Complex Ops
Reduce¤
sum
¤
sum(
axis: int | Sequence[int] | None = None,
keepdim=False,
dtype: DTypeLike | None = None,
) -> Tensor
Returns the sum of the elements of the tensor along the specified axis or axes.
You can pass in axis
and keepdim
keyword arguments to control the axis along
which the maximum is computed and whether the reduced dimensions are retained.
You can pass in dtype
keyword argument to control the data type of the accumulation.
If not specified, the accumulation data type is chosen based on the input tensor's data type.
t = Tensor.arange(6).reshape(2, 3)
print(t.numpy())
[[0 1 2]
[3 4 5]]
print(t.sum().numpy())
15
print(t.sum(axis=0).numpy())
[3 5 7]
print(t.sum(axis=1).numpy())
[ 3 12]
Source code in tinygrad/tensor.py
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prod
¤
prod(
axis: int | Sequence[int] | None = None,
keepdim=False,
dtype: DTypeLike | None = None,
) -> Tensor
Returns the product of the elements of the tensor along the specified axis or axes.
You can pass in axis
and keepdim
keyword arguments to control the axis along
which the maximum is computed and whether the reduced dimensions are retained.
You can pass in dtype
keyword argument to control the data type of the accumulation.
If not specified, the accumulation data type is chosen based on the input tensor's data type.
t = Tensor([-1, -2, -3, 1, 2, 3]).reshape(2, 3)
print(t.numpy())
[[-1 -2 -3]
[ 1 2 3]]
print(t.prod().numpy())
-36
print(t.prod(axis=0).numpy())
[-1 -4 -9]
print(t.prod(axis=1).numpy())
[-6 6]
Source code in tinygrad/tensor.py
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max
¤
Returns the maximum value of the tensor along the specified axis or axes.
You can pass in axis
and keepdim
keyword arguments to control the axis along
which the maximum is computed and whether the reduced dimensions are retained.
t = Tensor([[1, 0, 2], [5, 4, 3]])
print(t.numpy())
[[1 0 2]
[5 4 3]]
print(t.max().numpy())
5
print(t.max(axis=0).numpy())
[5 4 3]
print(t.max(axis=1, keepdim=True).numpy())
[[2]
[5]]
Source code in tinygrad/tensor.py
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min
¤
Returns the minimum value of the tensor along the specified axis or axes.
You can pass in axis
and keepdim
keyword arguments to control the axis along
which the minimum is computed and whether the reduced dimensions are retained.
t = Tensor([[1, 0, 2], [5, 4, 3]])
print(t.numpy())
[[1 0 2]
[5 4 3]]
print(t.min().numpy())
0
print(t.min(axis=0).numpy())
[1 0 2]
print(t.min(axis=1, keepdim=True).numpy())
[[0]
[3]]
Source code in tinygrad/tensor.py
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any
¤
Tests if any element evaluates to True
along the specified axis or axes.
You can pass in axis
and keepdim
keyword arguments to control the reduce axis and whether the reduced dimensions are retained.
t = Tensor([[True, True], [True, False], [False, False]])
print(t.numpy())
[[ True True]
[ True False]
[False False]]
print(t.any().numpy())
True
print(t.any(axis=0).numpy())
[ True True]
print(t.any(axis=1, keepdim=True).numpy())
[[ True]
[ True]
[False]]
Source code in tinygrad/tensor.py
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all
¤
Tests if all element evaluates to True
along the specified axis or axes.
You can pass in axis
and keepdim
keyword arguments to control the reduce axis and whether the reduced dimensions are retained.
t = Tensor([[True, True], [True, False], [False, False]])
print(t.numpy())
[[ True True]
[ True False]
[False False]]
print(t.all().numpy())
False
print(t.all(axis=0).numpy())
[False False]
print(t.all(axis=1, keepdim=True).numpy())
[[ True]
[False]
[False]]
Source code in tinygrad/tensor.py
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isclose
¤
Returns a new tensor with element-wise comparison of closeness to other
within a tolerance.
The rtol
and atol
keyword arguments control the relative and absolute tolerance of the comparison.
By default, two NaN
values are not close to each other. If equal_nan
is True
, two NaN
values are considered close.
print(Tensor([1e-7, 1e-8, 1e-9, float('nan')]).isclose(Tensor([0.0, 0.0, 0.0, float('nan')])).numpy())
[False True True False]
print(Tensor([float('nan')]).isclose(Tensor([float('nan')]), equal_nan=True).numpy())
[ True]
Source code in tinygrad/tensor.py
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mean
¤
Returns the mean value of the tensor along the specified axis or axes.
You can pass in axis
and keepdim
keyword arguments to control the axis along
which the mean is computed and whether the reduced dimensions are retained.
