On One-Bit Quantization
Not on the map. Why?
Abstract (arXiv)
We consider the one-bit quantizer that minimizes the mean squared error for a source living in a real Hilbert space. The optimal quantizer is a projection followed by a thresholding operation, and we provide methods for identifying the optimal direction along which to project. As an application of our methods, we characterize the optimal one-bit quantizer for a continuous-time random process that exhibits low-dimensional structure. We numerically show that this optimal quantizer is found by a neural-network-based compressor trained via stochastic gradient descent.
Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 3 of its 13 references that are in the map. First posted on arXiv 10 Feb 2022.
Builds on
3 of 13 references.
References · 3
- 2020Nonlinear Transform Codingcited by 136
- 2020Universally Quantized Neural Compressioncited by 64
- 2020Neural Networks Optimally Compress the Sawbridgecited by 11
Built on by
Not cited yet.
Similar, not cited
Close in wording, no citation either way
- 2025One-Bit Quantization for Random Features Models
- 2025GDNSQ: Gradual Differentiable Noise Scale Quantization for Low-bit Neural Networks
- 2025Beyond Discreteness: Sample Complexity Analysis of Straight-Through Estimator for 1-bit Quantization
- 2022AMED: Automatic Mixed-Precision Quantization for Edge Devices
- 2025The Fourth State: Signed-Zero Ternary for Stable LLM Quantization (and More)
- 2026Rounding in Preconditioner Space: Redesigning 4-bit AdamW Optimizer-State Quantization
- 2023Memory Efficient Optimizers with 4-bit States
- 20218-bit Optimizers via Block-wise Quantization