# Path-dependent Discrete Amortized Inference

arXiv: https://arxiv.org/abs/2608.08644 · HTML: https://mlsanity.com/paper/2608.08644/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 59 of its 104 references that are in the map.
- First posted on arXiv 9 Aug 2026.

## Builds on (most cited first, 30 of 59)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables](https://mlsanity.com/paper/1611.00712/) (2016)
- [Exact solutions to the nonlinear dynamics of learning in deep linear neural networks](https://mlsanity.com/paper/1312.6120/) (2013)
- [Linear Transformers Are Secretly Fast Weight Programmers](https://mlsanity.com/paper/2102.11174/) (2021)
- [Inductive Representation Learning on Temporal Graphs](https://mlsanity.com/paper/2002.07962/) (2020)
- [Lipschitz regularity of deep neural networks: analysis and efficient estimation](https://mlsanity.com/paper/1805.10965/) (2018)
- [Flow Network based Generative Models for Non-Iterative Diverse Candidate Generation](https://mlsanity.com/paper/2106.04399/) (2021)
- [The Expressive Power of Neural Networks: A View from the Width](https://mlsanity.com/paper/1709.02540/) (2017)
- [A Survey of Inverse Reinforcement Learning: Challenges, Methods and Progress](https://mlsanity.com/paper/1806.06877/) (2018)
- [GFlowNet Foundations](https://mlsanity.com/paper/2111.09266/) (2021)
- [Trajectory balance: Improved credit assignment in GFlowNets](https://mlsanity.com/paper/2201.13259/) (2022)
- [A Conceptual Introduction to Hamiltonian Monte Carlo](https://mlsanity.com/paper/1701.02434/) (2017)
- [Inductive Representation Learning in Temporal Networks via Causal Anonymous Walks](https://mlsanity.com/paper/2101.05974/) (2021)
- [Biological Sequence Design with GFlowNets](https://mlsanity.com/paper/2203.04115/) (2022)
- [Bayesian Structure Learning with Generative Flow Networks](https://mlsanity.com/paper/2202.13903/) (2022)
- [Underdamped Langevin MCMC: A non-asymptotic analysis](https://mlsanity.com/paper/1707.03663/) (2017)
- [Learning GFlowNets from partial episodes for improved convergence and stability](https://mlsanity.com/paper/2209.12782/) (2022)
- [Approximating Continuous Functions by ReLU Nets of Minimal Width](https://mlsanity.com/paper/1710.11278/) (2017)
- [Recurrent Model-Free RL Can Be a Strong Baseline for Many POMDPs](https://mlsanity.com/paper/2110.05038/) (2021)
- [GFlowNets and variational inference](https://mlsanity.com/paper/2210.00580/) (2022)
- [A theory of continuous generative flow networks](https://mlsanity.com/paper/2301.12594/) (2023)
- [Design-Bench: Benchmarks for Data-Driven Offline Model-Based Optimization](https://mlsanity.com/paper/2202.08450/) (2022)
- [Amortizing intractable inference in large language models](https://mlsanity.com/paper/2310.04363/) (2023)
- [The Logic of Graph Neural Networks](https://mlsanity.com/paper/2104.14624/) (2021)
- [Better Training of GFlowNets with Local Credit and Incomplete Trajectories](https://mlsanity.com/paper/2302.01687/) (2023)
- [VarGrad: A Low-Variance Gradient Estimator for Variational Inference](https://mlsanity.com/paper/2010.10436/) (2020)
- [Towards Understanding and Improving GFlowNet Training](https://mlsanity.com/paper/2305.07170/) (2023)

## Abstract (arXiv)

We consider the problem of sampling compositional and discrete objects from a given unnormalized posterior distribution. Notably, recent studies have shown that this problem can be efficiently solved by learning a deterministic Markov Decision Process (MDP) that progressively builds each object in proportion to the posterior. In this work, however, we demonstrate that the Markovian assumption can both hamper signal propagation during training and catastrophically reduce the learned sampler's expressivity due to state aliasing. To address these issues, we propose lifting the MDP with a learnable latent dynamical system that allows the underlying policy to depend on the entire past trajectory---and not only on the current state. In view of this, we refer to the resulting method as path-dependent discrete amortized inference. Importantly, we provably extend existing learning algorithms for discrete amortized samplers to our setting. In experiments on standard benchmark problems, we also show that our approach often leads to faster learning convergence and improved state space exploration relatively to prior techniques.