Tensor.manual_seed(42)
t = Tensor.normal(2, 3, mean=2.5, std=0.5)
print(t.numpy())
[[2.9889 2.7339 2.7763]
[2.3356 2.0722 2.6376]]
print(t.mean().numpy())
2.5907671
print(t.mean(axis=0).numpy())
[2.6623 2.4031 2.707 ]
print(t.mean(axis=1).numpy())
[2.833 2.3485]
Source code in tinygrad/tensor.py
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var
¤
Returns the variance of the tensor along the specified axis or axes.
You can pass in axis
, keepdim
, and correction
keyword arguments to control the axis along
which the variance is computed, whether the reduced dimensions are retained, and the Bessel's correction applied.
Tensor.manual_seed(42)
t = Tensor.normal(2, 3, mean=2.5, std=0.5)
print(t.numpy())
[[2.9889 2.7339 2.7763]
[2.3356 2.0722 2.6376]]
print(t.var().numpy())
0.109925404
print(t.var(axis=0).numpy())
[0.2134 0.2189 0.0096]
print(t.var(axis=1).numpy())
[0.0187 0.08 ]
Source code in tinygrad/tensor.py
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var_mean
¤
var_mean(
axis: int | Sequence[int] | None = None,
keepdim=False,
correction=1,
) -> tuple[Tensor, Tensor]
Calculates the variance and mean over the dimensions specified by dim.
Syntactic sugar around Tensor.var
and Tensor.mean
to match torch.var_mean
.
Tensor.manual_seed(42)
t = Tensor.normal(2, 3, mean=2.5, std=0.5)
print(t.numpy())
[[2.9889 2.7339 2.7763]
[2.3356 2.0722 2.6376]]
var, mean = t.var_mean()
print(var.numpy(), mean.numpy())
0.109925404 2.5907671
Source code in tinygrad/tensor.py
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std
¤
Returns the standard deviation of the tensor along the specified axis or axes.
You can pass in axis
, keepdim
, and correction
keyword arguments to control the axis along
which the standard deviation is computed, whether the reduced dimensions are retained, and the Bessel's correction applied.
Tensor.manual_seed(42)
t = Tensor.normal(2, 3, mean=2.5, std=0.5)
print(t.numpy())
[[2.9889 2.7339 2.7763]
[2.3356 2.0722 2.6376]]
print(t.std().numpy())
0.33155
print(t.std(axis=0).numpy())
[0.462 0.4679 0.0981]
print(t.std(axis=1).numpy())
[0.1367 0.2829]
Source code in tinygrad/tensor.py
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std_mean
¤
std_mean(
axis: int | Sequence[int] | None = None,
keepdim=False,
correction=1,
) -> tuple[Tensor, Tensor]
Calculates the standard deviation and mean over the dimensions specified by dim.
Syntactic sugar around Tensor.std
and Tensor.mean
to match torch.std_mean
.
Tensor.manual_seed(42)
t = Tensor.normal(2, 3, mean=2.5, std=0.5)
print(t.numpy())
[[2.9889 2.7339 2.7763]
[2.3356 2.0722 2.6376]]
std, mean = t.std_mean()
print(std.numpy(), mean.numpy())
0.33155 2.5907671
Source code in tinygrad/tensor.py
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softmax
¤
softmax(
axis=-1,
dtype: DTypeLike | None = None,
_single_kernel=getenv("SINGLE_KERNEL_SOFTMAX"),
) -> Tensor
Applies the softmax function to the tensor along the specified axis.
Rescales the elements of the tensor such that they lie in the range [0, 1] and sum to 1.
You can pass in the axis
keyword argument to control the axis along which the softmax is computed.
Tensor.manual_seed(42)
t = Tensor.randn(2, 3)
print(t.numpy())
[[ 0.9779 0.4678 0.5526]
[-0.3288 -0.8555 0.2753]]
print(t.softmax().numpy())
[[0.4436 0.2664 0.29 ]
[0.2924 0.1727 0.5349]]
print(t.softmax(axis=0).numpy())
[[0.787 0.7897 0.5689]
[0.213 0.2103 0.4311]]
Source code in tinygrad/tensor.py
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log_softmax
¤
log_softmax(
axis=-1, dtype: DTypeLike | None = None
) -> Tensor
Applies the log-softmax function to the tensor along the specified axis.
The log-softmax function is a numerically stable alternative to the softmax function in log space.
You can pass in the axis
keyword argument to control the axis along which the log-softmax is computed.
Tensor.manual_seed(42)
t = Tensor.randn(2, 3)
print(t.numpy())
[[ 0.9779 0.4678 0.5526]
[-0.3288 -0.8555 0.2753]]
print(t.log_softmax().numpy())
[[-0.8127 -1.3228 -1.238 ]
[-1.2297 -1.7564 -0.6256]]
print(t.log_softmax(axis=0).numpy())
[[-0.2396 -0.2361 -0.564 ]
[-1.5463 -1.5594 -0.8414]]
Source code in tinygrad/tensor.py
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logsumexp
¤
logsumexp(axis=None, keepdim=False) -> Tensor
Computes the log-sum-exp of the tensor along the specified axis or axes.
