dense and sparse update

# dense update
# forward 
input: 1, 48, 8, 8
weight: 240, 48, 1, 1
output: 1, 240, 8, 8

# input 
# (n, c, h, w) => (1, n * c, h, w)
input_1 = 1, 48, 8, 8

# grad
# (n, oc, oh, ow) = (tiling) => (n, c // g * oc , oh, ow)
                # => (n * c // g * oc , 1, oh, ow)
grad_1 = 1, 240, 8, 8 
       = (tiling) => 1, 11520, 8, 8 
       => 11520, 1, 8, 8 

# grad_weight
# (1, n * c, h, w) * (n * c // g * oc , 1, kh, Kw) | g=n*c  
grad_w = conv(input_1, grad_1, groups=48)
       = (1, 48, 8, 8) * (11520, 1, 8, 8)
       = (11520, 1, 1, 1)

# => (n * c // g * oc , 1, oh, ow)
# => (n, c // g * oc, 1, oh, ow)
#         = (reduce) =>  (c // g * oc, 1, oh, ow)   
#         =>  (c // g, oc,  oh, ow)   
grad_w = 11520, 1, 1, 1 => 1, 11520, 1, 1, 1 => 11520, 1, 1, 1 
        => 48, 240, 1, 1 => 240, 48, 1, 1
        
        
 # sparse update
# forward 
input: 1, 48, 8, 8
weight: 240, 48, 1, 1
output: 1, 240, 8, 8

# input 
# (n, c, h, w) => (1, n * c, h, w)
input_1 = 1, 24, 8, 8

# grad
# (n, oc, oh, ow) = (tiling) => (n, c // g * oc , oh, ow)
                # => (n * c // g * oc , 1, oh, ow)
grad_1 = 1, 120, 8, 8 
       = (tiling) => 1, 5760, 8, 8 
       => 5760, 1, 8, 8 

# grad_weight
# (1, n * c, h, w) * (n * c // g * oc , 1, kh, Kw) | g=n*c  
grad_w = conv(input_1, grad_1, groups=24)
       = (1, 24, 8, 8) * (5760, 1, 8, 8)
       = (5760, 1, 1, 1)

# => (n * c // g * oc , 1, oh, ow)
# => (n, c // g * oc, 1, oh, ow)
#         => (reduce) =>  (c // g * oc, 1, oh, ow)   
#         =>  (c // g, oc,  oh, ow)   
grad_w = 5760, 1, 1, 1 => 1, 5760, 1, 1, 1 => 5760, 1, 1, 1 
        => 24, 240, 1, 1 => 240, 24, 1, 1