Neural Classifiers with Limited Connectivity and Recurrent Readouts
Bibliographic record
Abstract
For many neural network models in which neurons are trained to classify inputs like perceptrons, the number of inputs that can be classified is limited by the connectivity of each neuron, even when the total number of neurons is very large. This poses the problem of how the biological brain can take advantage of its huge number of neurons given that the connectivity is sparse. One solution is to combine multiple perceptrons together, as in committee machines. The number of classifiable random patterns would then grow linearly with the number of perceptrons, even when each perceptron has limited connectivity. However, the problem is moved to the downstream readout neurons, which would need a number of connections as large as the number of perceptrons. Here we propose a different approach in which the readout is implemented by connecting multiple perceptrons in a recurrent attractor neural network. We prove analytically that the number of classifiable random patterns can grow unboundedly with the number of perceptrons, even when the connectivity of each perceptron remains finite. Most importantly, both the recurrent connectivity and the connectivity of downstream readouts also remain finite. Our study shows that feedforward neural classifiers with numerous long-range afferent connections can be replaced by recurrent networks with sparse long-range connectivity without sacrificing the classification performance. Our strategy could be used to design more general scalable network architectures with limited connectivity, which resemble more closely the brain neural circuits that are dominated by recurrent connectivity. SIGNIFICANCE STATEMENT The mammalian brain has a huge number of neurons, but the connectivity is rather sparse. This observation seems to contrast with the theoretical studies showing that for many neural network models the performance scales with the number of connections per neuron and not with the total number of neurons. To solve this dilemma, we propose a model in which a recurrent network reads out multiple neural classifiers. Its performance scales with the total number of neurons even when each neuron of the network has limited connectivity. Our study reveals an important role of recurrent connections in neural systems like the hippocampus, in which the computational limitations due to sparse long-range feedforward connectivity might be compensated by local recurrent connections.
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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 | 0.001 | 0.011 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.003 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| 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".