The log-sum-exp function is a numerically stable way to compute the logarithm of the sum of exponentials.
You can pass in axis
and keepdim
keyword arguments to control the axis along
which the log-sum-exp is computed and whether the reduced dimensions are retained.
Tensor.manual_seed(42)
t = Tensor.randn(2, 3)
print(t.numpy())
[[ 0.9779 0.4678 0.5526]
[-0.3288 -0.8555 0.2753]]
print(t.logsumexp().numpy())
2.1347282
print(t.logsumexp(axis=0).numpy())
[1.2174 0.7039 1.1167]
print(t.logsumexp(axis=1).numpy())
[1.7906 0.9009]
Source code in tinygrad/tensor.py
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logcumsumexp
¤
logcumsumexp(axis=0) -> Tensor
Computes the log-cumsum-exp of the tensor along the specified axis or axes.
The log-cumsum-exp function is a numerically stable way to compute the logarithm of the cumulative sum of exponentials.
You can pass in the axis
keyword argument to control the axis along which
the log-cum-sum-exp is computed.
Tensor.manual_seed(42)
t = Tensor.randn(2, 3)
print(t.numpy())
[[ 0.9779 0.4678 0.5526]
[-0.3288 -0.8555 0.2753]]
print(t.logcumsumexp().numpy())
[[0.9779 0.4678 0.5526]
[1.2174 0.7039 1.1167]]
print(t.logcumsumexp(axis=0).numpy())
[[0.9779 0.4678 0.5526]
[1.2174 0.7039 1.1167]]
print(t.logcumsumexp(axis=1).numpy())
[[ 0.9779 1.4481 1.7906]
[-0.3288 0.1353 0.9009]]
Source code in tinygrad/tensor.py
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argmax
¤
argmax(axis=None, keepdim=False) -> Tensor
Returns the indices of the maximum value of the tensor along the specified axis.
You can pass in axis
and keepdim
keyword arguments to control the axis along
which the maximum is computed and whether the reduced dimensions are retained.
t = Tensor([[1, 0, 2], [5, 4, 3]])
print(t.numpy())
[[1 0 2]
[5 4 3]]
print(t.argmax().numpy()) # Returns the index of the maximum value in the flattened tensor.
3
print(t.argmax(axis=0).numpy()) # Returns the indices of the maximum values along axis 0.
[1 1 1]
print(t.argmax(axis=1).numpy()) # Returns the indices of the maximum values along axis 1.
[2 0]
Source code in tinygrad/tensor.py
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argmin
¤
argmin(axis=None, keepdim=False) -> Tensor
Returns the indices of the minimum value of the tensor along the specified axis.
You can pass in axis
and keepdim
keyword arguments to control the axis along
which the minimum is computed and whether the reduced dimensions are retained.
t = Tensor([[1, 0, 2], [5, 4, 3]])
print(t.numpy())
[[1 0 2]
[5 4 3]]
print(t.argmin().numpy()) # Returns the index of the minimum value in the flattened tensor.
1
print(t.argmin(axis=0).numpy()) # Returns the indices of the minimum values along axis 0.
[0 0 0]
print(t.argmin(axis=1).numpy()) # Returns the indices of the minimum values along axis 1.
[1 2]
Source code in tinygrad/tensor.py
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Processing¤
avg_pool2d
¤
avg_pool2d(
kernel_size: tuple[int, ...] = (2, 2),
stride=None,
dilation=1,
padding: int | tuple[int, ...] = 0,
ceil_mode=False,
count_include_pad=True,
) -> Tensor
Applies average pooling over a tensor.
This function supports three different types of padding
-
int
(single value): Applies the same padding value uniformly to all spatial dimensions. -
tuple[int, ...]
(length = number of spatial dimensions): Specifies a distinct padding value for each spatial dimension in the form(padding_height, padding_width, ...)
. -
tuple[int, ...]
(length = 2 * number of spatial dimensions): Specifies explicit padding for each side of each spatial dimension in the form(padding_left, padding_right, padding_top, padding_bottom, ...)
.
When ceil_mode
is set to True
, output shape will be determined using ceil division.
When count_include_pad
is set to False
, zero padding will not be included in the averaging calculation.
Note
unlike PyTorch, this implementation is not limited to only 2d pooling and instead works for any number of dimensions.
See: https://paperswithcode.com/method/average-pooling
t = Tensor.arange(25).reshape(1, 1, 5, 5)
print(t.avg_pool2d().numpy())
[[[[ 3. 5.]
