pytorch中的loss计算

crossentropyloss = softmax + log + nllloss
L = − 1 N ∑ i p i lg ⁡ q i L=-frac{1}{N}sum_i{p_ilg q_i} L=−N1​i∑​pi​lgqi​

• p i p_i pi​​ 真实label
• q i q_i qi​ 预测lable概率

def test_NLLLoss():
    m = nn.LogSoftmax(dim=-1)
    loss = nn.NLLLoss()  # NLLLoss内部只会对input进行取负操作，往往需要自己在外部对input进行softmax和log操作
    loss1 = nn.CrossEntropyLoss()  # softmax + log + nllloss
    loss2 = nn.NLLLoss(reduction='none')
    # input is of size N x C = 3 x 5
    input = torch.randn(3, 5, requires_grad=True)
    # each element in target has to have 0 <= value < C
    # target = torch.empty(3, dtype=torch.long).random_(5)
    target = torch.tensor([1, 0, 4])
    output = loss(m(input), target)

    output_mine = -(torch.gather(m(input), index=target.unsqueeze(-1), dim=1)).sum() / target.size(0)

    print("NLLLoss")
    print("input:", input)
    print("log_softmax: ", m(input))
    print("target:", target)
    print("loss:", output)
    print("loss1:", loss1(input, target))
    print("none loss:", loss2(m(input), target))
    print("mine loss:", output_mine)
    
"""
NLLLoss
input: tensor([[-0.3630, -2.0179, -1.9629, -0.1293,  0.7163],
        [ 0.0691, -0.6838,  1.1787, -0.4356, -1.6239],
        [-1.1982,  0.4505, -0.8784,  1.1047,  0.9539]], requires_grad=True)
log_softmax:  tensor([[-1.7226, -3.3775, -3.3225, -1.4889, -0.6433],
        [-1.6661, -2.4191, -0.5566, -2.1709, -3.3592],
        [-3.2651, -1.6164, -2.9453, -0.9622, -1.1130]],
       grad_fn=)
target: tensor([1, 0, 4])
loss: tensor(2.0522, grad_fn=)
loss1: tensor(2.0522, grad_fn=)
none loss: tensor([3.3775, 1.6661, 1.1130], grad_fn=)
mine loss: tensor(2.0522, grad_fn=)
"""    

def test_CrossEntropyLoss():
    loss = nn.CrossEntropyLoss(ignore_index=1)  # CrossEntropyLoss内部会对input进行softmax和log操作
    loss1 = nn.CrossEntropyLoss(reduction='none', ignore_index=1)
    # input is of size N x C = 4 x 5
    input = torch.randn(4, 5, requires_grad=True)
    # each element in target has to have 0 <= value < C
    # target = torch.empty(4, dtype=torch.long).random_(5)
    target = torch.tensor([4, 2, 1, 1])
    output = loss(input, target)
    tar_mask = target.ne(1).float().detach()

    output_mine = (-torch.gather(F.log_softmax(input, dim=-1), index=target.unsqueeze(-1), dim=1) * tar_mask.unsqueeze(1)).sum() / tar_mask.sum()
    
    print("CrossEntropyLoss")
    print("input:", input)
    print("log_softmax: ", F.log_softmax(input, dim=-1))
    print("target:", target)
    print("loss:", output)
    print("none loss:", loss1(input, target))
    print("mine loss:", output_mine)
    
"""
CrossEntropyLoss
input: tensor([[ 0.5172,  0.4194, -1.2796,  1.0469, -1.2624],
        [-0.9485, -1.3813, -0.2962, -0.2169, -0.6744],
        [-1.9062,  0.0981, -2.3465,  0.1645,  0.5468],
        [ 0.6164, -0.7764, -0.3201, -0.6006,  0.9538]], requires_grad=True)
log_softmax:  tensor([[-1.3711, -1.4689, -3.1680, -0.8414, -3.1508],
        [-1.9405, -2.3733, -1.2882, -1.2089, -1.6664],
        [-3.3541, -1.3497, -3.7944, -1.2834, -0.9010],
        [-1.2053, -2.5981, -2.1418, -2.4223, -0.8679]],
       grad_fn=)
target: tensor([4, 2, 1, 1])
loss: tensor(2.2195, grad_fn=)
none loss: tensor([3.1508, 1.2882, 0.0000, 0.0000], grad_fn=)
mine loss: tensor(2.2195, grad_fn=)
"""

