On the Softmax Bottleneck of Recurrent Language Models
Bibliographic record
Abstract
Recent research has pointed to a limitation of word-level neural language models with softmax outputs. This limitation, known as the softmax bottleneck refers to the inability of these models to produce high-rank log probability (log P) matrices. Various solutions have been proposed to break this bottleneck, including Mixture of Softmaxes, SigSoftmax, and Linear Monotonic Softmax with Piecewise Linear Increasing Functions. They were reported to offer better performance in terms of perplexity on test data. A natural perception from these results is a strong positive correlation between the rank of the log P matrix and the model's performance. In this work, we show via an extensive empirical study that such a correlation is fairly weak and that the high-rank of the log P matrix is neither necessary nor sufficient for better test perplexity. Although our results are empirical, they are established in part via the construction of a rich family of models, which we call Generalized SigSoftmax. They are able to create diverse ranks for the log P matrices. We also present an investigation as to why the proposed solutions achieve better performance.
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How this classification was reachedexpand
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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.002 | 0.001 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".