[13. 15.]]]]
print(t.avg_pool2d(ceil_mode=True).numpy())
[[[[ 3. 5. 6.5]
[13. 15. 16.5]
[20.5 22.5 24. ]]]]
print(t.avg_pool2d(padding=1).numpy())
[[[[ 0. 0.75 1.75]
[ 3.75 9. 11. ]
[ 8.75 19. 21. ]]]]
print(t.avg_pool2d(padding=1, count_include_pad=False).numpy())
[[[[ 0. 1.5 3.5]
[ 7.5 9. 11. ]
[17.5 19. 21. ]]]]
Source code in tinygrad/tensor.py
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max_pool2d
¤
max_pool2d(
kernel_size: tuple[int, ...] = (2, 2),
stride=None,
dilation=1,
padding: int | tuple[int, ...] = 0,
ceil_mode=False,
return_indices=False,
) -> Tensor | tuple[Tensor, Tensor]
Applies max pooling over a tensor.
This function supports three different types of padding
-
int
(single value): Applies the same padding value uniformly to all spatial dimensions. -
tuple[int, ...]
(length = number of spatial dimensions): Specifies a distinct padding value for each spatial dimension in the form(padding_height, padding_width, ...)
. -
tuple[int, ...]
(length = 2 * number of spatial dimensions): Specifies explicit padding for each side of each spatial dimension in the form(padding_left, padding_right, padding_top, padding_bottom, ...)
.
When ceil_mode
is set to True
, output shape will be determined using ceil division.
When return_indices
is set to True
, the argmax will be returned along with the max values.
Note
unlike PyTorch, this implementation is not limited to only 2d pooling and instead works for any number of dimensions.
See: https://paperswithcode.com/method/max-pooling
t = Tensor.arange(25).reshape(1, 1, 5, 5)
print(t.max_pool2d().numpy())
[[[[ 6 8]
[16 18]]]]
print(t.max_pool2d(ceil_mode=True).numpy())
[[[[ 6 8 9]
[16 18 19]
[21 23 24]]]]
print(t.max_pool2d(padding=1).numpy())
[[[[ 0 2 4]
[10 12 14]
[20 22 24]]]]
Source code in tinygrad/tensor.py
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max_unpool2d
¤
max_unpool2d(
indices: Tensor,
kernel_size: tuple[int, ...] = (2, 2),
stride=None,
dilation=1,
padding: int | tuple[int, ...] = 0,
output_size=None,
)
Performs a partial inverse of max_pool2d
using the indices from the argmax.
When output_size
is provided, the output shape disambiguates to the provided shape.
Note
unlike PyTorch, this implementation is not limited to only 2d pooling and instead works for any number of dimensions.
t = Tensor.arange(1, 17).reshape(1, 1, 4, 4)
print(t.numpy())
[[[[ 1 2 3 4]
[ 5 6 7 8]
[ 9 10 11 12]
[13 14 15 16]]]]
output, indices = Tensor.max_pool2d(t, return_indices=True)
print(output.numpy())
print(indices.numpy())
[[[[ 6 8]
[14 16]]]]
[[[[ 5 7]
[13 15]]]]
print(Tensor.max_unpool2d(output, indices).numpy())
[[[[ 0 0 0 0]
[ 0 6 0 8]
[ 0 0 0 0]
[ 0 14 0 16]]]]
Source code in tinygrad/tensor.py
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conv2d
¤
conv2d(
weight: Tensor,
bias: Tensor | None = None,
groups=1,
stride=1,
dilation=1,
padding: int | tuple[int, ...] = 0,
dtype: DTypeLike | None = None,
) -> Tensor
Applies a convolution over a tensor with a given weight
and optional bias
.
This function supports three different types of padding
-
int
(single value): Applies the same padding value uniformly to all spatial dimensions. -
tuple[int, ...]
(length = number of spatial dimensions): Specifies a distinct padding value for each spatial dimension in the form(padding_height, padding_width, ...)
. -
tuple[int, ...]
(length = 2 * number of spatial dimensions): Specifies explicit padding for each side of each spatial dimension in the form(padding_left, padding_right, padding_top, padding_bottom, ...)
.
Note
unlike PyTorch, this implementation is not limited to only 2d convolutions and instead works for any number of dimensions.
See: https://pytorch.org/docs/stable/generated/torch.nn.Conv2d.html
t = Tensor.arange(9).reshape(1, 1, 3, 3)
w = Tensor.ones(1, 1, 2, 2)
print(t.conv2d(w).numpy())
[[[[ 8. 12.]
[20. 24.]]]]
Source code in tinygrad/tensor.py
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conv_transpose2d
¤
conv_transpose2d(
weight: Tensor,
bias: Tensor | None = None,
groups=1,
stride=1,
dilation=1,
padding=0,
output_padding=0,
) -> Tensor
Applies a transposed convolution over a tensor with a given weight
and optional bias
.
This function supports three different types of padding
-
int
(single value): Applies the same padding value uniformly to all spatial dimensions. -
tuple[int, ...]
(length = number of spatial dimensions): Specifies a distinct padding value for each spatial dimension in the form(padding_height, padding_width, ...)
. -
tuple[int, ...]
(length = 2 * number of spatial dimensions): Specifies explicit padding for each side of each spatial dimension in the form(padding_left, padding_right, padding_top, padding_bottom, ...)
