HoloByte: Continuous Hyperspherical Distillation for Tokenizer-Free Modeling

• URL: http://arxiv.org/abs/2603.16917v1
• Date: Tue, 10 Mar 2026 20:35:36 GMT
• Title: HoloByte: Continuous Hyperspherical Distillation for Tokenizer-Free Modeling
• Abstract summary: We introduce textbfHoloByte: a strictly tokenizer-free framework utilizing Continuous Hyperspherical Distillation.<n>HoloByte partitions discrete byte sequences into fixed-capacity chunks and projects them into a continuous, strictly bounded hyperspherical manifold.<n>These results establish Continuous Hyperspherical Distillation as a mathematically rigorous and computationally tractable foundation for vocabulary-in sequence modeling.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Sequence modeling universally relies on discrete subword tokenization to circumvent the $\mathcal{O}(N^2)$ computational intractability of native byte-level attention. However, this heuristic quantization imposes artificial morphological boundaries, enforces vocabulary dependence, and fractures the continuity of the optimization landscape. To resolve this dichotomy, we introduce \textbf{HoloByte}: a strictly tokenizer-free framework utilizing Continuous Hyperspherical Distillation. HoloByte partitions discrete byte sequences into fixed-capacity chunks and projects them into a continuous, strictly bounded hyperspherical manifold via an invertible, dimension-preserving orthogonal rotation operator. This spatial superposition allows a macroscopic transformer to operate exclusively on compressed continuous representations, formally reducing the exact attention time complexity from $\mathcal{O}(N^2D)$ to $\mathcal{O}\left( \frac{N^2}{W^2}D + ND^2 \right)$. A localized causal micro-decoder subsequently unbinds these representations to compute exact byte-level distributions. To govern this continuous trajectory, we propose a dual-objective formulation incorporating a mathematically precise Holographic Latent Mean Squared Error, which strictly bounds the gradient and guarantees asymptotic stability. Theoretically, we derive the minimal embedding dimension $D = Ω(W \ln |\mathcal{V}|)$ required to ensure error-free discrete recovery from the continuous manifold. Empirically, under strictly matched parameter constraints, HoloByte is systematically outperforming a comparable discrete Byte-Pair Encoding (BPE) baseline. These results establish Continuous Hyperspherical Distillation as a mathematically rigorous and computationally tractable foundation for vocabulary-invariant sequence modeling. The code is available at https://github.com/VladimerKhasia/HoloByte

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