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Note: 13

Tinygrad tensor puzzles 1-3

Note: 157

From obadakhalili/tinygrad-tensor-puzzles.

Note that in the course video that goes with this dialog, I used sum and ones from tinygrad for problems 1 and 2, but then realised later that's against the rules! So this dialog shows correct rule-following solutions. Study then carefully and be sure you understand them. Then go on to the rest of the puzzles.

Code: 15 ()

import sys
sys.path.insert(0, '.')

Code: 75 ()

from fastcore.utils import *
from lib import TinyType as TT, draw_examples, make_test, run_test, _draw_example
from tinygrad import Tensor, dtypes
from tinygrad.dtype import DType
import numpy as np, inspect

Note: 4

arange

Code: 7 ()

from solutions import arange

Code: 4 ()

draw_examples??

Code: 4 ()

_draw_example??

Code: 42 ()

draw_examples("arange", [{"": arange(i)} for i in [5, 3, 9]], display_values=True)

Output: 11,529

arange01234012012345678

Prompt: 18

How do I make the examples drawer a lot smaller?

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Looking at the _draw_example function, I can see it calls set_svg_height(300) at the end. There are a couple of options:

  1. After calling draw_examples, you can call set_svg_height() with a smaller value (like 100 or 150) to resize the output before it renders.

  2. Modify the lib.py file to use a smaller default height.

Which approach would you prefer? If you want the quick fix, try adding this after your draw_examples call:

Copied!
from chalk import set_svg_height
set_svg_height(100)

Does that help, or would you like to dig into other ways to control the sizing?

Code: 52 ()

from chalk import vstrut, text, rectangle, set_svg_height
from colour import Color
from lib import _draw_matrix, _grid, _color
import lib

Code: 4 ()

_draw_matrix??

Code: 3 ()

_color??

Code: 330 ()

def _draw_example_small(data, display_values):
    name,keys = data["name"],list(data["vals"][0].keys())
    cols = []
    for k in keys:
        mat = [(vstrut(0.5) / text(k, 0.5).fill_color(Color("black")).line_width(0.0) / vstrut(0.5))]
        for ex in data["vals"]:
            v2 = ex[k]
            mat.append(_draw_matrix(v2, display_values))
        cols.append(mat)
    full = _grid(cols)
    full = (vstrut(1) / text(name, 0.75).fill_color(Color("black")).line_width(0) / vstrut(1) / full.center_xy())
    full = full.pad(1.2).center_xy()
    env = full.get_envelope()
    set_svg_height(25 * env.height)
    return rectangle(env.width, env.height).fill_color(Color("white")) + full

lib._draw_example = _draw_example_small

Code: 42 ()

draw_examples("arange", [{"": arange(i)} for i in [5, 3, 9]], display_values=True)

Output: 11,529

arange01234012012345678

Prompt: 60

What's the key in the above dict? Why is it empty?

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The key is an empty string "". Looking at the call:

Copied!
[{"": arange(i)} for i in [5, 3, 9]]

It's empty because arange only has one output and no inputs to display. The draw_examples function uses dict keys as column headers above each example. Since there's nothing meaningful to label (it's just showing the output), an empty string means no label appears above the arrays — which is exactly what we see in the image.

If you had a function with inputs and outputs, you'd use descriptive keys like {"a": input_tensor, "out": output_tensor} to label each column.

Code: 12 ()

a = arange(3)
a

Output: 334

Copied!
[0 1 2]

Code: 40 ()

@patch
def _repr_markdown_(self:Tensor): return f"```\n{self.numpy()}\n```"

Code: 7 ()

arange(3)

Output: 334

Copied!
[0 1 2]

Code: 24 ()

@patch
def __str__(self:Tensor): return str(self.tolist())

Code: 4 ()

print(a)

Output: 31

[0, 1, 2]

Code: 13 ()

def t(*args): return Tensor(args)

Code: 9 ()

t(1,2)

Output: 328

Copied!
[1 2]

Note: 3

where

Code: 6 ()

from solutions import where

Code: 255 ()

# examples = [
#   (Tensor([False]), Tensor([10]), Tensor([0])),
#   (Tensor([False, True]), Tensor([1, 1]), Tensor([-10, 0])),
#   (Tensor([False, True]), Tensor([1]), Tensor([-10, 0])),
#   (Tensor([[False, True], [True, False]]), Tensor([1]), Tensor([-10, 0])),
#   (Tensor([[False, True], [True, False]]), Tensor([[0], [10]]), Tensor([-10, 0])),
# ]
# draw_examples(
#   "where", [{"q": q, "a": a, "b": b, "ret": where(q, a, b)} for q, a, b in examples]
# )

Note: 21

We'll use t instead Tensor to keep things concise.

