NumColor: Precise Numeric Color Control in Text-to-Image Generation

Text-to-image diffusion models excel at generating images from natural language descriptions, yet fail to interpret numerical colors such as hex codes (#FF5733) and RGB values (rgb(255,87,51)). This limitation stems from subword tokenization, which fragments color codes into semantically meaningless tokens that text encoders cannot map to coherent color representations. We present NumColor, that enables precise numerical color control across multiple diffusion architectures. NumColor comprises two components: a Color Token Aggregator that detects color specifications regardless of tokenization, and a ColorBook containing 6,707 learnable embeddings that map colors to embedding space of text encoder in perceptually uniform CIE Lab space. We introduce two auxiliary losses, directional alignment and interpolation consistency, to enforce geometric correspondence between Lab and embedding spaces, enabling smooth color interpolation. To train the ColorBook, we construct NumColor-Data, a synthetic dataset of 500K rendered images with unambiguous color-to-pixel correspondence, eliminating the annotation ambiguity inherent in photographic datasets. Although trained solely on FLUX, NumColor transfers zero-shot to SD3, SD3.5, PixArt-α, and PixArt-Σ without model-specific adaptation. NumColor improves numerical color accuracy by 4-9x across five models, while simultaneously improving color harmony scores by 10-30x on GenColorBench benchmark.

Combining GHOST and Casper

We present "Gasper," a proof-of-stake-based consensus protocol, which is an idealized version of the proposed Ethereum 2.0 beacon chain. The protocol combines Casper FFG, a finality tool, with LMD GHOST, a fork-choice rule. We prove safety, plausible liveness, and probabilistic liveness under different sets of assumptions.