Intracortical Speech (Willett et al., 2023)
Measured by Willett, Kunz, Fan, Hochberg, Druckmann, Shenoy & Henderson · Nature 620 (2023)
Inputs
The measured or assumed values behind the calculations, each with its source.
- N = 125000
- 125,000-word large-vocabulary decoding (Abstract): the reference operating point
- rate = 62 word/min
- Decoding rate of attempted speech (Abstract)
- P = 0.762
- 1 − 23.8% word error rate on the 125,000-word vocabulary (Abstract). On a constrained 50-word set the WER was 9.1%.
Strictest ITR
Each scoring method is an upper bound on the channel, so the headline is the strictest (smallest) one for this entry. Use the score selector on the home page to view any single method across entries.
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Error-corrected words per minute
(1 − WER) × rate = (1 − 0.238) × 62 = 47.2 net word/min
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Shannon per-word entropy of English
H ≈ 5.0 bits/word (1 bit/char × 5 chars/word)
Credits only the information in the English actually produced, independent of vocabulary size.
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Information transfer rate
47.2 word/min × 5.0 bits/word ÷ 60 s/min = 3.93 bits/s
What counts as a bit depends on the action space. The number of distinguishable actions and how likely each one is are design choices of the task, not the sensing hardware. The same modality can present a fixed set of targets, a set pruned per step by a grammar or language model, or a continuous control space. Each of these changes how many actions are live and how the probability mass is spread, and therefore the information per selection. Read the action space below before comparing headline numbers across entries.
Action space
What the user can produce at each step, and how those options are distributed.
- Structure
- Context-dependent (the live set changes per step)
- Size
- 125000 distinguishable actions
- Prior
- Context-conditioned: likelihoods depend on prior actions
- Notes
- Intracortical decoding of attempted speech through an n-gram/neural language model over a 125k-word vocabulary. The language model reweights candidates by context, so the uniform-prior Wolpaw figure is not directly comparable to the atlas English-output convention.
Comparability The strictest bound here is the Shannon entropy of the output text, under one predictor held constant across the whole atlas (≈1 bit per character). That shared predictor makes it directly comparable to every other text entry (keyboards, spellers, silent speech and speech BCIs) regardless of prior or vocabulary size. For most text interfaces it comes out tighter than the raw-selection bounds, but not always. Where a small vocabulary makes Wolpaw tighter, that wins instead. Any Fitts, Wolpaw or log₂(N) figure shown below is another bound on the same channel. Switch the home-page score selector to compare one across entries.
Other score types
Bounds the atlas keeps out of the default strictest headline: as-reported figures, alternate task conditions, or raw-channel ceilings that shouldn't win the headline by default. Each still carries a score type, so the home-page selector ranks this entry on it when you choose that type. Read its derivation before comparing across entries.
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Bits per selection (Wolpaw formula)
B = log2(N) + P*log2(P) + (1-P)*log2((1-P)/(N-1)) = log2(125000) + 0.762*log2(0.762) + 0.238*log2(0.238/124999) = 12.11 bits / selection
Term 1 is the information if every choice were correct; terms 2-3 subtract the bits lost to the error rate, assumed spread evenly over the other N-1 targets.
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Selections per second
T = 0.96774 s/selection -> 1 / 0.96774 = 1.033 selections/s
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Information transfer rate
ITR = B * selections/s = 12.11 * 1.033 = 12.514 bits/s
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Achieved-bitrate credit per net-correct word
N = 125,000 → log2(N − 1) = log2(124,999) ≈ 16.93 bits per net-correct selection (Nuyujukian 2015, which introduced the metric, used log2(N); at this N the difference is negligible).
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Net-correct word rate
net-correct = 2P − 1 = 2(0.762) − 1 = 0.524 of words. At 62 word/min (0.968 s/word) → 0.524 × 62 / 60 = 0.541 correct/s.
A word error commits the wrong word rather than timing out, so incorrect = 1 − P. Same N (125,000), word accuracy (76.2%) and rate (62 wpm) as the entry's Wolpaw calc. As that calc's own caveat notes, the 125k-word vocabulary is context-reweighted by the language model each step, so feeding it into log2(N − 1) is a large-vocabulary capacity view (~17 bits/word) — raw channel capacity, not communication, analogous to the nagel code-space figure. The ranked communication rate is the 3.93 bits/s word-entropy Shannon.
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Achieved bitrate
16.93 bits × 0.541 correct/s = 9.17 bits/s.
Source
- Authors
- Willett, Kunz, Fan, Hochberg, Druckmann, Shenoy & Henderson
- Publication
- Nature 620, 2023
- Reference
- Open-access full text (PMC)