autoeq

autoeq — plaintext math → LaTeX, live in the browser

A 3.3M-parameter encoder-decoder transformer that turns human-typed math into LaTeX on every keystroke. Trained entirely on synthetic data whose plaintext renderer encodes a human prior over ambiguous notation (/2a means "divide by 2a", sq means √, x1 means x_1, sin x/2 means (sin x)/2 …). Beam search (k=3) surfaces alternatives when the input is genuinely ambiguous.

• Live demo: https://mie00.github.io/autoeq/
• Code, generator, training, eval: https://github.com/mie00/autoeq

x = -b +- sq(b^2-4ac)/2a     →  x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}
e^-x^2/2                     →  e^{-\frac{x^2}{2}}
bold E = -grad phi           →  \mathbf{E}=-\nabla\phi
n_eff = c/v_p                →  n_{\mathrm{eff}}=\frac{c}{v_p}
delta x                      →  \delta x   (alt: \Delta x)
int_0^2pi sin x dx           →  \int_0^{2\pi}\sin x\,dx
{x^2 if x>0; 0 otherwise}    →  \begin{cases}x^2&\text{if}\,x>0\\0&\text{otherwise}\end{cases}
[[a,b],[c,d]]                →  \begin{bmatrix}a&b\\c&d\end{bmatrix}
\underline{M}                →  \underline{M}          (macros pass through)

Files

Graph I/O:

encoder: src_ids[B,S] int32, src_len[B] int32
      → cross_k[L,B,H,S,dh], cross_v[L,B,H,S,dh], src_bias[B,1,1,S]
decoder: tgt_ids[B,T_new] int32, pos_offset[1] int32,
         self_k[L,B,H,T_past,dh], self_v, cross_k, cross_v, src_bias
      → logprobs[B,T_new,V], new_self_k[L,B,H,T_past+T_new,dh], new_self_v

Decoding must be constrained beam search over the output tokens (braces balanced, &/\\ only inside environments, and \ followed only by letters) — a reference implementation lives in the repo (autoeq/decode.py, and the identical web/decode.js for the browser). Input: characters (≤128); output: characters + LaTeX macros as single tokens (420 tokens); vocab.json has everything needed.

Model

Pre-LN transformer, d_model 192, 4 heads, FFN 768, 3 encoder + 3 decoder layers, learned positions, tied decoder embeddings — 3.29M parameters. Trained 60k steps (batch 512, AdamW, label smoothing 0.1, EMA) ≈ 40 minutes on one RTX 4090, on ~30M unique synthetic examples (65% full expressions, 30% typing prefixes with aligned partial LaTeX, 5% famous formulas).

Evaluation (v1.4)

Latency: ~10.0 ms/keystroke typing the quadratic formula in onnxruntime-web (WASM, 1 thread), down from 12.6 ms in v1.3 despite the larger vocabulary — the beam search now selects the top k+1 candidates directly instead of sorting the whole vocabulary at every step.

Comparing against v1.3: the evaluation set is regenerated from the generator each release, so these numbers are not comparable across versions. Scored on one evaluation set both models can be run on, v1.4 gets 92.8% greedy / 91.2% beam and v1.3 gets 92.6% / 91.2% — pass-through cost nothing on the notation v1.3 already handled.

What's new in v1.4

Any macro the grammar does not model is now passed through exactly as typed, instead of being approximated by whatever the vocabulary happened to contain (\underline{M} previously decoded to \cup\nabla\{M\}).

164 macros are single output tokens. Everything else is spelled character by character behind a \ escape token, so coverage is not limited to that list and macros the model never saw in training still pass through. The plaintext for such a macro is its LaTeX, which is what keeps one input mapping to one canonical output.

Intended use & limitations

Real-time LaTeX entry in editors, note apps, chat UIs. Multi-line align, \left/\right and colors remain unreachable, and environments cannot be passed through the way macros can. Prose is only supported in quotes ("speed of light" → \text{…}). Trained on synthetic data only — unusual personal notation may be misread; the shown alternatives and explicit parentheses always let you force a reading. Some distinctions plain text simply cannot carry — bold vs arrow vectors, upright vs italic labels, delta vs Delta — so those are offered as alternatives rather than guessed at.

License

Apache License 2.0 — code and weights.