Bug: Numerically unstable loss at reward model

[s-isaev]

Hi! I have got an infinite loss when trained critic model at step 2:
Epoch 1/1 with loss inf
I've found a source of this problem: reward model loss is calculated with unstable formula:
https://github.com/microsoft/DeepSpeedExamples/blob/ab4e2e54620d0e80ead128b30dd39d9d55751eab/applications/DeepSpeed-Chat/training/utils/model/reward_model.py#L102
I propose to replace it with this expression:

loss += nn.functional.softplus( r_truncated_reward - c_truncated_reward).mean()

Mathematically -log(sigmoid(x)) is equal to softplus(-x) but the second one is stable. Here are outputs of these functions respectivelly with fp32:
-100.0: (inf,100.0) -90.0: (inf,90.0) -80.0: (80.0,80.0) -70.0: (70.0,70.0) -60.0: (60.0,60.0) -50.0: (50.0,50.0) -40.0: (40.0,40.0) -30.0: (30.0,30.0) -20.0: (20.0,20.0) -10.0: (10.000045776367188,10.000045776367188) 0.0: (0.6931471824645996,0.6931471824645996) 10.0: (4.541977250482887e-05,4.5398901420412585e-05) 20.0: (-0.0,2.06115369216775e-09) 30.0: (-0.0,9.357622912219837e-14) 40.0: (-0.0,4.24835413113866e-18) 50.0: (-0.0,1.9287498933537385e-22) 60.0: (-0.0,8.75651089272076e-27) 70.0: (-0.0,3.975449954226706e-31) 80.0: (-0.0,1.8048513285848406e-35) 90.0: (-0.0,8.194008692231508e-40)

[s-isaev]

If you agree with this, here is PR: #424

[minjiaz]

Hi @s-isaev,

Thank you for bringing this issue to our attention! I can help evaluate the impact of the loss calculation and the PR.

From a quick glance, this seems to be quite reasonable.If I understand correctly, softplus(x) is essentially max(0,x)+log(1+e−|x|), right? softplus(-x) avoids Inf values while having a very small delta (should be identical in theory) in comparison to -log(sigmoid(x)).

In the meantime, could you please provide more information about how you encountered this issue? Did it occur while following the step 2 training script or when changing certain parameters such as datasets or learning rate?

Best,
Minjia

[DanqingZ]

@minjiaz @s-isaev
I had infinity loss for step 2 and chatted with GPT4 to get a solution
When calculating the difference between c_truncated_reward and r_truncated_reward, the values might be too large, causing the sigmoid function to return either 0 or 1. In this case, the logarithm becomes undefined. To mitigate this issue, you can use the logsigmoid function instead:

loss += -torch.nn.functional.logsigmoid(c_truncated_reward - r_truncated_reward).mean()

This is consistent with trl implementation: https://github.com/lvwerra/trl/blob/main/examples/summarization/scripts/reward_summarization.py#L186

I believe this repository primarily re-implements the reward model based on trlx while also inheriting the unstable loss implementation: https://github.com/CarperAI/trlx/blob/main/examples/summarize_rlhf/reward_model/reward_model.py#L89

[HermitSun]

I found that if I use all four datasets given in the training script(i.e. Dahoas/rm-static, Dahoas/full-hh-rlhf, Dahoas/synthetic-instruct-gptj-pairwise, yitingxie/rlhf-reward-datasets), then I will get an infinite loss; but if I only use Dahoas/rm-static, the loss is a normal value.
Does anyone know why this happens?

[minjiaz]

@s-isaev and @DanqingZ, thank you both for your suggestion!

I have tested both softplus and logsigmoid. Both are numerically stable. -torch.nn.functional.logsigmoid(x) provides a slightly more accurate value while avoiding infinite loss than torch.nn.functiona.softplus(-x), so we will replace log(sigmoid) with torch.nn.functional.logsigmoid(x). I have created a PR (#501) to fix the issue.

i, -torch.log(torch.sigmoid(x)), torch.nn.functiona.softplus(-x), -torch.nn.functional.logsigmoid(x)
-100 , tensor(inf) tensor(100.) tensor(100.)
-90.0 , tensor(inf) tensor(90.) tensor(90.)
-80.0 , tensor(80.) tensor(80.) tensor(80.)
-70.0 , tensor(70.) tensor(70.) tensor(70.)
-60.0 , tensor(60.) tensor(60.) tensor(60.)
-50.0 , tensor(50.) tensor(50.) tensor(50.)
-40.0 , tensor(40.) tensor(40.) tensor(40.)
-30.0 , tensor(30.) tensor(30.) tensor(30.)
-20.0 , tensor(20.) tensor(20.) tensor(20.)
-10.0 , tensor(10.0000) tensor(10.0000) tensor(10.0000)
0.0 , tensor(0.6931) tensor(0.6931) tensor(0.6931)
10.0 , tensor(4.5420e-05) tensor(4.5399e-05) tensor(4.5418e-05)
20.0 , tensor(-0.) tensor(2.0612e-09) tensor(0.)
30.0 , tensor(-0.) tensor(9.3576e-14) tensor(0.)
40.0 , tensor(-0.) tensor(4.2484e-18) tensor(0.)
50.0 , tensor(-0.) tensor(1.9287e-22) tensor(0.)
60.0 , tensor(-0.) tensor(8.7565e-27) tensor(0.)
70.0 , tensor(-0.) tensor(3.9754e-31) tensor(0.)
80.0 , tensor(-0.) tensor(1.8049e-35) tensor(0.)
90.0 , tensor(-0.) tensor(8.1940e-40) tensor(0.)
100.0 , tensor(-0.) tensor(3.7835e-44) tensor(0.)

Best,
Minjia

[minjiaz]

Hi @HermitSun,

I found that if I use all four datasets given in the training script(i.e. Dahoas/rm-static, Dahoas/full-hh-rlhf, Dahoas/synthetic-instruct-gptj-pairwise, yitingxie/rlhf-reward-datasets), then I will get an infinite loss; but if I only use Dahoas/rm-static, the loss is a normal value. Does anyone know why this happens?

Yes, we have observed that adding certain datasets lead to performance degradation. We have updated step 3 training scripts to use just one dataset for now, as shown below.

https://github.com/microsoft/DeepSpeedExamples/blob/2ec4be783a99803740a9f8cd3fcddcf798f00e55/applications/DeepSpeed-Chat/training/step3_rlhf_finetuning/training_scripts/single_node/run_1.3b.sh#L28

Best,
Minjia

[HermitSun]

Hi @HermitSun,

I found that if I use all four datasets given in the training script(i.e. Dahoas/rm-static, Dahoas/full-hh-rlhf, Dahoas/synthetic-instruct-gptj-pairwise, yitingxie/rlhf-reward-datasets), then I will get an infinite loss; but if I only use Dahoas/rm-static, the loss is a normal value. Does anyone know why this happens?

Yes, we have observed that adding certain datasets lead to performance degradation. We have updated step 3 training scripts to use just one dataset for now, as shown below.

https://github.com/microsoft/DeepSpeedExamples/blob/2ec4be783a99803740a9f8cd3fcddcf798f00e55/applications/DeepSpeed-Chat/training/step3_rlhf_finetuning/training_scripts/single_node/run_1.3b.sh#L28

Best, Minjia

Thank you for your reply🥰.

Is there any conclusion about what kind of datasets will cause an unexpected performance degradation?

Maybe these datasets contain specific texts or something else?

[minjiaz]

Multiple log(sigmoid) implementations have been tested with end-to-end eval, changes merged at #501.