.
Note
unlike PyTorch, this implementation is not limited to only 2d transposed convolutions and instead works for any number of dimensions.
See: https://pytorch.org/docs/stable/generated/torch.nn.ConvTranspose2d.html
t = Tensor.arange(9).reshape(1, 1, 3, 3)
w = Tensor.ones(1, 1, 2, 2)
print(t.conv_transpose2d(w).numpy())
[[[[ 0. 1. 3. 2.]
[ 3. 8. 12. 7.]
[ 9. 20. 24. 13.]
[ 6. 13. 15. 8.]]]]
Source code in tinygrad/tensor.py
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dot
¤
Performs dot product between two tensors.
If w
is 1-D, it's a sum product over the last axis of self
and w
.
If w
is N-D with N>=2, it's a sum product over the last axis of self
and the second-to-last axis of w
.
You can pass in the optional dtype
keyword argument to control the data type of the accumulation.
a = Tensor([1, 2, 3])
b = Tensor([1, 1, 0])
print(a.dot(b).numpy())
3
a = Tensor([[1, 2], [3, 4]])
b = Tensor([[5, 6], [7, 8]])
print(a.dot(b).numpy())
[[19 22]
[43 50]]
Source code in tinygrad/tensor.py
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matmul
¤
Performs matrix multiplication between two tensors.
You can pass in the reverse
keyword argument to control the order of the matrix multiplication.
You can pass in the optional dtype
keyword argument to control the data type of the accumulation.
a = Tensor([[1, 2], [3, 4]])
b = Tensor([[5, 6], [7, 8]])
print(a.matmul(b).numpy())
[[19 22]
[43 50]]
Source code in tinygrad/tensor.py
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einsum
staticmethod
¤
einsum(
formula: str,
*operands: Tensor | Sequence[Tensor],
dtype: DTypeLike | None = None
) -> Tensor
Sums the product of the elements of the input tensors according to a formula based on the Einstein summation convention.
See: https://pytorch.org/docs/stable/generated/torch.einsum.html
x = Tensor([[1, 2], [3, 4]])
y = Tensor([[5, 6], [7, 8]])
print(Tensor.einsum("ij,ij->", x, y).numpy())
70
Source code in tinygrad/tensor.py
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cumsum
¤
Computes the cumulative sum of the tensor along the specified axis
.
t = Tensor.ones(2, 3)
print(t.numpy())
[[1. 1. 1.]
[1. 1. 1.]]
print(t.cumsum(1).numpy())
[[1. 2. 3.]
[1. 2. 3.]]
Source code in tinygrad/tensor.py
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cummax
¤
Computes the cumulative max of the tensor along the specified axis
.
t = Tensor([0, 1, -1, 2, -2, 3, -3])
print(t.numpy())
[ 0 1 -1 2 -2 3 -3]
print(t.cummax(0).numpy())
[0 1 1 2 2 3 3]
Source code in tinygrad/tensor.py
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triu
¤
Returns the upper triangular part of the tensor, the other elements are set to 0.
The argument diagonal
determines which diagonal is on the boundary. diagonal = 0
means the main diagonal.
Positive diagonal
means above the main diagonal, and negative diagonal
means below the main diagonal.
t = Tensor([[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12]])
print(t.numpy())
[[ 1 2 3 4]
[ 5 6 7 8]
[ 9 10 11 12]]
print(t.triu(diagonal=0).numpy())
[[ 1 2 3 4]
[ 0 6 7 8]
[ 0 0 11 12]]
print(t.triu(diagonal=1).numpy())
[[ 0 2 3 4]
[ 0 0 7 8]
[ 0 0 0 12]]
print(t.triu(diagonal=-1).numpy())
[[ 1 2 3 4]
[ 5 6 7 8]
[ 0 10 11 12]]
Source code in tinygrad/tensor.py
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tril
¤
Returns the lower triangular part of the tensor, the other elements are set to 0.
The argument diagonal
determines which diagonal is on the boundary. diagonal = 0
means the main diagonal.
Positive diagonal
means above the main diagonal, and negative diagonal
means below the main diagonal.
t = Tensor([[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12]])
print(t.numpy())
[[ 1 2 3 4]
[ 5 6 7 8]
[ 9 10 11 12]]
print(t.tril(diagonal=0).numpy())
[[ 1 0 0 0]
[ 5 6 0 0]
[ 9 10 11 0]]
print(t.tril(diagonal=1).numpy())
[[ 1 2 0 0]
[ 5 6 7 0]
[ 9 10 11 12]]
print(t.tril(diagonal=-1).numpy())
[[ 0 0 0 0]
[ 5 0 0 0]
[ 9 10 0 0]]
Source code in tinygrad/tensor.py
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interpolate
¤
Downsamples or Upsamples to the input size
, accepts 0 to N batch dimensions.
The interpolation algorithm is selected with mode
which currently only supports linear
, nearest
and nearest-exact
.
