mlsanityData to 14 Oct 2026

Adaptive Perturbation-Based Gradient Estimation for Discrete Latent Variable Models

arXiv 2209.04862 ↗First posted 11 Sep 2022cs.LG cs.AI cs.CLcited by 12

Not on the map. Why?

Abstract (arXiv)

The integration of discrete algorithmic components in deep learning architectures has numerous applications. Recently, Implicit Maximum Likelihood Estimation (IMLE, Niepert, Minervini, and Franceschi 2021), a class of gradient estimators for discrete exponential family distributions, was proposed by combining implicit differentiation through perturbation with the path-wise gradient estimator. However, due to the finite difference approximation of the gradients, it is especially sensitive to the choice of the finite difference step size, which needs to be specified by the user. In this work, we present Adaptive IMLE (AIMLE), the first adaptive gradient estimator for complex discrete distributions: it adaptively identifies the target distribution for IMLE by trading off the density of gradient information with the degree of bias in the gradient estimates. We empirically evaluate our estimator on synthetic examples, as well as on Learning to Explain, Discrete Variational Auto-Encoders, and Neural Relational Inference tasks. In our experiments, we show that our adaptive gradient estimator can produce faithful estimates while requiring orders of magnitude fewer samples than other gradient estimators.

Key facts. Cited by 12 papers in the map (data through 14 Oct 2026). Builds on 37 of its 66 references that are in the map. First posted on arXiv 11 Sep 2022.

Builds on

37 of 66 references.

References · 37

  1. 2014Adam: A Method for Stochastic Optimizationcited by 37,240
  2. 2013Auto-Encoding Variational Bayescited by 4,053
  3. 2016Categorical Reparameterization with Gumbel-Softmaxcited by 2,739
  4. 2013Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computationcited by 2,079
  5. 2016The Concrete Distribution: A Continuous Relaxation of Discrete Random Variablescited by 1,148
  6. 2020Mastering Atari with Discrete World Modelscited by 1,007
  7. 2018Machine Learning for Combinatorial Optimization: a Methodological Tour d'Horizoncited by 623
  8. 2017OptNet: Differentiable Optimization as a Layer in Neural Networkscited by 599
  9. 2019Differentiable Convex Optimization Layerscited by 465
  10. 2018Bilevel Programming for Hyperparameter Optimization and Meta-Learningcited by 405
  11. 2017Smart "Predict, then Optimize"cited by 339
  12. 2019Monte Carlo Gradient Estimation in Machine Learningcited by 283
25 more
  1. 2016Rationalizing Neural Predictionscited by 281
  2. 2018Learning to Explain: An Information-Theoretic Perspective on Model Interpretationcited by 248
  3. 2019Learning Discrete Structures for Graph Neural Networkscited by 231
  4. 2018Melding the Data-Decisions Pipeline: Decision-Focused Learning for Combinatorial Optimizationcited by 227
  5. 2019Differentiation of Blackbox Combinatorial Solverscited by 226
  6. 2017Learning Explanatory Rules from Noisy Datacited by 211
  7. 2019SATNet: Bridging deep learning and logical reasoning using a differentiable satisfiability solvercited by 173
  8. 2019Stochastic Optimization of Sorting Networks via Continuous Relaxationscited by 111
  9. 2017Backpropagation through the Void: Optimizing control variates for black-box gradient estimationcited by 106
  10. 2021Implicit MLE: Backpropagating Through Discrete Exponential Family Distributionscited by 98
  11. 2019MIPaaL: Mixed Integer Program as a Layercited by 94
  12. 2019Smart Predict-and-Optimize for Hard Combinatorial Optimization Problemscited by 89
  13. 2020Interior Point Solving for LP-based prediction+optimisationcited by 83
  14. 2020Deep Graph Matching via Blackbox Differentiation of Combinatorial Solverscited by 81
  15. 2017REBAR: Low-variance, unbiased gradient estimates for discrete latent variable modelscited by 79
  16. 2019Reparameterizable Subset Sampling via Continuous Relaxationscited by 70
  17. 2020Gradient Estimation with Stochastic Softmax Trickscited by 67
  18. 2018SparseMAP: Differentiable Sparse Structured Inferencecited by 62
  19. 2022Ordered Subgraph Aggregation Networkscited by 57
  20. 2020Estimating Gradients for Discrete Random Variables by Sampling without Replacementcited by 31
  21. 2021Conditional Neural Relational Inference for Interacting Systemscited by 28
  22. 2015Training Deep Neural Networks via Direct Loss Minimizationcited by 25
  23. 2018Rao-Blackwellized Stochastic Gradients for Discrete Distributionscited by 24
  24. 2020LP-SparseMAP: Differentiable Relaxed Optimization for Sparse Structured Predictioncited by 17
  25. 2016Parameter Learning for Log-supermodular Distributionscited by 2

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2022: 1; 2023: 1; 2024: 5; 2025: 2; 2026: 3.

12 papers.

  1. 2023LVM-Med: Learning Large-Scale Self-Supervised Vision Models for Medical Imaging via Second-order Graph Matchingcited by 60
  2. 2022SIMPLE: A Gradient Estimator for k-Subset Samplingcited by 34
  3. 2024Probabilistic Graph Rewiring via Virtual Nodescited by 15
  4. 2024LPGD: A General Framework for Backpropagation through Embedded Optimization Layerscited by 6
  5. 2024ExGra-Med: Extended Context Graph Alignment for Medical Vision-Language Modelscited by 6
  6. 2024SPHINX: Structural Prediction using Hypergraph Inference Networkcited by 3
  7. 2026Decision-Focused On-Policy Learning for Contextual Linear Optimization with Partial Feedbackcited by 1
  8. 2024MiranDa: Mimicking the Learning Processes of Human Doctors to Achieve Causal Inference for Medication Recommendationcited by 0
  9. 2025Preference-Based Gradient Estimation for ML-Guided Approximate Combinatorial Optimizationcited by 0
  10. 2025Beyond Softmax: A Natural Parameterization for Categorical Random Variablescited by 0
  11. 2026GraIP: A Benchmarking Framework For Neural Graph Inverse Problemscited by 0
  12. 2026Contextual Preference Distribution Learningcited by 0