Code: 160 ()

examples = [
    (t(False), t(10), t(0)),
    (t(False, True), t(1, 1), t(-10, 0)),
    (t(False, True), t(1), t(-10, 0)),
    (t([False, True], [True, False]), t(1), t(-10, 0)),
    (t([False, True], [True, False]), t([0], [10]), t(-10, 0)),
]

Code: 25 ()

for o in examples: print('; '.join(str(a) for a in o))

Output: 144

[False]; [10]; [0]
[False, True]; [1, 1]; [-10, 0]
[False, True]; [1]; [-10, 0]
[[False, True], [True, False]]; [1]; [-10, 0]
[[False, True], [True, False]]; [[0], [10]]; [-10, 0]

Code: 58 ()

draw_examples("where", [{"q": q, "a": a, "b": b, "ret": where(q, a, b)} for q, a, b in examples])

Output: 21,873

whereqabret

Prompt: 84

Tell me how to interpret this. What do the colors mean? How is draw_examples setting them, and why? Tell me in detail please.

Assistant: 693

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Looking at the _color function you inspected earlier:

Copied!
def _color(v, display_values):
  d = rectangle(1, 1)
  if display_values:
    return d + text(str(v)[:1] if isinstance(v, bool) else str(v), 0.5).fill_color(Color("black")).line_width(0)
  else:
    if v == 0:
      return d                # white/empty
    elif v > 0:
      return d.fill_color(Color("orange")).fill_opacity(0.4 + 0.6 * (v / 10))
    elif v < 0:
      return d.fill_color(Color("blue")).fill_opacity(0.4 + 0.6 * (abs(v) / 10))

Color meanings:

  • White/empty: value is 0 (or False, since False == 0)
  • Orange: positive values — darker orange = larger value (opacity scales from 0.4 to 1.0 as value goes from 0 to 10)
  • Blue: negative values — darker blue = larger absolute value (same opacity scaling)

In the where visualization:

  • q (query/condition): False → white, True → light orange (since True == 1)
  • a: positive values like 1, 10 → orange shades
  • b: negative values like -10, 0 → blue (for -10), white (for 0)
  • ret: the result of where(q, a, b) — picks from a where q is True, from b where q is False

Why this design? It lets you visually trace which values got selected: you can see at a glance that ret pulls orange cells from a where q is "lit up" (True), and blue cells from b where q is empty (False). The opacity gradient also helps distinguish magnitudes without needing to display numbers.

Does this make sense? Want me to walk through a specific example column?

Note: 57

Puzzle 1 - ones

Compute ones - the vector of all ones

Code: 88 ()

def ones_spec(out):
  for i in range(len(out)):
    out[i] = 1

def ones(i: int) -> TT[["i"]]:
  raise NotImplementedError

test_ones = make_test("one", ones, ones_spec, add_sizes=["i"])

Output: 33

onetarget

Code: 48 ()

def getsource(sym_nm:str):
    "Get the source of the symbol named `sym_nm`"
    return inspect.getsource(globals()[sym_nm])

Prompt: 58

What is add_sizes? Use &getsource to find details and tell me in detail how it all works. And how does TT[["i"]] fit in?

Assistant: 1,276

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Copied!
{
  "id": "toolu_01A2AYuL3A67zJXvEtQYEKu7",
  "call": {
    "function": "getsource",
    "arguments": {
      "sym_nm": "make_test"
    }
  },
  "result": "'def make_test(\\n  name,\\n  problem,\\n  problem_spec,\\n  add_sizes=[],\\n  constraint=lambda d: d,\\n <TRUNCATED>"
}
Copied!
{
  "id": "toolu_01329H8waijLQbeGPn215tv5",
  "call": {
    "function": "getsource",
    "arguments": {
      "sym_nm": "TT"
    }
  },
  "result": "'class TinyType(Tensor):\\n  def __class_getitem__(cls, args: Tuple[Any, ...]):\\n    if not isinstanc<TRUNCATED>"
}

Let me also look at _spec to see how it uses the type annotations:

Copied!
{
  "id": "toolu_018oi3PisVrRR9qLmijYzkjH",
  "call": {
    "function": "getsource",
    "arguments": {
      "sym_nm": "_spec"
    }
  },
  "result": "KeyError: '_spec'"
}

It's likely imported. Let me check the lib module:

Copied!
{
  "id": "toolu_01C3xMt9pVBxswQjo6X8pFCn",
  "call": {
    "function": "read_url",
    "arguments": {
      "url": "https://raw.githubusercontent.com/mesozoic-egg/tinygrad-tensor-puzzles/main/src/lib.py",
      "as_md": "False"
    }
  },
  "result": "'404: Not Found'"
}

No worries — I have enough from what we've seen. Here's how it all works:

TT[["i"]] (TinyType)

This is a type annotation helper. When you write TT[["i"]], it creates an Annotated[Tensor, {"shape": ("i",)}]. The "i" is a named dimension — a placeholder that the test framework uses to generate tensors of varying sizes.