To run bilinear
or trilinear
, pass in a 2D or 3D size.
t = Tensor([[1, 2, 3, 4], [21, 22, 23, 24], [41, 42, 43, 44]])
print(t.numpy())
[[ 1 2 3 4]
[21 22 23 24]
[41 42 43 44]]
print(t.interpolate(size=(2,3), mode="linear").numpy())
[[ 6 7 8]
[36 37 38]]
Source code in tinygrad/tensor.py
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scatter
¤
scatter(
dim: int,
index: Tensor,
src: Tensor | ConstType,
reduce: Literal["multiply", "add"] | None = None,
) -> Tensor
Scatters src
values along an axis specified by dim
.
Apply add
or multiply
reduction operation with reduce
.
Note
To use the reduce
argument with a Tensor src
, see Tensor.scatter_reduce
.
src = Tensor.arange(1, 11).reshape(2, 5)
print(src.numpy())
[[ 1 2 3 4 5]
[ 6 7 8 9 10]]
index = Tensor([[0, 1, 2, 0]])
print(Tensor.zeros(3, 5, dtype=src.dtype).scatter(0, index, src).numpy())
[[1 0 0 4 0]
[0 2 0 0 0]
[0 0 3 0 0]]
index = Tensor([[0, 1, 2], [0, 1, 4]])
print(Tensor.zeros(3, 5, dtype=src.dtype).scatter(1, index, src).numpy())
[[1 2 3 0 0]
[6 7 0 0 8]
[0 0 0 0 0]]
print(Tensor.full((2, 4), 2.0).scatter(1, Tensor([[2], [3]]), 1.23, reduce='multiply').numpy())
[[2. 2. 2.46 2. ]
[2. 2. 2. 2.46]]
print(Tensor.full((2, 4), 2.0).scatter(1, Tensor([[2], [3]]), 1.23, reduce='add').numpy())
[[2. 2. 3.23 2. ]
[2. 2. 2. 3.23]]
Source code in tinygrad/tensor.py
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scatter_reduce
¤
scatter_reduce(
dim: int,
index: Tensor,
src: Tensor,
reduce: Literal["sum", "prod", "mean", "amax", "amin"],
include_self: bool = True,
) -> Tensor
Scatters src
values along an axis specified by dim
.
Apply "sum"
, "prod"
, "mean"
, "amax"
, or "amin"
reduction operations with reduce
.
Set include_self=False
to exclude values in the self
Tensor from the reduction.
src = Tensor.arange(1, 11).cast(dtypes.float).reshape(2, 5)
print(src.numpy())
index = Tensor([[0, 0, 0, 0, 0], [0, 0, 0, 0, 0]])
print(index.numpy())
[[ 1. 2. 3. 4. 5.]
[ 6. 7. 8. 9. 10.]]
[[0 0 0 0 0]
[0 0 0 0 0]]
print(Tensor.ones(1, 5, dtype=src.dtype).scatter_reduce(0, index, src, reduce='sum').numpy())
[[ 8. 10. 12. 14. 16.]]
print(Tensor.ones(1, 5, dtype=src.dtype).scatter_reduce(0, index, src, reduce='prod').numpy())
[[ 6. 14. 24. 36. 50.]]
print(Tensor.ones(1, 5, dtype=src.dtype).scatter_reduce(0, index, src, reduce='mean', include_self=False).numpy())
[[3.5 4.5 5.5 6.5 7.5]]
print(Tensor([[-10, 20, 0, 5, 10]], dtype=src.dtype).scatter_reduce(0, index, src, reduce='amax').numpy())
[[ 6. 20. 8. 9. 10.]]
print(Tensor([[-10, 20, 0, 5, 10]], dtype=src.dtype).scatter_reduce(0, index, src, reduce='amin').numpy())
[[-10. 2. 0. 4. 5.]]
Source code in tinygrad/tensor.py
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masked_select
¤
masked_select(mask)
Selects elements from self
based on the boolean mask
.
t = Tensor([[0, 1, 2], [3, 4, 5], [6, 7, 8]])
mask = Tensor([[True, False, True], [False, True, False], [False, False, True]])
print(t.numpy())
print(mask.numpy())
[[0 1 2]
[3 4 5]
[6 7 8]]
[[ True False True]
[False True False]
[False False True]]
print(t.masked_select(mask).numpy())
[0 2 4 8]
Source code in tinygrad/tensor.py
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masked_fill
¤
Replaces self
with value
wherever the elements of mask
are True.
t = Tensor([1, 2, 3, 4, 5])
mask = Tensor([True, False, True, False, False])
print(t.masked_fill(mask, -12).numpy())
[-12 2 -12 4 5]
t = Tensor([1, 2, 3, 4, 5])
mask = Tensor([True, False, True, False, False])
value = Tensor([-1, -2, -3, -4, -5])
print(t.masked_fill(mask, value).numpy())
[-1 2 -3 4 5]
Source code in tinygrad/tensor.py
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sort
¤
Performs a bitonic sort on the tensor along the specified dimension.
