Research map / Probabilistic and scientific modeling / Variational and generative sampling
Gradient estimation for discrete variables
Backpropagates through discrete latents with straight-through, control-variate and perturbation estimators.
74 accepted papers at ICML, NeurIPS, ICLR, CVPR and AAAI (2016–2026) · an approach in Variational and generative sampling, keyword cluster “estimation · probabilistic · variables”
State History Tried Checklist Preprints Who Export
Where it stands
Not enough benchmark data Fewer than four papers report the same benchmark, so there is no record to follow.
15 papers in 2023–24 and 11 in 2025–26 (at ICML, NeurIPS, ICLR, CVPR and AAAI); its share of the topic shrank, from 3.6% to 2.2%.
How this is decided
A benchmark is tracked when at least four papers of this approach report their own method on the same dataset and metric in at least two different years. Its record is the best number reported up to 2024 compared with the best reported in 2025–26: still improving means at least 1% better, flat means at most 0.2% better with at least two papers from 2025–26 trying. Numbers on a different scale from the rest (a fraction among percentages) and far outliers are left out. Results come from different papers with different setups, so they are signals, not head-to-head comparisons. The share of papers is counted at ICML, NeurIPS, ICLR, CVPR and AAAI.
How it got here
Most cited paper of each year
- 2016 · Backprop KF: Learning Discriminative Deterministic State Estimators (NeurIPS 2016 · 101 citations)
- 2017 · Categorical Reparameterization with Gumbel-Softmax (ICLR 2017 · 3,310 citations)
- 2018 · Implicit Reparameterization Gradients (NeurIPS 2018 · 129 citations)
- 2019 · Analyzing Inverse Problems with Invertible Neural Networks (ICLR 2019 · 149 citations)
- 2020 · Gradient Estimation with Stochastic Softmax Tricks (NeurIPS 2020 · 33 citations)
- 2021 · LREN: Low-Rank Embedded Network for Sample-Free Hyperspectral Anomaly Detection (AAAI 2021 · 71 citations)
- 2022 · MetaNODE: Prototype Optimization as a Neural ODE for Few-Shot Learning (AAAI 2022 · 42 citations)
- 2023 · Backpropagation at the Infinitesimal Inference Limit of Energy-Based Models: Unifying Predictive Coding, Equilibrium Propagation, and Contrastive Hebbian Learning (ICLR 2023 · 6 citations)
- 2024 · Multiple Hypothesis Dropout: Estimating the Parameters of Multi-Modal Output Distributions (AAAI 2024 · 1 citation)
- 2025 · The Computational Advantage of Depth in Learning High-Dimensional Hierarchical Targets (NeurIPS 2025 · 0 citations)
- 2026 · A hitchhiker's guide to Poisson gradient estimation (ICML 2026 · 0 citations)
Earliest papers here
- Backprop KF: Learning Discriminative Deterministic State Estimators (NeurIPS 2016 · 101 citations)
- Reward Augmented Maximum Likelihood for Neural Structured Prediction (NeurIPS 2016 · 86 citations)
- Categorical Reparameterization with Gumbel-Softmax (ICLR 2017 · 3,310 citations)
What has been tried
59 papers here report 568 measured changes (a component added, removed or swapped, compared with a baseline): helped 64%, no clear effect 11%, hurt 17%, mixed 8%. Papers mostly publish changes that helped, so "helped" is over-represented.
Ablations in recent papers
| What was changed | Measured on | Result | Effect | Paper |
|---|---|---|---|---|
| Use a subset ratio between 0.5 and 0.7 during Stochastic WTA training | Toy multi-point dataset · SDD | Helped | Multiple Hypothesis Dropout: Estimating the Parameters of Multi-Modal Output Distributions (AAAI 2024 · 1 citation) | |
| Initialize model parameters without optimization | CIFAR-10, CIFAR-100, TinyImagenet · input-saliency cosine similarity trend with capacity | Hurt | Great Minds Think Alike: The Universal Convergence Trend of Input Salience (NeurIPS 2024 · 0 citations) | |
| replace the non-injective NCoV with an injective NF | 5-class miniImageNet 1-shot · accuracy | 59.10±1.52 -> 56.72±1.46 | Hurt | Meta-Learning Universal Priors Using Non-Injective Change of Variables (NeurIPS 2024 · 0 citations) |
| add the control variate to GEFA | Amazon Review Polarity · nAOPC | 0.7120 -> 0.7366 | Helped | GEFA: A General Feature Attribution Framework Using Proxy Gradient Estimation (ICML 2025) |
| Use Gaussian instead of KNIFE as the REMEDI base | MNIST test · accuracy (%) | 98.28 (0.105) -> 98.36 (0.076) | Helped | REMEDI: Corrective Transformations for Improved Neural Entropy Estimation (ICML 2024) |
What reviewers will expect
Datasets and baselines named in the 6 papers of this approach from 2025–2026 that have a full-text summary. Leaving out the common ones is a frequent review question.
Datasets
- ImageNet · 2 of 6 papers
Baselines
- Integrated Gradients · 2 of 6 papers
Recent preprints
Loading recent arXiv preprints…
Who publishes on it
Institutions on the most papers of this approach since 2023 (of 26 papers; from OpenAlex and the papers' affiliations).
- University of Amsterdam · 2 papers
- KTH Royal Institute of Technology · 2 papers
Use it
Download BibTeX of 38 key papersOpen the topic in the interactive map
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Related approaches
Same keyword cluster
- Likelihood-free and graphical model estimation (161 papers)
- Tractable probabilistic models (90 papers)
- Exact inference for probabilistic programs (103 papers)
- Latent variable marginalization and estimators (91 papers)
- Mutual information estimation (27 papers)
Elsewhere in the topic
- Flow matching and flow sampling (144 papers)
- Posterior sampling with diffusion guidance (137 papers)
- Score-based generative modeling analysis (128 papers)
- Structured latent VAEs (125 papers)
- Disentangled and discrete latent models (92 papers)
- Variational inference theory and gradients (89 papers)
- Hamiltonian Monte Carlo (89 papers)
- Regularizing VAE latent information (89 papers)
Benchmark numbers, ablations and baseline numbers are extracted by AI from each paper's full text and can be wrong; the paper is the authority. Data: results index of 2026-11-02, citation counts from OpenAlex (2026-10-09).