Exact Minimax One-Bit Unbiased Compression: Heavy-Tail Necessity and Finite-Randomness Approximation

arXiv:2609.27860 · cs.LG · Submitted 2026-08-20 · Read on arXiv

cs.LG

Submitted: 2026-08-20

Updated: 2026-08-20

Code: https://github.com/jiangxioabai/onebit

Terminology

• Decode — 4× in this paper · explained in 2 episodes
• Aggregation — 3× in this paper · explained in 1 episode
• Minimax optimality — 2× in this paper · explained in 2 episodes
• Quantization — 2× in this paper · explained in 12 episodes
• Abstraction — 1× in this paper · explained in 1 episode
• Generative AI — 1× in this paper · explained in 2 episodes

Sources

• Provable Quantization with Randomized Hadamard Transform
• Interaction Is Not Necessary for Order-Optimal 1-Bit Mean Estimation
• Information-Theoretic Lower Bounds for Bit-Constrained Stochastic Optimization via a Reduction to Compressed Gaussian Mean Estimation
• Order-Optimal Sequential 1-Bit Mean Estimation in General Tail Regimes
• Universal Refinement without Interaction: Order-Optimal 1-Bit Mean Estimation

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