HSL — Holistic Signal Language

🇰🇷 이 프로젝트는 개인 시간에 독립적으로 연구·공개한 오픈 연구 산출물입니다. 🇬🇧 This is an independent, open research project — researched and released on personal time.

A non-learned, byte-level signal encoder for PyTorch. Instead of splitting text into tokens, it reads raw bytes holistically as signal: change-rate (Δ, XOR-delta), 2nd-order change (Δ²), 편미분-boundary, exact complex Fourier, and phase — 27 dimensions per byte (35 with raw bits), losslessly invertible. One modality-agnostic input layer for text, image, audio, video — any byte stream.

Everything is information — a fluctuation between 0 and 1. HSL doesn't ask what a token means; it measures how the signal changes, with exact formulas, so the same representation works under every modality. It's one base embedding applied to every modality; which channels help which modality is decided downstream by your model's adapters — nothing is prematurely thrown away at the base.

import hsl_embedding as hsl

feats, phase = hsl.embed(b"hello")          # -> Tensor [L, 27], Tensor [L]
emb = hsl.Embedding()                        # an nn.Module, no parameters (like nn.Embedding)
feats = emb("강아지".encode())               # -> [L, 27]
assert hsl.decode(hsl.encode(b"hello")) == b"hello"   # lossless, by construction

Import name: the package is installed as hsl-embedding but imported as import hsl_embedding (import hsl will fail). embed(data) returns a tuple (feats, phase) — feats is a torch.Tensor [L, 27] (per-byte features; [L, 35] with include_bits=True) and phase is a torch.Tensor [L] (the raw phase angle θ). Unpack both: feats, phase = hsl.embed(...).

Install

pip install hsl_embedding      # import as `import hsl_embedding as hsl` (pip treats - and _ the same)
# deps: numpy, torch

Why not just nn.Embedding?

They solve different problems — this is not a performance claim, it's a "when to use which".

They compose. HSL is an input substrate, not a replacement for learned representations: nn.Embedding learns what tokens mean; HSL gives exact structural signal for free. Stack learned layers on top of HSL features.

Reach for HSL when you want: tokenizer-free input · one model across modalities · structure/change-aware features · exact reconstruction · small-data or from-scratch training · interpretable input channels.

What each channel captures (and where it's good)

HSL is built from exact formulas, each chosen to carry information a plain learned embedding tends to throw away. The default is the 27-D exact base — the pure change-rate substrate, every channel lossless:

The point: a single learned vector blurs all of this together. HSL keeps change (Δ), curvature (Δ²), spectrum (exact Fourier), and phase as separate, exact, interpretable channels — and your model selects which ones each modality needs (no premature compression at the base).

Optional 35-D: include_bits=True prepends the 8 raw byte bits. They're redundant (the per-byte Δ already encodes each byte losslessly) — an optional extra lens, not part of the base.

Practical notes (read before wiring into a model)

• Channel scales are heterogeneous by design — HSL ships exact values, not normalized ones. fft_re0 (the DC bin = the byte's bit count) spans 0–8 while most channels sit in ±1–2. Apply per-feature scaling at the model input boundary (a LayerNorm right after HSL, or a learned Linear(27, d) — either works); feeding raw features straight into attention lets fft_re0 dominate early training.
• Empty input: the bytes path returns [1, 27] — embed(b"") is treated as a single 0x00 byte (deliberate, keeps downstream batching safe), so it is indistinguishable from embed(b"\x00"). The tensor path instead returns [..., 0, 27] for zero-length ids (batching/padding is the caller's job there). If your pipeline must tell empties apart, mask them upstream.
• Fourier channels read the byte's 8-bit pattern, not the waveform's temporal spectrum (values 127 and 128 are spectrally distant); the phase channel is cyclic, so byte 255 sits next to byte 0. Every lens is exact — which lens fits which modality is your model's call, downstream.

Lossless by construction

The features are grounded in a lossless codec, so the substrate is byte-exact:

frame = hsl.encode(b"any bytes \x00\xff")
hsl.decode(frame) == b"any bytes \x00\xff"     # True

Δ is a per-byte XOR-delta from the symbolic anchor 0 — each byte is measured from the anchor (so bytes are independent), and integrating each byte's Δ from 0 recovers it exactly. That's why the raw bits channel is redundant and can be dropped.

27-D (default) vs 35-D (with raw bits)

hsl.embed(data)                      # 27-D  (default exact base; change-rate + exact Fourier + phase)
hsl.embed(data, include_bits=True)   # 35-D  (also prepend the 8 raw bits — redundant optional lens)
hsl.embed(data, momentum_phase=True) # 27-D  (phasor magnitude also carries |Δbyte| velocity)
hsl.Embedding(include_bits=True).out_dim   # 35

Batch

emb = hsl.Embedding()
feats, phase, mask = emb.pack([b"a", b"abcdef"], max_len=8)   # [B, L, D], [B, L], [B, L]

Tensor / GPU path (v0.4)

Embedding also accepts integer tensors of byte values (0..255) — batched, on any device, and bit-identical to the bytes path. The LUTs ride along as non-persistent buffers (state_dict() stays empty; .to(device) moves them with your model):

emb = hsl.Embedding().to(device)
ids = torch.randint(0, 256, (B, L), device=device)   # byte values you already batched yourself
feats = emb(ids)                                     # [B, L, 27] on `device` — torch ops end to end

Substrate ablation toolkit (v0.5)

