Nonuniform catalytic space and the direct sum for space
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
This paper initiates the study of k-catalytic branching programs, a nonuniform model of computation that is the counterpart to the uniform catalytic space model of Buhrman, Cleve, Kouck y, Lo and Speelman (STOC 2014). A k-catalytic branching program computes k boolean functions simultaneously on the same n-bit input. Each function has its own entry, accept and reject nodes in the branching program but internal nodes can otherwise be shared. The question of interest is to determine the conditions under which some form of a direct sum property for deterministic space can be shown to hold, or shown to fail. We exhibit both cases. There are functions that are correlated in such a way that their direct sum fails: a signicant amount of space can be saved by sharing internal computation among the k functions. By contrast, direct sum is shown to hold in some special cases, such as for the family of functions (l1 (l2 ( (ln 1 ln) ) where each li is a literal on variable xi, 1 i n and each stands individually for either^ or_.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it