Ill-Posedness Evolved in the Deep: Adaptive Evolutionary Latent Optimization, An Application to Recovering Volatility
Bibliographic record
Abstract
Optimizing complex high-dimensional latent spaces is a fundamental challenge in fields such as quantitative finance, molecular design, and structured data modeling, particularly when addressing ill-posed inverse problems characterized by nonlinearity and implicit input-output relationships. We introduce Adaptive Evolutionary Latent Optimization (AdELO), a novel framework that synergistically combines evolutionary algorithms with generative and objective models to iteratively refine latent space representations and solve complex optimization tasks. AdELO operates by alternating between evolutionary optimization of latent vectors and fine-tuning of both the generative and objective models, effectively navigating the latent space to discover optimal solutions. In our implementation, we utilize beta-Variational Autoencoders (beta-VAEs) to represent the latent space and Physics-Informed Neural Networks (PINNs) to enforce underlying physical laws. We apply AdELO to the recovery of local volatility surfaces from option prices, a quintessential ill-posed inverse problem in financial mathematics known for numerical instability and sensitivity to noise. The volatility surface is parameterized using Gaussian Radial Basis Functions (RBFs) with smoothness priors imposed to regularize the problem. By integrating beta-VAEs and PINNs within the AdELO framework, we effectively reconstruct the local volatility surface from market data. Experimental results demonstrate that AdELO successfully recovers volatility surfaces with high accuracy and stability, mitigating the ill-posedness inherent in the inverse problem. The proposed framework not only advances methodologies for volatility surface recovery but also offers a generalizable optimization paradigm applicable to a wide spectrum of complex, highdimensional problems in science and engineering.
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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 | 0.007 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.002 | 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".