How to interpret reg_max / dfl?

[LemonGraZ]

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Question

I am confused about the reasoning and advantages of the reg_max value and the DFL module.

When looking at the ultralytics head each grid cells predicts reg_max number boxes (regression to 4 offsets).

https://github.com/ultralytics/ultralytics/blob/b89d6f407044276b1f54753ef98c719e89928631/ultralytics/nn/modules/head.py#L37-L38

These boxes are then reduced to a single box (4 offsets from grid center) in the dfl module forward call:

https://github.com/ultralytics/ultralytics/blob/b89d6f407044276b1f54753ef98c719e89928631/ultralytics/nn/modules/head.py#L117-L118

https://github.com/ultralytics/ultralytics/blob/b89d6f407044276b1f54753ef98c719e89928631/ultralytics/nn/modules/block.py#L55-L73

In the DFL we end up with a [batch_size, 4, reg_max, n_anchors] tensor. So per grid cell reg_max times 4 predictions for offsets. Each of the 4 offsets are then softmaxed over the reg_max dimension. These are then dot producted (=weighted) with a range tensor range(0, reg_max).

So for a single anchorbox and a single offset the output from the feature map would look like this: [ -9.6771, -14.3445, -2.0779, 2.3168, 11.0486, 5.1030, 12.7565, 11.8883, 9.3741, -3.8249, -9.6758, -8.6363, 6.8299, -1.3159, 3.2808, 8.3574] (=16 offsets towards left from a single anchorbox) After softmaxing it looks like this: [0, 0, 0, 0, 0.1098, 0.0003, 0.6059, 0.2543, 0.0206, 0, 0, 0, 0.0016, 0, 0, 0.0074]) And this is then dot producted with the following range tensor: [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15] Resulting in a single offset of 6.1526. This value is then multiplied with the stride of the sourcing feature map and then we have the offset in pixel. This means the maximum object size is 15 * 2 * stride.

This process is skipped if reg_max=1. In this case every anchor box directly predicts 4 unbound offsets.

My Question:

1. Why doesn't every anchorbox directly predict 4 offsets like it is the case with reg_max=1? What is idea or reasoning behind that?
2. How can this dot producted be interpreted? The docstring states "Applies a transformer layer on input tensor..."? How can this be seen as a transformer layer?

I'd like to understand the thinking behind these design decisions. Thank you all!❤️

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[LemonGraZ]

According to ChatGPT and Gemini the following points are related to that decision. To me that sounds pretty reasobable.

• Quantization of Regression Outputs: Instead of directly predicting four offsets for each anchor box (as done when reg_max=1), the use of reg_max and the DFL module allows the model to predict a distribution for each offset. This distribution is then used to compute a weighted average, resulting in the final offset value. This approach transforms the regression problem into a classification-like problem, where the model predicts the probability of the offset being at each discrete position within a range.

• Improved Precision: By predicting a distribution over possible offsets (with the range defined by reg_max), the model can capture more nuanced information about the position of the object. This helps in improving the precision of the bounding box predictions, as it allows for a more fine-grained representation of the offsets compared to a single direct prediction.

• Robustness to Small Variations: Predicting a distribution can make the model more robust to small variations and noise in the training data. Instead of committing to a single prediction, the model can express uncertainty by spreading probability mass over multiple positions, which can lead to better generalization.

• Regularization Effect: The softmax operation and subsequent dot product act as a form of regularization. The model is encouraged to produce smooth and coherent distributions, which can help in preventing overfitting to the training data.

[Y-T-G]

You can find the justification for it in YOLOv6 paper

https://arxiv.org/abs/2209.02976

[LemonGraZ]

@Y-T-G Thanks, under what key-word do I find that? Is this part of the Distributed Focal Loss (DFL) and thus more related to that paper?

[Y-T-G]

Section 2.3.2

reg_max is part of DFL.

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