PHINN: Persistent Homology Inspired Neural Network for Outlier Synthesis

Battle Count: 54

PHINN is highly relevant to quantitative trading in the domain of extreme event modeling and risk management. It matches practitioner-grade jump-diffusion models (Merton, Bates GARCH-Jump) in statistical tail coverage (ECov95: 0.91 vs 0.93-0.94) while substantially exceeding them in structural shape fidelity (β-RMSE: 0.71 vs 2.11-2.29). Applications include: (1) generating plausible crisis scenarios for portfolio stress-testing, (2) modeling flash crashes and liquidity freezes with topological fidelity, (3) regulatory compliance (DORA, CCAR/DFAST), (4) understanding structural dynamics of market disruptions beyond statistical moments. However, it is primarily a scenario generation tool rather than a direct trading signal generator, and the financial subset (54 events) is relatively small. The sub-500ms inference makes it operationally viable for real-time risk assessment.

Extremely high complexity combining: (1) persistent homology computation via Ripser with sliding-window embeddings, (2) dynamic window sizing with total variation, (3) differentiable persistence landscape losses with Gaussian kernel approximations, (4) rectified flow matching with cross-attention conditioning, (5) multivariate joint Vietoris-Rips filtrations on product point clouds, (6) fine-tuned LLM (Mistral-7B with LoRA) for NL-to-Betti translation, (7) MAML-style meta-learning across domains, (8) retrieval-augmented generation with topological memory banks, (9) certified adversarial robustness (Type-I ℓ∞ certificates + Type-II structural detection), (10) streaming homology updates with union-find structures. Requires expertise in TDA, generative modeling, NLP, meta-learning, and adversarial ML. Witness complexes needed for scalability beyond T≈5,000.

Code is proprietary to Defense.Codes/CapaCloud Corp and cannot be shared externally. ERP-Disruption data (62 events) are under NDA. However, SynTop-v2 (15,000 synthetic series) is released, AIS-Multi public subset (41 events) results are provided in Appendix C, full hyperparameters are documented, and all quantitative claims include 95% CIs over 5 seeds. The operational decision study (n=2 per group) is acknowledged as underpowered. No GitHub repository is provided.