x\_tymatrA'Nm {'= \m= sD #31 , 28Hyperdimensional…
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{'= \m= sD #31 , 28Hyperdimensional Connections – A Lossless, Queryable Semantic Reasoning Framework
Hi all, I'm happy to share a focused research paper and benchmark suite highlighting the Hyperdimensional Connection Method, a key module of the open-source \MatrixTransformer\ https://github.com/fikayoAy/MatrixTransformer library
What is it?
Unlike traditional approaches that compress data and discard relationships, this method offers a
lossless framework for discovering hyperdimensional connections across modalities, preserving full matrix structure, semantic coherence, and sparsity.
This is not dimensionality reduction in the PCA/t-SNE sense. Instead, it enables:
\-Queryable semantic networks across data types (by either using the matrix saved from the connection\_to\_matrix method or any other ways of querying connections you could think of)
Lossless matrix transformation (1.000 reconstruction accuracy)
100% sparsity retention
Cross-modal semantic bridging (e.g., TF-IDF ↔ pixel patterns ↔ interaction graphs)
Benchmarked Domains:
\- Biological: Drug–gene interactions → clinically relevant pattern discovery
\- Textual: Multi-modal text representations (TF-IDF, char n-grams, co-occurrence)
\- Visual: MNIST digit connections (e.g., discovering which 6s resemble 8s)
🔎 This method powers relationship discovery, similarity search, anomaly detection, and structure-preserving feature mapping — all \*\*without discarding a single data point\*\*.
Usage example:
from matrixtransformer import MatrixTransformer
import numpy as np
\# Initialize the transformer
transformer = MatrixTransformer(dimensions=256)
\# Add some sample matrices to the transformer's storage
sample\_matrices = \
np.random.randn(# Image-like matrix
np.eye(10) # Identity matrix
np.random.randn(15, 5), # Random square matrix
np.random.randn(20, 0), # Rectangular matrix
np.diag(np.random.randn(12)iagonal matrix
\]
\# Store matrices in the transformer
transformer.matricple\_matrices
\# Optional: Add some metadata about the matrices
transformer.layer\type': 'image', 'source': 'synthetic'},
{'type': 'identity', 'source': 'standard'},
{'type': 'random', 'source': 'synthetic'},
{'type': 'rectangular', 'source': 'synthetic'},
{'type': 'diagonal', 'source': 'synthetic'}
\]
\# Find hyperdimensional connections
print("Finding hyperdimensional connections...")
connections = transformer.find\_hyperdimensional\_connections(num\_dims=8)
\# Access stored matrices
print(f"\\nAccessing stored matrices:")
print(f"Number of matrices stored: {len(transformer.matrices)}")
for i, matrix in enumerate(transformer.matrices):
print(f"Matrix {i}: shape {matrix.shape}, type: {transformer.\_detect\_matrix\_type(matrix)}")
\# Convert connections to matrix representation
print("\\nConverting connections to matrix format...")
coords3d = \[\]
for i, matrix in enumerate(transformer.matrices):
coords = transformer.\_generate\_matrix\_coordinates(matrix, i)
coords3d.append(coords)
coords3d = np.array(coords3d)
indices = list(range(len(transformer.matrices)))
\# Create connection matrix with metadata
conn\_matrix, metadata = transformer.connections\_to\_matrix(
connections, coords3d, indices, matrix\_type='general'
)
print(f"Connection matrix shape: {conn\_matrix.shape}")
print(f"Matrix sparsity: {metadata.get('matrix\_sparsity', 'N/A')}")
print(f"Total connections found: {metadata.get('connection\_count', 'N/A')}")
\# Reconstruct connections from matrix
print("\\nReconstructing connections from matrix...")
