Invariance, Encodings, and Generalization: Learning Identity Effects With Neural Networks
Bibliographic record
Abstract
Often in language and other areas of cognition, whether two components of an object are identical or not determines if it is well formed. We call such constraints identity effects. When developing a system to learn well-formedness from examples, it is easy enough to build in an identity effect. But can identity effects be learned from the data without explicit guidance? We provide a framework in which we can rigorously prove that algorithms satisfying simple criteria cannot make the correct inference. We then show that a broad class of learning algorithms, including deep feedforward neural networks trained via gradient-based algorithms (such as stochastic gradient descent or the Adam method), satisfies our criteria, dependent on the encoding of inputs. In some broader circumstances, we are able to provide adversarial examples that the network necessarily classifies incorrectly. Finally, we demonstrate our theory with computational experiments in which we explore the effect of different input encodings on the ability of algorithms to generalize to novel inputs. This allows us to show similar effects to those predicted by theory for more realistic methods that violate some of the conditions of our theoretical results.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.005 | 0.032 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.005 |
| Scholarly communication | 0.001 | 0.006 |
| Open science | 0.001 | 0.004 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.002 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".