Why PyTorch Doesn't Work for Spatial Storage

Why PyTorch Doesn’t Work for Spatial Storage

The Fundamental Mismatch

PyTorch is designed for tensor operations on fixed-size arrays. MagickCache requires dynamic spatial storage with variable geometry. These are fundamentally incompatible paradigms.

PyTorch’s Tensor Model

What PyTorch Excels At

# PyTorch tensor operations
x = torch.tensor([[1, 2, 3], [4, 5, 6]])  # Fixed 2x3 matrix
y = torch.tensor([[7, 8, 9], [10, 11, 12]])  # Same dimensions required
result = torch.matmul(x, y.T)  # Matrix multiplication

Characteristics:

Fixed dimensions: Tensors have predetermined shapes
Dense operations: Every element participates in calculations
Batch processing: Operations on entire arrays at once
GPU parallelization: SIMD operations across tensor elements

What PyTorch Struggles With

# What we need for spatial storage
space = SpatialStorage()
space.store_at((15.7, 23.1, 8.9), "data1")  # Arbitrary coordinates
space.store_at((156.3, 2.7, 99.1), "data2")  # Completely different location
results = space.query_sphere((15.0, 23.0, 9.0), radius=2.0)  # Variable results

Problems:

Dynamic coordinates: Can’t predefine tensor dimensions
Sparse data: Most spatial coordinates are empty
Variable results: Query results have unpredictable sizes
Geometric operations: Spatial relationships aren’t matrix math

Tensor Operations vs Spatial Operations

Matrix Multiplication (PyTorch)

[a b] [e f]   [ae+bg af+bh]
[c d] [g h] = [ce+dg cf+dh]

Properties:

Fixed input/output dimensions
Every element affects every result
Parallelizable with SIMD
Mathematically regular

Spatial Query (BALLS Cache)

Query: Find all points within sphere(center=(0,0,0), radius=5)
Result: Variable number of points with irregular distribution

Properties:

Dynamic input/output sizes
Only nearby elements affect results
Requires spatial indexing
Geometrically irregular

Memory Layout Issues

PyTorch Memory Model

# Dense tensor - every position has a value
tensor = torch.zeros(1000, 1000, 1000)  # 1 billion floats allocated
# Uses 4GB+ memory even if mostly empty

Spatial Storage Memory Model

# Sparse spatial storage - only occupied coordinates
spatial = SpatialStorage()
spatial.store_at((100, 500, 750), value)  # Only allocates what's needed
spatial.store_at((200, 600, 850), value)  # Minimal memory usage

Dynamic vs Static Structure

PyTorch: Static Structure

# Must know dimensions at creation time
model = torch.nn.Linear(784, 128)  # Fixed: 784 inputs → 128 outputs
# Cannot dynamically add new input dimensions or change structure

Spatial Storage: Dynamic Structure

# Can add data anywhere, anytime
storage.store_at((x, y, z), data)  # Any coordinates allowed
storage.expand_region(new_bounds)  # Dynamic space expansion

Indexing and Access Patterns

PyTorch Indexing

# Array-style indexing
tensor[0, 5, 10]  # Access element at fixed indices
tensor[0:5, :, 10:20]  # Slice rectangular regions

Spatial Indexing

# Coordinate-based indexing
storage.get_at((15.7, 23.1, 8.9))  # Access by spatial coordinate
storage.query_sphere(center, radius)  # Query by geometric relationship

Computational Complexity

PyTorch Operations

Matrix multiplication: O(n³)
Element-wise operations: O(n)
Reduction operations: O(n)

All operations scale with tensor size.

Spatial Operations

Spatial query: O(r³) where r = search radius
Point insertion: O(log n) with spatial indexing
Neighborhood search: O(k) where k = results found

Operations scale with geometric parameters, not total data size.

GPU Utilization Differences

PyTorch GPU Usage

# Utilizes all GPU cores for dense operations
result = torch.matmul(large_tensor_a, large_tensor_b)  # Every core working

Spatial Storage GPU Usage

// Custom CUDA kernels for spatial operations
__global__ void spatial_query_kernel(Point* points, Query query, Result* results) {
    // Each thread handles one spatial region
    // Irregular workload distribution
}

Why We Built Custom CUDA Kernels

PyTorch Limitations

No spatial primitives: No built-in sphere queries, distance calculations
Tensor constraints: Can’t efficiently represent sparse spatial data
Memory overhead: Dense tensor allocation for sparse spatial data
Fixed operations: Limited to linear algebra operations

Custom CUDA Benefits

Spatial primitives: Native sphere queries, distance calculations, spatial indexing
Memory efficiency: Only allocate space for actual data points
Geometric operations: Optimized for spatial relationships
Variable workloads: Handle irregular spatial distributions

Performance Comparison

PyTorch Approach (Hypothetical)

# Trying to do spatial query with PyTorch
def pytorch_spatial_query(tensor_space, center, radius):
    # Create coordinate grids
    x_coords = torch.arange(tensor_space.shape[0])
    y_coords = torch.arange(tensor_space.shape[1])
    z_coords = torch.arange(tensor_space.shape[2])

    # Compute distances (very expensive)
    distances = torch.sqrt((x_coords - center[0])**2 +
                          (y_coords - center[1])**2 +
                          (z_coords - center[2])**2)

    # Find elements within radius
    mask = distances <= radius
    return tensor_space[mask]  # Still O(n³) complexity!

BALLS Cache Approach

// Native spatial query - O(r³) complexity
SearchResult* spatial_query(SpatialStorage* storage, Point center, float radius) {
    // Only check grid cells within radius
    GridCell* relevant_cells = get_cells_in_sphere(center, radius);

    // Only examine points in relevant cells
    for (cell in relevant_cells) {
        check_points_in_cell(cell, center, radius);
    }
}

Framework Design Philosophy

PyTorch Philosophy

“Provide building blocks for neural networks through tensor operations”

Assumes dense, regular computational patterns
Optimizes for batch processing
Designed for gradient-based optimization

BALLS Cache Philosophy

“Provide native spatial storage with geometric operations”

Assumes sparse, irregular spatial patterns
Optimizes for proximity relationships
Designed for spatial locality

When PyTorch Makes Sense

Neural Network Training

# Perfect for this
loss = criterion(model(batch_input), batch_targets)
loss.backward()
optimizer.step()

Dense Linear Algebra

# Perfect for this
embeddings = torch.matmul(input_vectors, weight_matrix)

When Spatial Storage Makes Sense

Proximity Searches

# Perfect for this
nearby_items = storage.query_sphere(user_location, search_radius)

Dynamic Spatial Data

# Perfect for this
storage.store_at(gps_coordinate, sensor_reading)
spatial_clusters = storage.find_dense_regions()

The Bottom Line

PyTorch is a hammer, and not every problem is a nail.

For spatial storage, we need:

Geometric operations, not tensor operations
Sparse efficiency, not dense parallelism
Dynamic structure, not fixed dimensions
Spatial indexing, not array indexing

This is why MagickCache required custom C implementation with specialized CUDA kernels - no existing framework was designed for our spatial storage paradigm.

Sometimes you have to build the tool that doesn’t exist yet.