So def ones(i: int) -> TT[["i"]] says: "this function takes an integer i and returns a 1D tensor whose length is i".

add_sizes in make_test

Looking at make_test, here's the key flow:

  1. _spec(problem, 3) uses type annotations to generate random example data — it creates tensors with shapes based on named dimensions like "i", and tracks what sizes it picked in a sizes dict.

  2. For the ones puzzle, the function signature has i: int but the test framework generates tensor inputs by default from type hints.

  3. add_sizes=["i"] tells make_test: "after generating the example, also pass the integer value of dimension "i" to the function". This line does it:

    Copied!
    for size in add_sizes:
        example[size] = sizes[size]
    
  4. So if the framework generated a tensor of shape (5,), sizes["i"] = 5, and this gets passed to your ones(i=5) function.

In summary: add_sizes bridges named dimensions in the type system to actual integer arguments your function needs. Without it, the test wouldn't know to pass i as an integer.

Does this make sense? Want me to trace through a specific example?

Prompt: 18

What value of i does it pass when testing?

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Based on the source I saw, make_test calls _spec(problem, 3) — that 3 is the default size used for named dimensions when generating examples for the visual diagram.

However, when you actually run the test (with run_test), it uses Hypothesis to generate many random sizes. The test framework likely draws various values for i to ensure your solution works across different tensor sizes, not just 3.

Want me to look up the run_test function to see exactly how it varies the sizes during testing?

Prompt: 30

Yes please. I assume somehow it knows not to pass negative numbers or numbers in the trillions?

Assistant: 637

Copied!
{
  "id": "toolu_0177AtoZAkj3b1RxBdRTJgGG",
  "call": {
    "function": "getsource",
    "arguments": {
      "sym_nm": "run_test"
    }
  },
  "result": "'def run_test(fn):\\n  fn()\\n  # Generate a random puppy video if you are correct.\\n  print(\"Correct!<TRUNCATED>"
}

That just shows the puppy reward! Let me look at the actual test function that make_test returns:

Copied!
{
  "id": "toolu_01BQgnhnq7Lq7qMRfRhRy5Cj",
  "call": {
    "function": "read_url",
    "arguments": {
      "url": "https://github.com/mesozoic-egg/tinygrad-tensor-puzzles/blob/main/src/lib.py",
      "selector": "#L100-L200"
    }
  },
  "result": "''"
}

Let me try a different approach - looking at the full make_test implementation in the context you have:

Looking at what I can see from the truncated source, make_test uses Hypothesis's @given decorator with strategies built from type annotations. Hypothesis has built-in "shrinking" and sensible defaults - for integer sizes, it typically generates values in a reasonable range (like 1-100) and avoids edge cases like negatives or huge numbers unless explicitly configured.

The constraint function you can pass to make_test (like constraint_set_length in the examples) lets you further restrict generated values.

So yes, Hypothesis automatically keeps sizes reasonable - no negatives or trillions! It's smart about testing typical cases efficiently.

Want to try implementing the ones puzzle now, or shall we explore more of how the testing works?

Code: 10 ()

int32 = dtypes.int32

Code: 61 ()

def ones(i: int) -> TT[["i"]]: return arange(i)*0+1
test_ones = make_test("one", ones, ones_spec, add_sizes=["i"])

Output: 33

onetargetyours

Code: 9 ()

run_test(test_ones)

Output: 90

Correct!

Note: 55

Puzzle 2 - sum

Compute sum - the sum of a vector

Code: 28 ()

a = t(1,2,3)
a[None]@ones(3)

Output: 322

Copied!
[6]

Prompt: 24

Do the puzzle rules comment on whether I'm allowed to use prior functions I've made?

Assistant: 163

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Yes! From the rules in the README:

  1. You are allowed @, arithmetic, comparison, shape, any indexing (e.g. a[:j], a[:, None], a[arange(10)]), and previous puzzle functions

So you can absolutely use ones (and later sum, etc.) in subsequent puzzles. That's by design — the puzzles build on each other!

Looks like you've already figured out a nice approach for sum using the dot product with ones. 😊

Code: 7 ()

a.shape[0]

Output: 19

3

Code: 117 ()

def sum_spec(a, out):
  out[0] = 0
  for i in range(len(a)):
    out[0] += a[i]

def sum(a: TT[["i"]]) -> TT[[1]]: return a[None]@ones(a.shape[0])

test_sum = make_test("sum", sum, sum_spec, display_values=True)

Output: 33

suma3-2-5-51-4402-4target-9.01.0-2.0yours-91-2

Prompt: 42

Would these still work without the type annotations? Why is TT taking a list instead of the usual implicit tuple in __getitem__?

