Neurogebra: A Symbolic–Neural Framework for Transparent and Composable Deep Learning

Neurogebra is an open-source Python library (v2.5.3) that treats mathematical transparency as a first-class design requirement in deep learning. Unlike PyTorch and TensorFlow, which represent every neural network operation as an opaque numerical primitive, Neurogebra represents every component, activation functions, loss functions, optimisers, metrics, and layer transforms, as a first-class symbolic expression built on SymPy and NumPy. Each expression is simultaneously a LaTeX-renderable formula, analytically differentiable, numerically evaluable, and annotated with structured educational metadata. Core Library The library ships with 285 verified mathematical expressions across 10 ML domains (activations, losses, regularisers, algebra, calculus, statistics, linear algebra, optimisation, metrics, and transforms), verified by 470+ automated tests. Over 100 curated datasets are included for immediate experimentation, spanning classification, regression, synthetic patterns, time series, and image benchmarks. Training Observatory The Training Observatory is the first training logging system to render exact symbolic forward and backward pass equations layer by layer during live training. At expert verbosity, every layer displays its precise mathematical operation in real-time colour-coded in the terminal-giving practitioners complete visibility into what is happening inside the network at every step. Observatory Pro Observatory Pro extends the Training Observatory into a six-component active diagnostic engine: (1) Adaptive Logging, which reduces expert-level log volume by 80–90% by staying quiet on healthy epochs and escalating automatically when anomalies are detected; (2) Automated Health Warnings, a ten-rule engine that detects dying ReLU neurons, vanishing and exploding gradients, NaN/Inf values, overfitting, underfitting, loss stagnation, weight stagnation, loss divergence, and activation saturation issuing structured diagnoses with specific remediation steps during training, not post-hoc; (3) Epoch Summarisation, reporting mean, standard deviation, minimum, and maximum for every tracked metric across all batches per epoch; (4) Tiered Storage, writing events to three separate NDJSON files for basic metrics, health warnings, and full debug detail; (5) Visual Dashboard, generating a self-contained interactive HTML report with Chart.js loss curves, accuracy charts, timing bars, and a health diagnostics timeline; and (6) Training Fingerprint, capturing a complete reproducibility snapshot including random seed, SHA-256 dataset hash, all library versions, hardware specifications, OS, git commit hash, model architecture hash, and hyperparameters. Additional Features Neurogebra includes a from-scratch autograd engine built on Value and Tensor objects for educational transparency, framework bridges to export verified models directly to PyTorch, TensorFlow, and JAX, and an EducationalTrainer with real-time step-by-step commentary. In controlled experiments, Observatory Pro detected a 58.3% dying ReLU condition that seven epochs of standard aggregate logging completely concealed. Installation: pip install neurogebra GitHub: https://github.com/fahiiim/NeuroGebra Documentation: https://neurogebra.readthedocs.io Licence: MIT