Joshua R. Gutierrez

Joshua leads Axion Deep Labs as a research-first C-corporation: every commercial product is, by design, an applied counterpart to an open research question, and every research program is built to a standard of operational rigor inherited from a decade of full-stack engineering. He sets the laboratory's scientific direction, owns its grant portfolio, and writes the production code that ships its products.

As Principal Investigator on PERSIST — the laboratory's flagship research program — Joshua designed and led a 57-experiment study across 19 architectures and three datasets (CIFAR-100, CUB-200-2011, RESISC-45), applying persistent homology to two-dimensional cross-sections of neural loss landscapes to test whether landscape topology predicts a model's resistance to catastrophic forgetting. The headline result — that the H0 Betti number predicts elastic-weight-consolidation regularization benefit, replicating across datasets at ρ = 0.76 on CIFAR-100 (p = 2×10⁻⁴) and ρ = 0.86 on RESISC-45 (p = 2.4×10⁻⁶) — establishes loss-landscape connectivity as a mitigation-sensitivity marker for continual-learning interventions.

The PERSIST manuscript, “Basin Fragmentation Predicts Regularization Benefit in Continual Learning,” is in preparation as an arXiv preprint, incorporating Phase I-A (ImageNet-100 scale validation) and Phase I-B (cross-dataset sweep, 114 runs). Phase I scale validation is currently underway on the NMSU Discovery HPC cluster (NVIDIA A100-PCIE-40GB), with eight ImageNet-100 configurations complete across architectures from 20M to 304M parameters (ViT-B, ViT-L, ConvNeXt-S/B/L, ResNet-101, EfficientNet-B5, DenseNet-201). An NSF SBIR Phase I application ($275,000) on topology-informed continual learning for production ML systems is in progress.

His second active research line, EXP-04, investigates the topological dynamics of grokking: the abrupt generalization phase transition observed in small transformers trained on modular arithmetic. Joshua identified and corrected three methodological bugs that invalidated earlier published approaches in this area — a structural invariance issue in H0 feature counts on grid filtrations, a single-batch dataloader masking commutator-defect dynamics, and a missing tensor detach that forced the discrete Hessian to be symmetric by construction. The corrected pipeline now resolves a 700× dynamic range in H0 total persistence and a clean pre-grokking saddle-to-basin transition in Hessian sharpness.

Beyond PERSIST and EXP-04, Joshua maintains a parallel applied program. He is the architect and full-stack author of six production AI/SaaS products: DeepAudit AI, an SEO audit platform built on AWS Lambda + Puppeteer with 60+ checks across 9 categories and AI-generated remediation plans; Made4Founders, a multi-tenant B2B platform that orchestrates per-platform AI rewrites and image adaptation across seven social channels; Vesper, an autonomous penetration-testing platform built on a dual-agent Operator/Analyst architecture (PyQt6 desktop + FastAPI backend, 12K+ LOC); Site2CRM, a real-time lead-capture CRM with a published Zapier integration and a WordPress plugin; Forma, a builder product line; and QUANTA, a quantum-computing education platform.

His engineering work runs across PyTorch, persistent homology (Ripser, GUDHI), Hessian analysis, distributed training on university HPC, AWS serverless infrastructure, and Next.js/FastAPI product engineering. He writes the research code, the production code, the grant prose, and the marketing copy, and is open to research-scientist, applied-research, and technical AI-leadership conversations alongside his work at Axion Deep Labs.