Tensor Logic Community Implementation

This project translates Tensor Logic: The Language of AI into a runnable, well-tested Python codebase. It serves two complementary purposes:

1. Learning companion – walk through each section of the paper with annotated code and executable experiments.
2. Reusable library – import tensor_logic into your own projects to build neural, symbolic, kernel, graphical, or embedding-based systems using tensor equations.

Getting Started

python3 -m venv .venv
source .venv/bin/activate
pip install -e .
python3 -m pytest  # run the full validation suite

If you use pre-commit, install the hooks once via pre-commit install.

For optional tutorial dependencies (Apple MLX + Weights & Biases logging), install:

pip install -e .[examples]

Learn the Paper by Coding

The docs/ directory contains a guided reading of the paper with links into the code:

• docs/paper_companion.md – section-by-section outline mapping paper concepts to modules.
• docs/library_usage.md – short recipes that exercise the core APIs.
• docs/tutorials/neurosymbolic_recommendation.md – build a neuro-symbolic recommendation pipeline end-to-end.
• docs/tutorials/mlx_xor_classifier.md – train a neural network with MLX and bridge the weights back into tensor logic.

Prefer working directly in notebooks? Each test under tests/ doubles as an executable example; start with tests/models/test_neural.py to explore Section 4.1.

Library Overview

Paper Section	Code	Tests	Highlights
§3 Tensor Logic	tensor_logic/core/{tensor,ops,equation,program}.py	tests/core/	Named-axis tensors, joins, projections, inference, derivatives
§4.1 Neural	tensor_logic/models/neural.py	tests/models/test_neural.py	MLPs, convolutions, GNN layer, single-head attention
§4.2 Symbolic	tensor_logic/models/symbolic.py	tests/models/test_symbolic.py	Recursive ancestor reasoning with tensor joins
§4.3 Kernel	tensor_logic/models/kernel.py	tests/models/test_kernel.py	Linear kernel construction and prediction
§4.4 Graphical	tensor_logic/models/graphical.py	tests/models/test_graphical.py	Bayesian marginal inference via tensor equations
§5 Embeddings	tensor_logic/models/embedding.py	tests/models/test_embedding.py	Superposition reasoning in embedding space

Using the Library

from tensor_logic import Tensor, TensorStore, TensorProgram
from tensor_logic.models.neural import (
    DenseLayerSpec,
    build_mlp_program,
)

store = TensorStore()
store.add(Tensor("X", ("i",), [1.0, -2.0, 0.5]))
store.add(Tensor("W1", ("h", "i"), [[0.5, -0.3, 0.8], [-0.2, 0.4, 0.1]]))
store.add(Tensor("W2", ("o", "h"), [[1.0, -1.5]]))

program = build_mlp_program(
    store=store,
    input_name="X",
    input_axes=("i",),
    layer_specs=[
        DenseLayerSpec(weight_name="W1", output_name="Hidden"),
        DenseLayerSpec(weight_name="W2", output_name="Output"),
    ],
)
program.forward()

print(store.get("Output").data)

See docs/library_usage.md for more examples spanning symbolic reasoning, kernel machines, graphical models, and embedding-based queries.

Development Workflow

• Python ≥ 3.9 (see pyproject.toml for dependencies)
• Run python3 -m pytest before proposing changes
• Keep docstrings and inline comments focused on intent; the repository is meant to be read alongside the paper
• Contributions should extend docs/ to explain new ideas or experiments