Research map / Probabilistic and scientific modeling / Variational and generative sampling
Beyond Communication Overhead: A Multilevel Monte Carlo Approach for Mitigating Compression Bias in Distributed Learning
Read the paperCheck your idea against 108,967 papers
AI-extracted summary. Written by AI from the paper's full text. Numbers and claims can be wrong or missing context, so check the paper before you cite or build on it.
Proposes Multilevel Monte Carlo (MLMC) compression that turns biased gradient compressors (Top-k, s-Top-k, bit-wise) into unbiased estimators for distributed SGD, with an adaptive per-sample level distribution, validated on BERT/SST-2 and ResNet18/CIFAR-10.
Problem
Gradient compression in distributed learning trades off biased compressors (strong empirical performance but need error feedback and worse theory) against unbiased compressors (clean theory but poor empirical efficiency). The paper asks whether one can get the benefits of both.
Approach
Apply Multilevel Monte Carlo to a family of multilevel biased compressors: sample a compression level from a distribution and send a reweighted residual between adjacent levels, yielding an unbiased gradient estimate whose variance is controlled. An adaptive variant chooses level probabilities per sample proportional to residual norms.
Key results
- On BERT SST-2 fine-tuning, Adaptive MLMC-Top-k reports higher test accuracy than Top-k, EF21-SGDM and Rand-k at equal communicated bits across sparsification levels k in {0.01n,0.05n,0.1n,0.5n}, with M=4 and M=32 machines (averaged over 5 seeds).
- Fixed-point MLMC quantization is claimed to be about x32 cheaper in communication than uncompressed 64-bit gradients, transmitting roughly 2d bits per iteration.
- Theory: MLMC-compressed SGD keeps the parallel SGD rate up to an extra term scaled by compression coefficient, allowing parallelization over M=O(T) machines versus M=O(sqrt(T)) for EF21-SGDM.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use Adaptive MLMC-Top-k instead of the compared compression methods | BERT fine-tuning · GLUE SST-2, communication efficiency | test accuracy | Helped |
| Use Adaptive MLMC-Top-k instead of the compared compression methods | BERT fine-tuning · GLUE SST-2, iteration efficiency | test accuracy | Helped |
| Use Adaptive MLMC-Top-k instead of uncompressed SGD | BERT fine-tuning · GLUE SST-2, iteration efficiency | test accuracy | No clear effect |
| Use Fixed-Point MLMC instead of 2-bit Fixed-Point quantization, 2-bit QSGD, or uncompressed SGD | ResNet18 · CIFAR-10, communication efficiency | test accuracy | Helped |
| Increase the number of machines from M=4 to M=32 | Adaptive MLMC-Top-k · GLUE SST-2 | convergence rate | Helped |
Surprising findings
- Adaptive MLMC-Top-k is reported to match uncompressed SGD in iteration efficiency on BERT SST-2 despite sending far fewer bits.
Limitations
- Variance of MLMC estimator adds a compression-dependent term; heterogeneous data setting adds an O(omega*xi/sqrt(MT)) term.
- Experiments are limited to fine-tuning BERT on SST-2 and ResNet18 on CIFAR-10 with a single seed setup of 5 seeds and small batch sizes.
Experimental setup
Datasets: GLUE SST-2 CIFAR-10
Benchmarks: GLUE SST-2 CIFAR-10
Metrics: test accuracy communicated bits epochs
Baselines: Top-k EF21-SGDM Rand-k uncompressed SGD 2-bit QSGD 2-bit fixed-point quantization
Builds on: Multilevel Monte Carlo EF21-SGDM QSGD Rand-k
Closest papers by meaning
- On the Discrepancy between the Theoretical Analysis and Practical Implementations of Compressed Communication for Distributed Deep Learning (AAAI 2020 · similarity 0.90)
- EF-BV: A Unified Theory of Error Feedback and Variance Reduction Mechanisms for Biased and Unbiased Compression in Distributed Optimization (NeurIPS 2022 · similarity 0.90)
- Accelerated Methods with Compressed Communications for Distributed Optimization Problems Under Data Similarity (AAAI 2025 · similarity 0.89)
- Sketched Adaptive Distributed Deep Learning: A Sharp Convergence Analysis (NeurIPS 2025 · similarity 0.87)
- Approximate Gradient Coding for Distributed Learning with Heterogeneous Stragglers (NeurIPS 2025 · similarity 0.87)
- Don't Compress Gradients in Random Reshuffling: Compress Gradient Differences (NeurIPS 2024 · similarity 0.86)
Writing a paper in this area? scime draft is a free LaTeX editor with AI included, real-time co-authors and a check of your references and venue rules before you submit. It also imports OpenAI Prism projects.