HEE_3D

HEE_3D is a Mathematica project that chains a bank of ONNX models to iteratively build a three-dimensional tensor from an input latent vector. The repository ships the full set of pre-trained models together with the Wolfram Language utilities required to orchestrate the inference loop.

Repository structure

Path	Description
onnx/model_*.onnx	Sequential ONNX checkpoints (model_1.onnx … model_101.onnx). Each stage refines the tensor produced by the previous model.
model.m	Mathematica package that loads the ONNX models and exposes the helper functions documented below.
example.nb	Wolfram Notebook with a minimal walkthrough for interactive exploration.

Requirements

• Wolfram Mathematica 12.1 or newer.
• ONNXRuntimeLink paclet for accelerated execution (Mathematica's built-in ONNX runtime also works on CPU).
• ~1.3 GB of free disk space for the collection of ONNX checkpoints.

Installation

1. Clone the repository and ensure the onnx/ directory containing model_1.onnx … model_101.onnx remains adjacent to model.m.

2. Launch Mathematica and set the working directory to the project root:

   SetDirectory["/path/to/HEE_3D"]; (* Update with your local path *)
   << model.m

3. Load the ONNXRuntimeLink paclet if you plan to offload execution to GPU:

   Needs["ONNXRuntimeLink`"];
   ONNXRuntimeLoadLibrary["GPU"]; (* optional; defaults to CPU if omitted *)

Usage

The model.m package defines two public helpers:

• geogen[lzt_] — consumes a latent tensor lzt and runs it through the 101-stage ONNX chain, returning the accumulated tensor tgt.
• findlzt[func_] — numerically estimates an appropriate latent tensor by solving a root-finding problem based on a user-supplied function func.

A minimal session looks like:

(* Load the package as shown in the installation section *)
latent = findlzt[targetFunction];
result = geogen[latent];
Dimensions[result]

The helper returns a tensor of shape {101, 1, 1}. Mathematica's standard visualisation tools (for example, ListPointPlot3D, ListSliceDensityPlot, ListDensityPlot3D) work well for exploring the output.

Notebook walkthrough

Open example.nb in Mathematica to follow a guided, cell-by-cell execution of the same workflow. The notebook preloads model.m, prepares a latent tensor, and demonstrates exporting intermediate tensors for further analysis.

Troubleshooting

• ONNX import errors — Confirm that your Mathematica version can import ONNX models. Installing the ONNXRuntimeLink paclet resolves most compatibility issues.
• Dimension mismatches — geogen expects lzt with dimensions {101, 1}. The helper reshapes it internally, but providing tensors in other shapes may trigger pattern-match errors.
• Performance — Running 101 ONNX models sequentially is compute-intensive. Consider enabling GPU support through ONNXRuntimeLink or batching experiments to amortise the load time of the checkpoints.

Citation

If you use HEE_3D in academic or industrial research, please cite the repository and any related publications that describe the method.