🌐 Taylor-Data: Large-Scale Neural Dynamics & Optimization Dataset (V4)

Taylor-Data is a comprehensive, large-scale dataset containing 2 Billion parameter transitions and loss landscape interactions collected across diverse neural network architectures, optimization regimes, and multi-scale horizons.

It is designed for training World Models of Neural Dynamics, Meta-Optimizers, Quasi-Newton Credit Assignment Networks, and Continual Learning Controllers.

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📌 Overview & Purpose

Traditional optimization operates locally via first-order derivatives without holistic awareness of loss landscape geometry, higher-order curvature, or multi-step trajectory evolution.

Taylor-Data provides high-fidelity, structured trajectory transitions to train models capable of:

• Modeling second-order loss curvature and Taylor series consequences $\Delta L(\theta, \delta)$.
• Predicting analytical derivative dynamics and chain-rule transitions without explicit backpropagation.
• Simulating multi-horizon kinematic parameter evolution across complex loss landscapes.
• Performing selective, surgical parameter interventions and continual learning.

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📦 Dataset Composition (2 Billion Transitions)

The dataset is partitioned into three specialized subsets:

Subset Name	Volume	Description
base_moe_v4	1,000,000,000	Canonical 148-D state representations paired with multi-directional geometric probes (Newton, Hessian, Orthogonal, SPSA, NES, LoRA, Langevin) and true $\Delta L$ consequences.
expert_e8_derivatives	500,000,000	Analytical chain-rule derivative transitions and gradient vector mappings under parameter displacement steps across real architectures.
expert_e9_forward	500,000,000	Multi-horizon kinematic rollouts ($H \in {4, 8, 16, 32, 64, 128}$) with adaptive Brownian diffusion and noise scale dynamics $\sigma \propto \sqrt{H}$.

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🔬 Feature Schema

Each sample is stored in high-performance Parquet format (Zstandard compression) containing 32-dimensional canonical coordinate blocks:

• s_148 / s_0_148 (FixedSizeList[float16, 148]): Compact 148-D kinematic state vector (normalized weights, velocities, accelerations, momentum, spectral rank, SNR, Rayleigh quotient, loss EMA history, and layer topology metadata).
• delta_32 / dW_32 / dW_accum_32 (FixedSizeList[float16, 32]): Parameter perturbation and action vectors.
• delta_L (float32): Ground-truth scalar loss variation observed on the target landscape.
• grad_32 (FixedSizeList[float16, 32]): True analytical gradient vectors for derivative modeling.
• s_target_148 (FixedSizeList[float16, 148]): Future state vector reached after horizon $H$.
• horizon_H (int16): Step horizon ($4 \le H \le 128$).
• noise_level (float32): Applied perturbation magnitude during the rollout trajectory.

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⚙️ Optimization & Landscape Diversity

The transitions encompass a wide spectrum of synthetic and real optimization dynamics:

• Landscape Geometries: Ill-Conditioned QR Haar ($\kappa \in [1, 10^6]$), Rosenbrock ravines, Barren Plateaus, High-Order Polynomial Wells, Non-Smooth $L_1$/Cusp frontiers, and Discrete Quantized landscapes.
• Optimization Algorithms: Momentum SGD, Nesterov, AdamW, Muon (Newton-Schulz Matrix Orthogonalization), SPSA (Zero-Order), NES (Evolutionary Strategies), and Langevin Diffusion.

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📄 License & Terms

This dataset is released under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License (CC-BY-NC-ND-4.0).