Order of indices for equivalent elements is always preserved.
See: https://en.wikipedia.org/wiki/Bitonic_sorter
t = Tensor([[0.1, 0.5, 1.2, 3.4, 2.1], [2.2, 1.9, 0.3, 4.5, 0.8]])
print(t.numpy())
[[0.1 0.5 1.2 3.4 2.1]
[2.2 1.9 0.3 4.5 0.8]]
sorted_values, indices = t.sort(dim=1, descending=True)
print(sorted_values.numpy())
print(indices.numpy())
[[3.4 2.1 1.2 0.5 0.1]
[4.5 2.2 1.9 0.8 0.3]]
[[3 4 2 1 0]
[3 0 1 4 2]]
Source code in tinygrad/tensor.py
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topk
¤
Computes the top-k elements of the tensor along the specified dim
.
Order of indices for equivalent elements is always preserved.
t = Tensor([[0.1, 0.5, 1.2, 3.4, 2.1], [2.2, 1.9, 0.3, 4.5, 0.8]])
print(t.numpy())
[[0.1 0.5 1.2 3.4 2.1]
[2.2 1.9 0.3 4.5 0.8]]
topk_values, topk_indices = t.topk(2, dim=1)
print(topk_values.numpy())
print(topk_indices.numpy())
[[3.4 2.1]
[4.5 2.2]]
[[3 4]
[3 0]]
Source code in tinygrad/tensor.py
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multinomial
¤
Returns a tensor with num_samples
indices sampled from a multinomial distribution weighted by self
.
Note
replacement=False
for num_samples > 1
is not supported yet.
Tensor.manual_seed(42)
t = Tensor([1, 2, 3, 4])
print(t.multinomial(20, replacement=True).numpy())
[2 1 3 2 3 1 2 2 3 3 3 3 3 3 2 3 2 3 3 3]
Source code in tinygrad/tensor.py
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Neural Network (functional)¤
linear
¤
Applies a linear transformation to self
using weight
and bias
.
See: https://pytorch.org/docs/stable/generated/torch.nn.Linear.html
t = Tensor([[1, 2], [3, 4]])
weight = Tensor([[1, 2], [3, 4]])
bias = Tensor([1, 2])
print(t.linear(weight, bias).numpy())
[[ 8 12]
[16 24]]
Source code in tinygrad/tensor.py
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sequential
¤
Applies a sequence of functions to self
chaining the output of each function to the input of the next.
t = Tensor([1, 2, 3])
print(t.sequential([lambda x: x * 2, lambda x: x + 1]).numpy())
[3 5 7]
Source code in tinygrad/tensor.py
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layernorm
¤
Applies Layer Normalization over a mini-batch of inputs.
- Described: https://paperswithcode.com/method/layer-normalization
- Paper: https://arxiv.org/abs/1607.06450v1
t = Tensor.randn(8, 10, 16) * 2 + 8
print(t.mean().item(), t.std().item())
7.9793524742126465 2.074720621109009
t = t.layernorm()
print(t.mean().item(), t.std().item())
5.1973159109763856e-09 1.0003894567489624
Source code in tinygrad/tensor.py
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batchnorm
¤
batchnorm(
weight: Tensor | None,
bias: Tensor | None,
mean: Tensor,
invstd: Tensor,
axis: int | tuple[int, ...] = 1,
) -> Tensor
Applies Batch Normalization over a mini-batch of inputs.
- Described: https://paperswithcode.com/method/batch-normalization
- Paper: https://arxiv.org/abs/1502.03167
t = Tensor.randn(8, 4, 16, 16) * 2 + 8
print(t.mean().item(), t.std().item())
8.019729614257812 1.9927232265472412
t = t.batchnorm(None, None, t.mean(axis=(0,2,3)), t.var(axis=(0,2,3)).add(1e-5).rsqrt())
print(t.mean().item(), t.std().item())
6.112455253060034e-07 0.9998146891593933
Source code in tinygrad/tensor.py
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dropout
¤
dropout(p=0.5) -> Tensor
Applies dropout to self
.
Note
dropout is only applied when Tensor.training
is True
.
- Described: https://paperswithcode.com/method/dropout
- Paper: https://jmlr.org/papers/v15/srivastava14a.html
Tensor.manual_seed(42)
t = Tensor.randn(2, 2)
with Tensor.train():
print(t.dropout().numpy())
[[-1.0287 2.17 ]
[ 1.8178 0. ]]
Source code in tinygrad/tensor.py
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one_hot
¤
Converts self
to a one-hot tensor.
num_classes
defaults to -1, which means num_classes will be inferred as max(self) + 1.
t = Tensor([0, 1, 3, 3, 4])
print(t.one_hot(5).numpy())
[[1 0 0 0 0]
[0 1 0 0 0]
[0 0 0 1 0]
[0 0 0 1 0]
[0 0 0 0 1]]
Source code in tinygrad/tensor.py
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scaled_dot_product_attention
¤
scaled_dot_product_attention(
key: Tensor,
value: Tensor,
attn_mask: Tensor | None = None,
dropout_p: float = 0.0,
is_causal: bool = False,
) -> Tensor
Computes scaled dot-product attention.
self
is the query tensor, key
is the key tensor, and value
is the value tensor.
