Rethinking GSPO: The Perplexity-Entropy Equivalence
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866917045266808832 |
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| author | Liu, Chi |
| author_facet | Liu, Chi |
| contents | We provide a new perspective on GSPO's length-normalized importance ratios by establishing their connection to information-theoretic quantities. We show that GSPO's sequence-level weight $s(θ) = (π_θ/π_{θ_{\text{old}}})^{1/|y|}$ can be equivalently expressed as the inverse perplexity ratio $\text{PPL}_{θ_{\text{old}}}/\text{PPL}_θ$ and as the exponential cross-entropy change $\exp(ΔH)$. While the perplexity-entropy relationship follows from standard definitions, this observation provides a useful lens for understanding GSPO: the algorithm weights policy gradient updates by perplexity ratios, offering an information-theoretic interpretation of the importance weights. This perspective helps explain GSPO's empirical properties, including log-domain variance reduction through geometric averaging and stability in training mixture-of-experts models. We validate the mathematical equivalences and variance predictions through controlled experiments on mathematical reasoning tasks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_23142 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Rethinking GSPO: The Perplexity-Entropy Equivalence Liu, Chi Machine Learning Artificial Intelligence Computation and Language We provide a new perspective on GSPO's length-normalized importance ratios by establishing their connection to information-theoretic quantities. We show that GSPO's sequence-level weight $s(θ) = (π_θ/π_{θ_{\text{old}}})^{1/|y|}$ can be equivalently expressed as the inverse perplexity ratio $\text{PPL}_{θ_{\text{old}}}/\text{PPL}_θ$ and as the exponential cross-entropy change $\exp(ΔH)$. While the perplexity-entropy relationship follows from standard definitions, this observation provides a useful lens for understanding GSPO: the algorithm weights policy gradient updates by perplexity ratios, offering an information-theoretic interpretation of the importance weights. This perspective helps explain GSPO's empirical properties, including log-domain variance reduction through geometric averaging and stability in training mixture-of-experts models. We validate the mathematical equivalences and variance predictions through controlled experiments on mathematical reasoning tasks. |
| title | Rethinking GSPO: The Perplexity-Entropy Equivalence |
| topic | Machine Learning Artificial Intelligence Computation and Language |
| url | https://arxiv.org/abs/2510.23142 |