Easy to anticipate, hard to compute: boundary dependence finds the computed outputs that entropy patching misses
Mirrored from arXiv — NLP / Computation & Language for archival readability. Support the source by reading on the original site.
Computer Science > Computation and Language
arXiv:2610.11790 (cs)
[Submitted on 8 Oct 2026]
Title:Easy to anticipate, hard to compute: boundary dependence finds the computed outputs that entropy patching misses
Authors:Nicolás Vera Zúñiga
View a PDF of the paper titled Easy to anticipate, hard to compute: boundary dependence finds the computed outputs that entropy patching misses, by Nicol\'as Vera Z\'u\~niga
View PDF
HTML (experimental)
Abstract:Byte-level language models such as the Byte Latent Transformer (BLT) group bytes into patches and run their large global model once per patch. BLT starts a patch where a small model's next-byte entropy is high, so global compute goes where the next byte is hard to predict. We show that this rule has a systematic blind spot: positions whose type is predictable but whose value must be computed, such as the number after "=" in a worked math solution. Under tight patch budgets, entropy-triggered layouts skip these positions, and accuracy on them collapses. In Meta's BLT-1B with patch starts on 10% of bytes, the entropy rule puts a patch start at 16% of the computed results in GSM8K solutions and gets 19.0% of them exactly right; a boundary after each "=" at the same patch count gets 51.8%, and entropy combined with a label-free boundary-dependence signal gets 67.1% (default layout at 26% of bytes: 76.8%). The gap survives adapting BLT-1B to the budget with low-rank fine-tuning (32.9% vs 72.7%, three runs per rule, paired p < 1e-200) and grows with model size in byte models trained from scratch at a 10% budget: at 1M, 12M and 50M parameters, boundary dependence beats entropy on final answers by -1.6, +10.1 and +19.8 points, and at 50M it gets 35.9% of computed results against 13.9% (3 seeds each). BLT's entropy-jump rule helps neither target at 50M. The entropy trigger of Scratchpad Patching is likewise indistinguishable from random scratchpads on final answers (5.6% vs 5.9%, 5 seeds), while answer-start scratchpads give 38.1%. The effect is specific to computed values: copies and lookups gain little, and values the model cannot compute gain nothing. Boundary dependence, the rise in the model's own loss when a patch start is removed, measured per two-byte context, finds these positions without labels: combined with entropy it beats the hand-written rule on computed results.
| Comments: | 13 pages, 4 figures, 6 tables. Code, logs and results: this https URL (archived: doi:https://doi.org/10.5281/zenodo.23238215) |
| Subjects: | Computation and Language (cs.CL) |
| Cite as: | arXiv:2610.11790 [cs.CL] |
| (or arXiv:2610.11790v1 [cs.CL] for this version) | |
| https://doi.org/10.48550/arXiv.2610.11790
arXiv-issued DOI via DataCite (pending registration)
|
Full-text links:
Access Paper:
- View PDF
- HTML (experimental)
- TeX Source
View a PDF of the paper titled Easy to anticipate, hard to compute: boundary dependence finds the computed outputs that entropy patching misses, by Nicol\'as Vera Z\'u\~niga
Additional Features
References & Citations
Loading...
Bookmark
Bibliographic Tools
Code, Data, Media
Demos
Related Papers
About arXivLabs
Bibliographic and Citation Tools
Bibliographic Explorer Toggle
Bibliographic Explorer (What is the Explorer?)
Connected Papers Toggle
Connected Papers (What is Connected Papers?)
Litmaps Toggle
Litmaps (What is Litmaps?)
scite.ai Toggle
scite Smart Citations (What are Smart Citations?)
Code, Data and Media Associated with this Article
alphaXiv Toggle
alphaXiv (What is alphaXiv?)
Links to Code Toggle
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub Toggle
DagsHub (What is DagsHub?)
GotitPub Toggle
Gotit.pub (What is GotitPub?)
Huggingface Toggle
Hugging Face (What is Huggingface?)
ScienceCast Toggle
ScienceCast (What is ScienceCast?)
Demos
Replicate Toggle
Replicate (What is Replicate?)
Spaces Toggle
Hugging Face Spaces (What is Spaces?)
Spaces Toggle
TXYZ.AI (What is TXYZ.AI?)
Recommenders and Search Tools
Link to Influence Flower
Influence Flower (What are Influence Flowers?)
Core recommender toggle
CORE Recommender (What is CORE?)
arXivLabs: experimental projects with community collaborators
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.
Discussion (0)
Sign in to join the discussion. Free account, 30 seconds — email code or GitHub.
Sign in →No comments yet. Sign in and be the first to say something.