Unveiling the Transport Dynamics of Neural Networks : a Least Action Principle for Deep Learning
Bibliographic record
Abstract
Residual connections are ubiquitous in deep learning, since besides residual networks and their variants, they are also present in Transformers. The dynamic view of residual networks views them as analogous to a forward Euler scheme for an ordinary differential equation. We can then say that residual networks transport input points in space, time being represented by the depth of the network. This viewpoint has, for example, led to new architecture inspired by other numerical schemes for differential equations. On the other hand, a bias of residual networks towards small perturbations of the input has been observed. In the context of the dynamic view of residual networks mentioned above, this means a bias towards a small transport cost. In a first paper, we experimentally verify that this bias is beneficial and should be encouraged and we show that forcing the network to approximate an optimal transport map by regularizing its transport cost improves its generalization ability and training stability. In a second paper, we show that applying this transport regularization to successive neural modules that don’t back-propagate to each other amounts to following a gradient flow for minimizing the loss in distribution space, thus improving the performance of module-wise training, which consumes a lot less memory than end-to-end training. In a third paper, we propose a detector of adversarial and out-of-distribution samples that is based on the view of residual networks as discrete dynamical systems and show that transport regularization makes adversarial detection easier.
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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 | 0.002 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.001 | 0.004 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.002 | 0.004 |
| 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".