## 5 Conclusions
In line with the above, future extensions of our method could incorporate LPPLS diagnostics or hybridize machine learning with parametric bubble models to improve interpretation capabilities and early warning. Our main results indicate that when the probability of instability is very low or near zero, conditions exist for a bubble to start forming; that is, the market index or stock prices will gradually increase at an accelerating rate. The evidence indicates that high probabilities of financial bubbles do not materialize suddenly or spontaneously; instead, they rise incrementally over time, providing valuable insights to investors, regulators, and market participants. Conversely, when the probability of instability is very high (indicating the full development of the crisis), the likelihood of an emerging bubble diminishes to values close to zero. An important contribution of this study lies in using the generative capabilities of the trained GGRBM to perform a novel form of sensitivity analysis. Rather than solely focusing on the direct interpretability of the latent representations, which remains an open challenge in neural-network-based models, we propose an alternative route that exploits the RBM's ability to generate synthetic samples under controlled conditions. We can simulate and analyze hypothetical market scenarios by clamping certain input features (e.g., volatility and return lags) and allowing others to vary. These synthetic cases are then evaluated using the full RBM-BRF pipeline, offering a detailed view of the model's responses under different economic configurations. Our approach provides three key advantages. First, it allows us to explore the model's behavior under stylized economic regimes, such as high-return/low-volatility environments often associated with speculative bubbles, without requiring explicit labeling of real data. Second, it offers an economically intuitive way to evaluate model outputs beyond standard statistical performance metrics, thus enhancing model transparency. Third, it opens the door to integrating unsupervised learning as a feature extraction technique and a diagnostic tool for stress-testing market hypotheses. Notwithstanding the above, our strategy has limitations. While it reveals how the model responds to stylized combinations of stock market features, it does not provide a mechanistic or structural explanation of how specific hidden units encode economic behaviors such as volatility clustering, leverage effects, or herding. The analysis is scenario-based rather than grounded in the inner workings of the learned latent space. Therefore, further studies are necessary to deepen interpretability. These could include correlation analyses between hidden unit activations and canonical market indicators or the construction of event-aligned activation profiles to examine how hidden units behave in proximity to known financial crises or bubble periods. Such approaches would complement our generative analysis and help bridge the neural representations and economic insight gap. We believe this generative sensitivity analysis, still underexplored in the financial modeling literature, offers a valuable tool for practitioners and researchers interested in detecting and understanding financial instability. It highlights the dual utility of unsupervised learning models as powerful input transformers and economic scenario simulators. While this generative sensitivity analysis does not yield a direct economic interpretation of individual hidden units, it nonetheless provides a robust framework for uncovering latent patterns consistent with known market behaviors. A limitation of the present study lies in the challenge of benchmarking our model against alternative early warning systems. As noted in the literature, there is no widely accepted framework for evaluating the predictive accuracy of models that aim to detect financial bubbles or anticipate systemic regime shifts.