L = − 1 N ∑ i ( p i lg ⁡ q i + ( 1 − p i ) lg ⁡ ( 1 − q i ) ) L=-frac{1}{N}sum_i{left( p_ilg q_i+left( 1-p_i right) lg left( 1-q_i right)right)} L=−N1​i∑​(pi​lgqi​+(1−pi​)lg(1−qi​))

def test_BCELoss():
    m = nn.Sigmoid()
    loss = nn.BCELoss()  # BCELoss内部会对input进行log操作
    loss1 = nn.BCEWithLogitsLoss()  # sigmoid + BCE
    loss2 = nn.BCELoss(reduction='none')
    input = torch.randn(5, requires_grad=True)
    # target = torch.empty(3).random_(2)
    target = torch.tensor([1, 0, 1, 0, 1]).float()
    output = loss(m(input), target)

    output_mine = -(target * m(input).log() + (1 - target) * (1 - m(input)).log()).sum() / input.size(0)

    print("nBCELoss")
    print("input:", input)
    print("sigmoid input:", m(input))
    print("target:", target)
    print("loss:", output)
    print("loss1:", loss1(input, target))
    print("loss2:", loss2(m(input), target))
    print("mine loss:", output_mine)
"""
BCELoss
input: tensor([-1.5962, -0.2057, -0.2376, -0.1843,  0.3428], requires_grad=True)
sigmoid input: tensor([0.1685, 0.4487, 0.4409, 0.4540, 0.5849], grad_fn=)
target: tensor([1., 0., 1., 0., 1.])
loss: tensor(0.8674, grad_fn=)
loss1: tensor(0.8674, grad_fn=)
loss2: tensor([1.7807, 0.5956, 0.8190, 0.6052, 0.5364],
       grad_fn=)
mine loss: tensor(0.8674, grad_fn=)
"""

L = − ∑ i ( p i lg ⁡ q i − p i lg ⁡ p i ) L=-sum_i{left( p_ilg q_i-p_ilg p_iright)} L=−i∑​(pi​lgqi​−pi​lgpi​)

def test_KLDivLoss():
    loss = nn.KLDivLoss(reduction='batchmean')  # 仅仅除以batch_size
    loss1 = nn.KLDivLoss(reduction='none')  # KLDivLoss内部不会对input进行softmax和log操作
    input = torch.log_softmax(torch.tensor([[-2., -6., -8.], [-7., -1., -2.]], requires_grad=True), dim=-1)
    target = torch.tensor([[0.8, 0.1, 0.1], [0.1, 0.7, 0.2]])
    output = loss(input, target)

    output_mine = torch.sum(torch.log(target)*target - target*input) / input.size(0)

    print("nKLDivLoss")
    print("input:", input)
    print("target:", target)
    print("loss:", output)
    print("none loss:", loss1(input, target))
    print("mine loss:", output_mine)
"""
KLDivLoss
input: tensor([[-0.0206, -4.0206, -6.0206],
        [-6.3151, -0.3151, -1.3151]], grad_fn=)
target: tensor([[0.8000, 0.1000, 0.1000],
        [0.1000, 0.7000, 0.2000]])
loss: tensor(0.3474, grad_fn=)
none loss: tensor([[-0.1620,  0.1718,  0.3718],
        [ 0.4012, -0.0291, -0.0589]], grad_fn=)
mine loss: tensor(0.3474, grad_fn=)
"""