Positioning of TC in ML Software stacks

TC is a concise notation which can easily be used to write ML layers. The positioning of TC in the ML ecosystem aims at achieving the following:

  1. Easy to integrate with any ML framework and any tensor library.
  2. Carry the minimal amount of information to write layers concisely.
  3. Be automatically translated to HPC implementations on various runtimes / HW.
  4. Carry the minimal amount of information to support automatic transformation to HPC implementations.
  5. Be usable by our intended target audience.
  6. Be non-ambiguous and non-surprising.

For now, we detail the first two points below:

Implications of ML Framework Integration

The simple fact that TC wants to be ML-framework agnostic has deeper implications that we will look into lifting in the future.

One TC function one kernel

A single TC function must correspond to exactly one synthesized HPC kernel. If TC doesn’t guarantee that invariant, it will have to handle the integration of kernel launches and their proper synchronization in each framework it targets. This is off the table for now because it is counter-productive; the moment one operates at this level of control, one is effectively competing with frameworks and wants to write one’s own.

No Variable Allocations

TC cannot allocate memory and handle host <-> accelerator copies. This is for the same reason stated above. As a consequence there is never a notion of TC variable definition, local scope in a TC, allocations etc (i.e. all the basic stuff you expect from a Programming Language). As a consequence TC is not a Programming Language but a concise notation. For now, it should not try to be a Programming Language.

As a result of this, everything in TC should be either an input or output. For example: consider the TC definition below:

def softmax(float(N, D) I) -> (O, expsum) {
    expsum(n) +=! exp(I(n, d))
       O(n, d) =  exp(I(n, d)) / expsum(n)

In this TC, expsum is a temporary variable that needs to be computed but since TC doesn’t do allocations itself, we set it as another output. User can chose to ignore this output. We will work on enhancing this and deal with temporary allocations better in future.

Graph Level

For allocations, variable definitions, unique names, SSA etc. one probably wants to work at the NNVM / XLA level which is not what TC wants to work at for now. Probably if one wants function calls (i.e. TC def functions calling other TC def functions) then the TC notation is probably not where it should happen. TC calling built-in functions with side effects is fine though.

Minimal information to write ML layers concisely

This should be as simple as possible but no simpler. Let’s discuss TC in the context of alternative solutions:

C-style loops

C loops over multi-dimensional arrays are non-ambiguous and general. For the purpose of writing programs operating on dense tensors, they are quite verbose and generally quite tedious to write and maintain code in. Still C loops are very informative because they are understandable by anyone who wants to program a layer. So C loops are a good fit for emitting a baseline implementation and debugging. TC must be able to emit simple C loops that compiles and run.


Halide could be viewed as a specialization of C loops for image processing. This specialization is a trade-off, you can only express box regions within boxes (no triangular loops). This specialization fits our application domain and we are using it heavily. Halide’s backwards shape inference allows removing much of the boilerplate specification for intermediate tensors. The tradeoff is you need to specify input tensor shapes (also in TC), output tensor shapes (omitted in TC) and the ranges of all reduction indices (omitted in TC).


The current TC implementation sits somewhere here; less verbose than Halide, more verbose than matrix algebra. The inference procedure has been one subtle tradeoff in TC. It has been designed to follow an intuitive enough mental model, but may still evolve in the future towards greater expressiveness, see Range Inference.

Matrix Languages

Matrix languages such as Matlab are very concise and make sense mathematically but don’t naturally extend to tensors (what does the operator * mean on 3-D tensors?). As a consequence loops need to be introduced prematurely; TC avoids this pit-hole.