reconstructed\_connections = transformer.matrix\_to\_connections(conn\_matrix, etadata)
\# Compare original vs reconstructed
print(f"Original connections: {len(connections)} matrices")
print(f"Reconstructed connections: {len(reconstructed\_connections)} matrices")
\# Access specific matrix and its connections
matrix\_idx = 0
if matrix\_idx in connections:
print(f"\\nMatrix {matrix\_idx} connections:")
print(f"Original matrix shape: {transformer.matrices\[matrix\_idx\].shape}")
print(f"Number of connections: {len(connections\[matrix\_idx\])}")
\# Show first few connections
for i, conn in enumerate(connections\[matrix\_idx\]\[:3\]):
target\_idx = conn\['target\_idx'\]
strength = conn.get('strength'')
print(f" -> Connected to matrix {target\_idx} (shape: {transformer.matrices\[target\_idx\].shape}) with strength: {strength}")
\# Example: Process a specific matrix through the transformer
print("\\nProcessing a matrix through transformer:")
test\_matrix = transformer.matrices\[0\]
matrix\_type = transformer.\_detect\_matrix\_type(test\_matrix)
print(f"Detected matrix type: {matrix\_type}")
\# Transform the matrix
transformed = transformer.process\_rectangular\_matrix(test\_pe)
print(f"Transformed matrix shape: {transformed.shape}")
Clone from github and Install from wheel file
git clone [https://github.com/fikayoAy/MatrixTransformer.git https://github.com/fikayoAy/MatrixTransformer.git
cd MatrixTransformer
pip install dist/matrixtransformer-0.1.0-py3-none-any.whl
Links:
\- Research Paper (Hyperdimensional Module): \Zenodo DOI\ https://doi.org/10.5281/zenodo.16051260
Parent Library – MatrixTransformer: \GitHub\ https://github.com/fikayoAy/MatrixTransformer
MatrixTransformer Core Paper: \https://doi.org/10.5281/zenodo.15867279\ https://doi.org/10.5281/zenodo.15867279
Would love to hear thoughts, feedback, or questions. Thanks!
#technology
matriix, /,
_in[fo aes ) , 28),
{'= \m= sD #31 , 28Hyperdimensional Connections – A Lossless, Queryable Semantic Reasoning Framework
Hi all, I'm happy to share a focused research paper and benchmark suite highlighting the Hyperdimensional Connection Method, a key module of the open-source \MatrixTransformer\ https://github.com/fikayoAy/MatrixTransformer library
What is it?
Unlike traditional approaches that compress data and discard relationships, this method offers a
lossless framework for discovering hyperdimensional connections across modalities, preserving full matrix structure, semantic coherence, and sparsity.
This is not dimensionality reduction in the PCA/t-SNE sense. Instead, it enables:
\-Queryable semantic networks across data types (by either using the matrix saved from the connection\_to\_matrix method or any other ways of querying connections you could think of)
Lossless matrix transformation (1.000 reconstruction accuracy)
100% sparsity retention
Cross-modal semantic bridging (e.g., TF-IDF ↔ pixel patterns ↔ interaction graphs)
Benchmarked Domains:
\- Biological: Drug–gene interactions → clinically relevant pattern discovery
\- Textual: Multi-modal text representations (TF-IDF, char n-grams, co-occurrence)
\- Visual: MNIST digit connections (e.g., discovering which 6s resemble 8s)
🔎 This method powers relationship discovery, similarity search, anomaly detection, and structure-preserving feature mapping — all \*\*without discarding a single data point\*\*.