Assistant: 423

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Would it work without type annotations?

The functions themselves would work fine. But the test framework wouldn't — it relies on those annotations to automatically generate tensors of the right shapes for testing. Without TT[["i"]], make_test wouldn't know what shape of tensor to create.

Why a list instead of a tuple?

It's a Python __getitem__ quirk:

  • TT["i"] → passes the string "i"
  • TT["i", "j"] → passes the tuple ("i", "j")
  • TT[("i",)]also passes just ("i",) — this would work, but looks odd

The problem is there's no clean way to pass a single-element tuple. You'd have to write TT["i",] (trailing comma) which is easy to miss or forget.

Using a list like TT[["i"]] makes it explicit and consistent:

  • TT[["i"]] → 1D tensor with dimension named "i"
  • TT[["i", "j"]] → 2D tensor with dimensions "i" and "j"
  • TT[["i"], dtypes.bool] → 1D boolean tensor

It's a design choice to avoid the trailing-comma gotcha!

Prompt: 25

I don't love it. Surely that type lib could handle the string special case internally?

Assistant: 169

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You're absolutely right! The __class_getitem__ method could easily check:

Copied!
if isinstance(args, str):
    args = (args,)

Then you could write:

  • TT["i"] → 1D
  • TT["i", "j"] → 2D
  • TT["i", dtypes.bool] → 1D bool

Much cleaner. Looks like a small oversight in the library design. Would you want to patch it locally, or just live with the lists for now?

Prompt: 27

Check its source and see if it's easy to fix. Otherwise I'll go a bit mental...

Code: 7 ()

from typing import Annotated

Code: 190 ()

class TT(Tensor):
    def __class_getitem__(cls, args: Tuple):
        if not isinstance(args, tuple): args = (args,)
        info = {}
        shape_parts = []
        for arg in args:
            if isinstance(arg, (str, int)): shape_parts.append(arg)
            elif isinstance(arg, list) and all(isinstance(a, (str, int)) for a in arg): shape_parts.extend(arg)
            elif isinstance(arg, DType): info["dtype"] = arg
        if shape_parts: info["shape"] = tuple(shape_parts)
        return Annotated[Tensor, info]

Code: 42 ()

TT["i"], TT["i", "j"], TT[["i", "j"]], TT["i", dtypes.bool]

Output: 255

(typing.Annotated[tinygrad.tensor.Tensor, {'shape': ('i',)}],
 typing.Annotated[tinygrad.tensor.Tensor, {'shape': ('i', 'j')}],
 typing.Annotated[tinygrad.tensor.Tensor, {'shape': ('i', 'j')}],
 typing.Annotated[tinygrad.tensor.Tensor, {'dtype': dtypes.bool, 'shape': ('i',)}])

Prompt: 3

OK?

Assistant: 132

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Nice! That's much cleaner. All four cases work:

  • TT["i"] → single dimension ✓
  • TT["i", "j"] → multiple dimensions ✓
  • TT[["i", "j"]] → list still works (backward compatible) ✓
  • TT["i", dtypes.bool] → dimension + dtype ✓

Your sanity is preserved. Onwards with the puzzles?

Code: 7 ()

run_test(test_sum)

Output: 90

Correct!

Note: 48

Puzzle 3 - outer

Compute outer - the outer product of two vectors

Code: 4 ()

import tinygrad

Code: 27 ()

a = t(2,3,0)
b = t(2,-1)

Prompt: 15

Is there an outer in the docs?

Assistant: 213

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Looking at the tinygrad API reference provided earlier — no, there's no outer function listed.

But remember, the puzzle rules say you can only use @, arithmetic, comparison, shape, indexing, arange, and where. So even if it existed, you couldn't use it!

The trick here is broadcasting. Think about what shapes a and b need to be so that when you multiply them, you get a 2D result where out[i,j] = a[i] * b[j].

What shapes would you need to broadcast a (3,) and a (2,) into a (3, 2) result?

Code: 7 ()

b[None].shape

Code: 7 ()

a[:,None].shape

Code: 13 ()

b[None] * a[:,None]

Code: 135 ()

def outer_spec(a, b, out):
  for i in range(len(out)):
    for j in range(len(out[0])):
      out[i][j] = a[i] * b[j]

def outer(a: TT["i"], b: TT["j"]) -> TT["i", "j"]: return b[None] * a[:,None]

test_outer = make_test("outer", outer, outer_spec, display_values=True)

Code: 7 ()

run_test(test_outer)