Examples

The default interface is torch.Tensor. Start with python examples/torch_quickstart.py. Expected output is approximately [11.1, 8.2, 17.3], with temperature gradient [7, 10, 3].

Core snippets may omit setup; run the linked script or the expanded full source. Native tg.Tensor supports standalone execution without Torch, as well as currently unsupported Torch features: hierarchy memory, distributed execution, structured control flow, custom reducers, and direct native Tensor IR / checkpoint inspection. Ordinary aggregation, GCN, diffusion and radius examples use Torch.

Every example is an ordinary user program — none calls a Tiga algorithm operator. Each page below explains the problem being solved (with a schematic and the formula), then shows its core snippet and expandable complete source. All of them run from a source checkout after installing Tiga and the example's dependencies. The CPU starting point is python examples/message_passing_autograd.py:

python examples/message_passing_autograd.py

CUDA examples require a supported NVIDIA GPU and the cuda extra. Install Torch separately before Tiga for Torch examples; native examples run without it. Distributed and visualization examples have additional requirements documented on their pages. A successful run under auto does not by itself demonstrate JIT execution; inspect execution diagnostics.

Message passing and graph algorithms

Example	What it computes
message_passing_autograd.py	custom neighbor aggregation with Torch autograd; inspect diagnostics to distinguish compiled VJP from semantic replay
gcn.py	a GCN layer: weighted sum of neighbor features (SpMM) with automatic gradients
diffusion.py	one explicit Euler diffusion step over a graph
custom_reducer.py	a neighbor mean written as custom (sum, count) reducer algebra
compiler_probes/pagerank.py	20 PageRank iterations captured as one rolled repeat op — a compiler probe

Dynamic and generated relations

Example	What it computes
stencil_message_passing.py	von Neumann macro, five-point periodic averaging and Torch autograd
distance_metrics.py	Euclidean defaults, custom cosine radius and normalized cosine kNN
radius_autograd.py	differentiable messages on a radius relation, with selected neighbors held fixed during backward
knn_message_passing.py	an exact k-nearest-neighbor graph feeding a message-passing consumer

Distributed and memory hierarchy

Example	What it computes
distributed_halo.py	one graph split across two processes with automatic halo exchange
hierarchical_memory.py	tg.execution budgets, spill and value snapshots
paged_giant_graph.py	a 1M-node graph saved to disk, streamed page by page with prefetch, result written back
auto_offload.py	a per-CSR size threshold that offloads topology to disk, with optional page read-ahead

Tensor kernels, programs and Torch interop

Example	What it computes
tensor_matmul.py	matrix multiply C = A·B with compiler-derived gradients for both operands
complex_autograd.py	differentiates through complex-number tensors (conjugate-Wirtinger gradients)
linear_recurrence.py	causal linear-attention recurrence fused into one CUDA kernel from generic map/cumsum/contract
graph_program.py	automatic cross-kernel capture with @tg.jit: horizontal kernel fusion
joint_autograd.py	forward and backward compiled into one executable
torch_interop.py	torch tensors calling a Tiga UDF with zero-copy storage sharing
torch_library.py	a UDF registered as a torch.library op, Inductor-compatible
edge_nn_message_passing.py	a torch.nn MLP on every edge, compiled into one fused tile kernel

Visualization

Example	What it computes
gpu_heatmap.py	turns a scalar field into an RGB heatmap with tensor broadcast and arithmetic
visualize_fields.py	relaxes steady heat conduction on a triangulated disc (Jacobi via mean reducer), rendered as particles, Delaunay mesh and GIF video
visualize_mesh.py	loads an OBJ icosphere, diffuses a bump over its mesh edges, renders flat/wireframe/particles plus an orbit GIF, and exports PLY/OBJ for Blender
visualize_gaussians.py	renders a colored torus of anisotropic 3-D Gaussians as splats and as a ray-marched density volume, plus an orbit GIF

Linear solvers and control flow

Example	What it computes
fem_poisson_minimal.py	Poisson in three steps: define a neighbor operator, solve, check the answer
fem_poisson.py	advanced Poisson solve: fixed iterations and load gradients
meshfree_linear_solve.py	the same solver style on a radius graph generated from point positions
solvers.py	one linear_solve entry — method="cg" / "bicgstab" / "richardson" — as plain Python loops under @tg.jit
nonlinear_solve.py	nonlinear diffusion −∇·((1+u²)∇u) = f solved by Picard fixed-point iteration, VJP through the loop

Attention and dense relations

Example	What it computes
full_attention.py	exact attention with no mask — every query attends every key
causal_dense_relation.py	causal attention expressed as a triangular graph — no masking code
varlen_causal_attention.py	independent causal sequences composed with Graph.cat and Graph.triangular
tile_pruned_attention.py	approximate attention that skips value work for selected tiles after computing scores; forward only

Current native example boundary

The examples above are executable claims, not API sketches. Coverage boundaries live in one canonical place: native and Torch-adapter support matrix.