Usage example:
from matrixtransformer import MatrixTransformer
import numpy as np
\# Initialize the transformer
transformer = MatrixTransformer(dimensions=256)
\# Add some sample matrices to the transformer's storage
sample\_matrices = \
np.random.randn(# Image-like matrix
np.eye(10) # Identity matrix
np.random.randn(15, 5), # Random square matrix
np.random.randn(20, 0), # Rectangular matrix
np.diag(np.random.randn(12)iagonal matrix
\]
\# Store matrices in the transformer
transformer.matricple\_matrices
\# Optional: Add some metadata about the matrices
transformer.layer\type': 'image', 'source': 'synthetic'},
{'type': 'identity', 'source': 'standard'},
{'type': 'random', 'source': 'synthetic'},
{'type': 'rectangular', 'source': 'synthetic'},
{'type': 'diagonal', 'source': 'synthetic'}
\]
\# Find hyperdimensional connections
print("Finding hyperdimensional connections...")
connections = transformer.find\_hyperdimensional\_connections(num\_dims=8)
\# Access stored matrices
print(f"\\nAccessing stored matrices:")
print(f"Number of matrices stored: {len(transformer.matrices)}")
for i, matrix in enumerate(transformer.matrices):
print(f"Matrix {i}: shape {matrix.shape}, type: {transformer.\_detect\_matrix\_type(matrix)}")
\# Convert connections to matrix representation
print("\\nConverting connections to matrix format...")
coords3d = \[\]
for i, matrix in enumerate(transformer.matrices):
coords = transformer.\_generate\_matrix\_coordinates(matrix, i)
coords3d.append(coords)
coords3d = np.array(coords3d)
indices = list(range(len(transformer.matrices)))
\# Create connection matrix with metadata
conn\_matrix, metadata = transformer.connections\_to\_matrix(
connections, coords3d, indices, matrix\_type='general'
)
print(f"Connection matrix shape: {conn\_matrix.shape}")
print(f"Matrix sparsity: {metadata.get('matrix\_sparsity', 'N/A')}")
print(f"Total connections found: {metadata.get('connection\_count', 'N/A')}")
\# Reconstruct connections from matrix
print("\\nReconstructing connections from matrix...")
reconstructed\_connections = transformer.matrix\_to\_connections(conn\_matrix, etadata)
\# Compare original vs reconstructed
print(f"Original connections: {len(connections)} matrices")
print(f"Reconstructed connections: {len(reconstructed\_connections)} matrices")
\# Access specific matrix and its connections
matrix\_idx = 0
if matrix\_idx in connections:
print(f"\\nMatrix {matrix\_idx} connections:")
print(f"Original matrix shape: {transformer.matrices\[matrix\_idx\].shape}")
print(f"Number of connections: {len(connections\[matrix\_idx\])}")
\# Show first few connections
for i, conn in enumerate(connections\[matrix\_idx\]\[:3\]):
target\_idx = conn\['target\_idx'\]
strength = conn.get('strength'')
print(f" -> Connected to matrix {target\_idx} (shape: {transformer.matrices\[target\_idx\].shape}) with strength: {strength}")
\# Example: Process a specific matrix through the transformer
print("\\nProcessing a matrix through transformer:")
test\_matrix = transformer.matrices\[0\]
matrix\_type = transformer.\_detect\_matrix\_type(test\_matrix)
print(f"Detected matrix type: {matrix\_type}")
\# Transform the matrix
transformed = transformer.process\_rectangular\_matrix(test\_pe)
print(f"Transformed matrix shape: {transformed.shape}")
Clone from github and Install from wheel file
git clone [https://github.com/fikayoAy/MatrixTransformer.git https://github.com/fikayoAy/MatrixTransformer.git
cd MatrixTransformer
pip install dist/matrixtransformer-0.1.0-py3-none-any.whl
Links:
\- Research Paper (Hyperdimensional Module): \Zenodo DOI\ https://doi.org/10.5281/zenodo.16051260
Parent Library – MatrixTransformer: \GitHub\ https://github.com/fikayoAy/MatrixTransformer
MatrixTransformer Core Paper: \https://doi.org/10.5281/zenodo.15867279\ https://doi.org/10.5281/zenodo.15867279
Would love to hear thoughts, feedback, or questions. Thanks!
#technology
matriix, /,
_in[fo aes ) , 28),
5
1
| 12,000 mlx | |
| 18 | |
| 6 |