GFlowNets are substantial across various domains, particularly where generating diverse solutions or sampling from complex distributions is crucial. By amortizing the traditionally expensive sampling processes found in MCMC while also learning effective generative policies, GFlowNets open new avenues in probabilistic modeling and decision-making processes.

Practically, the ability of GFlowNets to operate in domains with high-dimensional, structured data, such as with graphs and sets, suggests potential applications in fields like molecular generation, causal inference, and combinatorial optimization. Furthermore, the introduction of detailed balance and handling of continuous spaces may inspire new models and algorithms in both theoretical and applied machine learning.

Theoretically, GFlowNets provide an interesting intersection between reinforcement learning (RL) and probabilistic inference, each of which traditionally focuses on deterministic policy generation and sampling from distributions, respectively. This duality encourages continued exploration into hybrid models that can leverage strengths from both RL and generative modeling.

In summary, "GFlowNet Foundations" significantly extends the understanding and application of GFlowNets, positioning them as a versatile tool in the field of machine learning. Future work will likely explore more efficient training algorithms, deeper integration with other generative models, and further practical evaluations across diverse datasets and tasks.

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