# One Proposal for Every Margin: Zero-Shot Amortized Sequential Importance Sampling for Binary Matrices

arXiv: https://arxiv.org/abs/2609.35514 · HTML: https://mlsanity.com/paper/2609.35514/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 59 references that are in the map.
- First posted on arXiv 28 Sep 2026.

## Builds on (most cited first, 22 of 22)

- [Flow Network based Generative Models for Non-Iterative Diverse Candidate Generation](https://mlsanity.com/paper/2106.04399/) (2021)
- [GFlowNet Foundations](https://mlsanity.com/paper/2111.09266/) (2021)
- [Trajectory balance: Improved credit assignment in GFlowNets](https://mlsanity.com/paper/2201.13259/) (2022)
- [Neural Importance Sampling](https://mlsanity.com/paper/1808.03856/) (2018)
- [GFlowNets and variational inference](https://mlsanity.com/paper/2210.00580/) (2022)
- [Solving Statistical Mechanics Using Variational Autoregressive Networks](https://mlsanity.com/paper/1809.10606/) (2018)
- [Probabilistic Inference in Language Models via Twisted Sequential Monte Carlo](https://mlsanity.com/paper/2404.17546/) (2024)
- [VarGrad: A Low-Variance Gradient Estimator for Variational Inference](https://mlsanity.com/paper/2010.10436/) (2020)
- [Robust Scheduling with GFlowNets](https://mlsanity.com/paper/2302.05446/) (2023)
- [Generative Flow Networks as Entropy-Regularized RL](https://mlsanity.com/paper/2310.12934/) (2023)
- [Ant Colony Sampling with GFlowNets for Combinatorial Optimization](https://mlsanity.com/paper/2403.07041/) (2024)
- [Discrete Probabilistic Inference as Control in Multi-path Environments](https://mlsanity.com/paper/2402.10309/) (2024)
- [Neural Adaptive Sequential Monte Carlo](https://mlsanity.com/paper/1506.03338/) (2015)
- [Inference Compilation and Universal Probabilistic Programming](https://mlsanity.com/paper/1610.09900/) (2016)
- [Inference Networks for Sequential Monte Carlo in Graphical Models](https://mlsanity.com/paper/1602.06701/) (2016)
- [Configuring Random Graph Models with Fixed Degree Sequences](https://mlsanity.com/paper/1608.00607/) (2016)
- [Reinforced sequential Monte Carlo for amortised sampling](https://mlsanity.com/paper/2510.11711/) (2025)
- [Action abstractions for amortized sampling](https://mlsanity.com/paper/2410.15184/) (2024)
- [f-Trajectory Balance: A Loss Family for Tuning GFlowNets, Generative Models, and LLMs with Off- and On-Policy Data](https://mlsanity.com/paper/2605.15417/) (2026)
- [PowerFlow: Unlocking the Dual Nature of LLMs via Principled Distribution Matching](https://mlsanity.com/paper/2603.18363/) (2026)
- [A stopping rule for randomly sampling bipartite networks with fixed degree sequences](https://mlsanity.com/paper/2305.04937/) (2023)
- [Spectral Gap for the Binary Fixed-Margin Swap Chain](https://mlsanity.com/paper/2606.22636/) (2026)

## Abstract (arXiv)

In ecology, psychometrics, and the analysis of social and financial networks, binary matrices are often analyzed conditional on their observed row and column sums, which restricts the problem to a finite sample space of matrices with the same margins. Two fundamental problems are to count this space and to sample uniformly from it. Sequential importance sampling (SIS) addresses both with independent weighted samples and an unbiased count estimator, but its efficiency depends critically on the proposal distribution. Existing proposals are analytically designed, and their accuracy can vary substantially with the margins. We show that the ideal SIS proposal, under which every weight equals the count and the variance vanishes, is exactly the policy of a generative flow network (GFlowNet) with unit reward on every matrix that has the given margins. We therefore propose MarginFlow, a framework that turns the design of the proposal into a learning problem and amortizes it across margins by exploiting their self-similarity. Every partial matrix is itself an instance with reduced margins, so one set transformer that reads the remaining margins serves every margin. We train MarginFlow on a pool of 1904 margins and evaluate it zero-shot on 1190 held-out margins, synthetic and real, from 3×3 to 870×6. On 1187 of the 1190 margins it matches or beats the best of 31 analytically designed configurations, chosen post hoc for each margin, and its median effective sample fraction is 99.8%. On the 56 margins where that best loses more than one nat of effective sample size, MarginFlow wins every one and raises the median effective sample fraction from 10.3% to 94.1%.