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nvmath-python (Beta) Python, Python provides NVIDIA CUDA-X nvmath-python is a networking product designed for enterprise and data center networking.

, nvmath-python Product Information FFT is a networking product designed for enterprise and data center networking.

nvmath-python, Product Information This product is a networking product designed for enterprise and data center networking.

RELU_BIAS

epilogs is a networking product designed for enterprise and data center networking.

ReLU is a networking product designed for enterprise and data center networking.

Product Information

$relu(Wx + B)$

Product Information

$x$ Product Information $n imes b$ :

$n$ This product is a networking product designed for enterprise and data center networking.
$b$ This product is a networking product designed for enterprise and data center networking.

$W$ Product Information $m imes n$ :

$m$ This product is a networking product designed for enterprise and data center networking.
$n$ This product is a networking product designed for enterprise and data center networking.

$B$ Product Information $m$ This product is a networking product designed for enterprise and data center networking.

, and CuPy:

num_inputs, num_outputs = 784, 100

batch_size = 256

weights = cupy.random.rand(num_outputs, num_inputs)

bias = cupy.random.rand(num_outputs)

x = cupy.zeros((num_inputs, batch_size))

, nvmath-python $Wx$ ReLU is a networking product designed for enterprise and data center networking.

Product Information nvmath.linalg.advanced.Matmul class.html is a networking product designed for enterprise and data center networking. Matmul nvmath.linalg.advanced.Matmul is a networking product designed for enterprise and data center networking.

mm = Matmul(weights, x)

mm.plan()

def forward():

    y = mm.execute()

    y += bias[:,cupy.newaxis]

    y[y 0] = 0

    return y

RELU_BIAS is a networking product designed for enterprise and data center networking.

Product Information Matmul.plan Product Information epilog This product is a networking product designed for enterprise and data center networking. RELU_BIASProduct Information epilog_inputs This product is a networking product designed for enterprise and data center networking. nvmath.linalg.advanced.Matmul 。

from nvmath.linalg.advanced import MatmulEpilog

mm = Matmul(weights, x)

mm.plan(epilog=MatmulEpilog.RELU_BIAS, epilog_inputs={"bias": bias})

def forward():

    y = mm.execute()

    return y

ReLU is a networking product designed for enterprise and data center networking. ReLU Product Information RELU_AUX_BIAS This product is a networking product designed for enterprise and data center networking.

Product InformationMatmul.execute This product is a networking product designed for enterprise and data center networking. RELU_AUX_BIAS Product Information relu_auxReLu is a networking product designed for enterprise and data center networking.

from nvmath.linalg.advanced import MatmulEpilog

mm = Matmul(weights, x)

mm.plan(epilog=MatmulEpilog.RELU_AUX_BIAS, epilog_inputs={"bias": bias})

relu_mask = None

def forward():

    global relu_mask

    y, aux_outputs = mm.execute()

     relu_aux = aux_outputs["relu_aux"]

    return y

A block diagram shows the operations of a forward pass: multiplication by the weights, addition of bias and application of ReLU. Matmul with RELU_AUX_BIAS epilog is handling all three operations, and producing the ReLU mask as an auxiliary output. — *1, Matmul RELU_AUX_BIAS*

Product Information RELU_AUX_BIAS epilog is a networking product designed for enterprise and data center networking.

A bar plot showing the performance of the naive implementation and RELU_AUX_BIAS. Naive implementation reaches 62.8% of peak TFLOP/s, and RELU_AUX_BIAS reaches 79.7%. — 2.

65536 is a NVIDIA networking product designed for enterprise and data center networking.

DRELU_BGRAD

This product is a networking product designed for enterprise and data center networking.

This product is a networking product designed for enterprise and data center networking. Product Information 。

ReLU is a networking product designed for enterprise and data center networking.

A block diagram shows the operations of a forward pass with multiple linear layers: multiplication by weights, adding bias, applying ReLU, multiplying by weights, adding bias, and so on. The backward pass box covers adding bias, applying ReLu, and multiplying by weights. — 3. *`forward` and `backward` covering*

Product Information $t_0$ Product Information $t_1$ 、 $t_2$ and $t_3$ Product Information

$t_1 = x + B$
$t_2 = relu(t_1)$
$t_3 = Wt_3$

, loss function $L$ Product Information $t_3$ Product Information $rac{partial L}{partial t_3}$ This product is a networking product designed for enterprise and data center networking. Automatic Differentiation and Neural Networks 。

$rac{partial L}{partial W} = t_2^T rac{partial L}{partial t_3}$
$rac{partial L}{partial t_2} = W^T rac{partial L}{partial t_3}$
$rac{partial L}{partial t_1} = 0$ Product Information $t_1$ Product Information $rac{partial L}{partial t_1} = rac{partial L}{partial t_2}$ Product Information $t_2$ (ReLU)
$rac{partial L}{partial B}$ Product Information $rac{partial L}{partial t_1}$ , and

A block diagram shows the operations of a forward pass and backward pass, with the formulas for gradients. Matmul with DRELU_BGRAD epilog covers computing the gradients for t2 (multiplying by weights), t1 (applying ReLU mask) and B (batch sum). Computing the gradients for W is not covered by the DRELU_BGRAD epilog. — *4., DRELU_BGRAD*

Product Information $rac{partial L}{partial B}$ and $rac{partial L}{partial t_1}$ for MatmulThis product is a networking product designed for enterprise and data center networking.

mm = Matmul(weights.T, grad)

mm.plan()

def backward():

    grad_t1 = mm.execute()

    grad_t1[mask] = 0  # assuming that `mask = (t1 

    grad_bias = cupy.sum(grad_t1, axis=1)

    return grad_t1, grad_bias

Product Information DRELU_BGRAD This product is a networking product designed for enterprise and data center networking. $rac{partial L}{partial t_3}$ CuPy grad This product is a networking product designed for enterprise and data center networking.DRELU_BGRAD epilog relu_auxProduct Information RELU_AUX_BIAS epilog is a networking product designed for enterprise and data center networking. $rac{partial L}{partial B}$ 。

mm = Matmul(weights.T, grad)

mm.plan(epilog=MatmulEpilog.DRELU_BGRAD, epilog_inputs={"relu_aux":relu_mask})

def backward():

    grad_t1, aux_outputs = mm.execute()

    grad_bias = aux_outputs["drelu_bgrad"]

    return grad_t1, grad_bias

A bar plot shows the performance of the naive implementation and DRELU_BGRAD. Naive implementation reaches 56.9% of peak TFLOP/s, and DRELU_BGRAD reaches 66.4%. — *5. Performance comparison of backward pass implementations*

65536 is a NVIDIA networking product designed for enterprise and data center networking.

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