Balancing Embedding Spectrum for Recommendation
Bibliographic record
Abstract
Modern recommender systems heavily rely on high-quality representations learned from high-dimensional sparse data. While significant efforts have been invested in designing powerful algorithms for extracting user preferences, the factors contributing to good representations have remained relatively unexplored. In this work, we shed light on an issue in the existing pairwise learning paradigm (i.e., embedding collapse), that the representations tend to span a subspace of the whole embedding space, leading to a suboptimal solution and reducing the model capacity. Specifically, we show that alignment of positive pairs is equivalent to a low-pass filter causing users and items to collapse to a constant vector. While negative sampling can partially mitigate this issue by acting as a high-pass filter to balance the spectrum, leading to an incomplete collapse. To tackle this issue, we present a novel learning paradigm DirectSpec, which directly optimizes the spectrum distribution to ensure that users and items effectively span the entire embedding space. We demonstrate that many self-supervised learning algorithms without explicit negative sampling can be considered as special cases of DirectSpec. Furthermore, we show that optimizing the spectrum inappropriately could also be detrimental to data representation, where the key lies in a dynamic balance between alignment of positive pairs and spectrum balancing. Finally, we propose an enhanced and practical implementation DirectSpec + to balance the embedding spectrum more adaptively and effectively. We implement DirectSpec + on two popular recommender models: matrix factorization and LightGCN. Our experimental results demonstrate its effectiveness and efficiency over competitive baselines.
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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 | 0.010 |
| 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 | 0.001 |
| Scholarly communication | 0.001 | 0.003 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.004 | 0.002 |
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".