The 27-D base factors as 18 value dims (Δ8 + Fourier8 + phase2 — pure functions of the byte's value, i.e. ONE frozen 256×18 LUT; a consequence of the anchor rule) + 9 context dims (Δ²8 + boundary1, the only sequence-dependent channels). hsl_embedding.ablation ships the controlled A/Bs that isolate the value geometry — every control keeps HSL's exact context dims and the exact 27-column layout, so the same downstream model runs unchanged:

from hsl_embedding import ablation as ab

ab.ControlEmbedding("hsl")                 # frozen exact LUT — the claim under test
ab.ControlEmbedding("learned", seed=0)     # trainable nn.Embedding(256,18): can SGD find an equivalent?
ab.ControlEmbedding("random", seed=0)      # FIXED injective LUT, HSL per-channel moments —
                                           #   "is invertibility alone enough?" (it preserves all info)
ab.ControlEmbedding("permuted", seed=0)    # HSL's own rows, permuted — identical marginals,
                                           #   geometry destroyed: capacity vs geometry

ab.feature_groups()["value"]               # 18 per-value dims / ["context"] → 9 sequence dims
no_fft = ab.select_channels(feats, ("dxor", "d2xor", "boundary", "phase"))   # feature-family ablations

The cheapest, sharpest minimal pair needs no control at all: raw bits (8) vs Δ (8) — both per-byte invertible, identical information / dimensionality / {0,1} scale; the only difference is geometry (Δ ≡ Gray code: a ±1 value step moves exactly one coordinate; raw bits flip up to all 8). embed(data, include_bits=True) + select_channels(..., ("bits",)) vs ("dxor",).

python examples/substrate_ablation.py     # the full protocol in one screen

Examples

python examples/quickstart.py        # bytes in, features out; named channels
python examples/roundtrip_all.py     # text / image / audio / video -> embed -> EXACT reconstruction
python examples/vs_nn_embedding.py   # nn.Embedding vs hsl.Embedding — when to use which
python examples/benchmark_vs_nn.py   # honest capability + speed comparison

roundtrip_all.py — one modality-agnostic encoder, lossless by construction:

modality              bytes     feat shape   reconstruction
----------------------------------------------------------------
text  (utf-8)            98       (98, 27)   EXACT ✓
image (RGB u8)         3072     (3072, 27)   EXACT ✓
audio (PCM i16)        8000     (8000, 27)   EXACT ✓
video (6 frames)       4608     (4608, 27)   EXACT ✓

Scope (honest)

HSL is a non-learned input substrate — a possibility-proof from an independent, single-GPU project, not a benchmark-beating system. It gives exact structural signal; the meaning still comes from a model you stack on top. See the paper and live demo:

• 📄 Paper: A Feasibility Study of Change-Rate-Based Multimodal Unification (Zenodo)
• 🌐 Live demo: https://holo-demo-p5txmh4dda-as.a.run.app
• 💻 HoLo project: https://github.com/Woojiggun/holo-hsl

Changelog

0.5.1 — docs only: "Practical notes" (heterogeneous channel scales — normalize at the model input boundary; empty-input behavior on both paths; Fourier = bit-pattern spectrum, phase is cyclic). PyPI metadata now points at this dedicated repo.

0.5.0 — substrate-ablation toolkit (hsl_embedding.ablation): channel-group selection (feature_groups / select_channels), the frozen 256×18 value-LUT export (value_lut), and capacity-matched control substrates (ControlEmbedding: hsl / learned / random / permuted) sharing HSL's exact context dims and layout — controlled A/Bs over the value geometry, reproducible from pip install alone. Core encoder untouched: outputs bit-identical to 0.4.0; the base substrate remains zero-parameter (the learned control is an explicitly-labeled experimental baseline).

0.4.0 — fast paths & exactness hardening. Feature values are unchanged — bit-identical to 0.3.0 (verified over text/image/audio/random/edge inputs × all flag combos):

• Tensor / GPU path: Embedding()(ids) with integer tensors [..., L] — batched, device-agnostic, bit-identical to the bytes path (measured ~30× faster than the 0.3 bytes path on CUDA, ~2.7× on CPU).
• embed() now computes straight from 256-entry LUTs (no per-call bit unpacking) — valid precisely because of the anchor rule: every byte departs from the same virtual origin 0, so every per-byte channel is a pure function of the byte's own value.
• boundary made exact at every input length: 0.3.0 accumulated the windowed transition energy in a float32 running sum, which silently rounded the boundary channel above ~1.4 MB of input (on a 3 MB random input, ~44% of rows were off by up to 1.0). Now closed-form per-window sums with a float64 divide — exact at any length. All other channels were already exact; no approximation ships.
• Documented the identity Δ(v) ≡ binary-reflected Gray code v ^ (v >> 1) — adjacent byte values differ in exactly one Δ coordinate (raw bits flip up to all 8, e.g. 127→128); exhaustive anchor-rule tests added (every byte's Δ is identical alone, after any prefix, at any position).
• Removed the dead legacy chain-mode helpers (_xor_delta, _integrate, _bits_to_bytes) — only the per-byte anchor rule ships.

License & citation

MIT License — © 2026 Jinhyun Woo (ggunio5782@gmail.com). Free to use, modify, and distribute, including for commercial use — the only condition is that the copyright notice and attribution to Jinhyun Woo are kept. See LICENSE.

@software{woo_hsl_2026,
  author = {Jinhyun Woo},
  title  = {HSL: a byte-native, modality-agnostic signal embedding},
  year   = {2026},
  doi    = {10.5281/zenodo.20581805},
  url    = {https://github.com/Woojiggun/hsl-embedding}
}