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Playground
Write a small graph in the browser and read it six ways, live: the spec, the gradient, the plan, the StableHLO, the values, the picture.
Write a small graph and read it six ways. The engine on this page is the crate compiled to WebAssembly: your program records onto a real Tape, and every tab is the reading the library answers for it — the spec, the gradient differentiate appends, the plan an entry lowers to, the StableHLO it emits, the values a run computes, and the picture. Change a line and every reading remakes itself.
Loading the engine…
The tape language#
A program is a list of assignments, one per line. Each line records one or more nodes on the tape; a name is the symbol of the node it names. The language exists only on this page: it is a thin spelling of the calls Tape and Value already offer, so every reading it produces is one the crate produces.
| line | records |
|---|---|
w = parameter [2, 2] | a trainable parameter of that shape, seeded deterministically |
x = input [1, 2] | an input with a seeded default, fed per run |
c = leaf [3] | a constant |
b = parameter 0.5 | a rank-0 parameter holding that value; input 1.5 and leaf 2.0 likewise |
y = a + b, a - b, a * b, a / b, -a | elementwise arithmetic; a rank-0 operand is broadcast explicitly, and the spec shows it |
y = a @ b | the matrix product |
tanh(a), exp(a), ln(a), sqrt(a), sin(a), cos(a), relu(a) | maps |
sum(a) | the sum of every element, rank 0 |
sum_along(a, 1), log_softmax(a, 1), logsumexp(a, 1), softmax(a, 1), mean_along(a, 1) | one axis |
transpose(a) | the two axes of a matrix, swapped |
broadcast(a, [3, 4]), reshape(a, [12]) | shape changes |
2.0 | a numeric literal is a rank-0 leaf |
# ... | a comment |
Choose which scalar to differentiate and which interior to observe from the controls; the parameters are the wrt set, and the differentiate target must be rank 0 — sum it first if it is not. A shape that does not fit is refused before the crate sees it, with the two shapes in the message, the same way the recording line panics in Rust.
What to try#
- Record the README's loss,
w * x - ysquared, and watch the derivative append four Leaf-then-Add pairs: one gradient started at zero, one consumer's share added at a time. That is accumulation, stated once in the engine. - Add
h = tanh(x @ w)as a second line and observe it. One line of the plan turns fromfreedtokept; nothing else moves. - Turn on exact numerics. On this page no backend is ever on, so the plan's values do not change, and that is the point:
Exactis the interpreter's bits in every build. - Write
log_softmax(x @ w, 1)and read the StableHLO: the stable composition an industrial compiler receives, one fused primitive and the plain arithmetic around it.