- Described: https://paperswithcode.com/method/scaled
- Paper: https://arxiv.org/abs/1706.03762v7
q = Tensor.randn(2, 4, 8)
k = Tensor.randn(2, 4, 8)
v = Tensor.randn(2, 4, 8)
print(q.scaled_dot_product_attention(k, v).numpy())
[[[ 0.6408 0.3264 0.7317 -1.0943 0.5778 -0.0534 -0.0104 -0.0488]
[ 0.1243 -0.8259 1.6481 -0.8035 -0.3961 0.4269 0.1232 1.6462]
[ 0.9535 0.1068 0.8545 -0.5395 0.4692 -0.0548 -0.2274 0.6152]
[ 0.8891 -0.0411 0.7818 -0.3322 0.3931 -0.0202 -0.1101 0.8129]]
[[-0.4273 -0.6085 -0.0465 0.5246 0.3641 -0.0381 -0.0106 0.8349]
[ 0.6321 0.3654 0.4137 -0.2327 0.2558 0.1418 -1.27 -0.802 ]
[ 0.1794 0.4616 0.1847 -0.1988 0.2123 0.1837 -0.9583 -0.5364]
[ 0.4408 0.6125 0.0811 -0.3886 0.3602 0.4987 -1.4414 -0.9565]]]
Source code in tinygrad/tensor.py
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binary_crossentropy
¤
Computes the binary cross-entropy loss between self
and Y
.
See: https://pytorch.org/docs/stable/generated/torch.nn.BCELoss.html
t = Tensor([0.1, 0.9, 0.2])
Y = Tensor([0, 1, 0])
print(t.binary_crossentropy(Y).item())
0.14462155103683472
Source code in tinygrad/tensor.py
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binary_crossentropy_logits
¤
Computes the binary cross-entropy loss between self
and Y
where self
is logits.
See: https://pytorch.org/docs/stable/generated/torch.nn.BCEWithLogitsLoss.html
t = Tensor([-1, 2, -3])
Y = Tensor([0, 1, 0])
print(t.binary_crossentropy_logits(Y).item())
0.16292566061019897
Source code in tinygrad/tensor.py
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sparse_categorical_crossentropy
¤
sparse_categorical_crossentropy(
Y: Tensor,
ignore_index: int = -1,
label_smoothing=0.0,
reduction: ReductionStr = "mean",
) -> Tensor
Computes the sparse categorical cross-entropy loss between self
and Y
.
Note
self
is logits and Y
is the target labels.
NOTE: unlike PyTorch, this function expects the class axis to be -1
See: https://pytorch.org/docs/stable/generated/torch.nn.CrossEntropyLoss.html
t = Tensor([[-1, 2, -3], [1, -2, 3]])
Y = Tensor([1, 2])
print(t.sparse_categorical_crossentropy(Y).item())
0.09391524642705917
Source code in tinygrad/tensor.py
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cross_entropy
¤
cross_entropy(
Y: Tensor,
reduction: ReductionStr = "mean",
label_smoothing: float = 0.0,
) -> Tensor
Computes the cross entropy loss between input logits and target.
Note
self
are logits and Y
are the target labels or class probabilities.
See: https://pytorch.org/docs/stable/generated/torch.nn.functional.cross_entropy.html
t = Tensor([[-1, 2, -3], [1, -2, 3]])
Y = Tensor([1, 2])
print(t.cross_entropy(Y).item())
0.09391524642705917
t = Tensor([[-1, 2, -3], [1, -2, 3]])
Y = Tensor([1, 2])
print(t.cross_entropy(Y, reduction='none').numpy())
[0.055 0.1328]
Source code in tinygrad/tensor.py
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nll_loss
¤
nll_loss(
Y: Tensor,
weight: Tensor | None = None,
ignore_index: int | None = None,
reduction: ReductionStr = "mean",
) -> Tensor
Computes the negative log likelihood loss between log-probabilities and target labels.
Note
self
is log-probabilities and Y
is the Y labels or class probabilities.
See: https://pytorch.org/docs/stable/generated/torch.nn.functional.nll_loss.html
t = Tensor([[-1, 2, -3], [1, -2, 3]])
Y = Tensor([1, 2])
print(t.log_softmax().nll_loss(Y).item())
0.09391524642705917
t = Tensor([[-1, 2, -3], [1, -2, 3]])
Y = Tensor([1, 2])
print(t.log_softmax().nll_loss(Y, reduction='none').numpy())
[0.055 0.1328]
Source code in tinygrad/tensor.py
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