<table><caption>Table A.1: Results comparison for COCO using the dedicated challenge metrics on the test-dev 2017 dataset.</caption><thead><tr><th></th><th>AP<sub>0.5:0.95</sub></th><th>AP<sub>0.5</sub></th><th>AP<sub>0.75</sub></th><th>AP<sub>S</sub></th><th>AP<sub>M</sub></th><th>AP<sub>L</sub></th><th>AR<sub>1</sub></th><th>AR<sub>10</sub></th><th>AR<sub>100</sub></th><th>AR<sub>S</sub></th><th>AR<sub>M</sub></th><th>AR<sub>L</sub></th></tr></thead><tbody><tr><th>YOLO-V2</th><td>21.6</td><td>44.0</td><td>19.2</td><td>5.0</td><td>22.4</td><td>35.5</td><td>20.7</td><td>31.6</td><td>33.3</td><td>9.8</td><td>36.5</td><td>54.4</td></tr><tr><th>YOLO-CIANNA</th><td>21.9</td><td>40.1</td><td>21.8</td><td>4.1</td><td>22.8</td><td>37.9</td><td>20.7</td><td>30.2</td><td>31.2</td><td>4.5</td><td>34.6</td><td>55.0</td></tr></tbody></table>

averaged mAP over a given IoU range. Overall, this metric has the advantage of sampling the full sensitivity of a given detector, corresponding to its discrimination capability between the background and the objects to detect (Sect. 5.1).

### A.8.3. PASCAL-VOC object detection

The PASCAL-VOC (PASCAL Visual Object Classes, Everingham et al. 2010) dataset was a yearly computer vision challenge that ran from 2005 to 2012, and that included an object detection task. This dataset is still commonly used as a benchmark to compare the performances of different object detectors. One classical approach is to combine the training and validation dataset from the 2007 and 2012 editions onto a single training sample comprising around 16500 images containing multiple bounding boxes belonging to 20 possible classes. The evaluation of the detector performances is then done on the 2007 test dataset of 5000 images. Using our high-resolution pretrained backbone on ImageNet, we can drop the last pooling and output layer and add three new convolutional layers with 3×3 filters plus group normalization. Finally, we add our detection layer. The input resolution is changed for a 416×416 input, which results in a 13×13 output grid. Regarding the setup of our advanced association function, we use the DIoU as our matching score, $S_{ar} = 3$, $L_{low}^{floU} = -0.1$, $L_{C}^{floU} = -0.1$, $\alpha_{best} = 0.05$, and some difficult object flagging. After training this network for a few hundred epochs, we achieve an mAP@0.5 of 74.98 on the PASCAL 2007 test dataset. At an identical resolution, the original YOLO-V2 model achieves 76.8. Considering the structural limitations of our approximated darknet-19 backbone, this result demonstrates the efficiency of our YOLO-CIANNA method.

### A.8.4. COCO object detection

The COCO (Common Objects in Context, Lin et al. 2014) dataset was also a yearly computer vision challenge that ran from 2014 to 2017, and that included an object detection task. Like PASCAL, COCO is still commonly used as a benchmark to compare the performances of different object detectors. In the 2017 version, the training set comprises roughly 118000 images, the validation set comprises 5000 images, and the hidden test set comprises roughly 40000 images (accessible through a test server). For the detection task, the objects are labeled with over 1000 classes. We use the same network backbone pretrained on ImageNet, with the same set of hyperparameters we used for PASCAL and a 416×416 input resolution. Our result on the test dataset obtained using the submission server is presented in Table A.1 with all the COCO metrics and is compared with the result of the classical YOLO-V2 model. We first observe that our method is competitive with the classical YOLO-V2 detector on this dataset despite our structural limitations. In addition, these metrics indicate that our method retrieves more large objects and better reconstructs the objects it manages to detect. However, the lower mAP@0.5 score indicates that we recover fewer objects overall. This is likely due to a poorer detection of small objects, confirmed by the small AR<sub>S</sub> corresponding to recall at small scales. This result

was expected, considering that we lack the ending skip connection to allow our method to preserve more resolved features at the detection layer.

Regarding computing performances, we can achieve 690 images per second at this resolution using an RTX 4090 GPU with mixed precision enabled. On a much lighter A2000 mobile GPU, we still reach above 60 images per second, meaning that our implementation allows real-time detection on modern entry-level hardware. We note that this level of performance is similar to the one achieved by the original YOLO-V2 darknet implementation.

Finally, we highlight that our result is far from the current top scores on the COCO dataset, which require much stronger architectures, but it is not our scope to compete with them. The presented benchmarks validate the method for a given relatively light architecture. Most of the time, the architectures that are truly useful for astronomical datasets are relatively shallow due to much less feature diversity and complexity, the main challenges being placed in other aspects of the method design.

## Appendix B: Classical YOLO-V2 backbone for SDC1

When exploring the suitability of a given method to a new problem, the classical approach is to look at how this method was applied to a similar problem. This is especially true for network architectures and hyperparameters since exploring these aspects from scratch can be extremely costly in terms of time and computing resources. If the new application is sufficiently close to other well-known applications of the same method, one could even use pretrained models to save some training time or improve the performance of their new model. For example, it is the approach used in Sortino et al. (2023) where they test the capability of a YOLO architecture on a source detection problem. They conclude that the results were improved when using a pretrained model. However, achieving apparently good results with known architectures or with pretrained models does not guarantee that the new application will have close to optimal results. In cases where it achieves bad results, it can even lead to the false conclusion that the whole approach is inefficient while only the backbone architecture might be unsuited for the task. To participate in this global discussion, we explore in this section the results we obtained on the SDC1 dataset using the classical YOLO-V2 darknet-19 architecture in a naive way and compare it to our reference result with our custom architecture.

### B.1. Selection of architectures and training setups

While the classical YOLO-V2 formalism could be emulated with our implementation, doing a thorough and documented comparison of the individual effects of all the differences would be too complicated. In this section, we preserved all the data preparation, training setup, hyperparameters selection, detection units setup, and prediction pipeline construction that we defined in Sect. 3 and studied variations in the network backbone and starting weights. To achieve the same reduction factor of 16 as our reference SDC1 model with pretrained darknet-19 backbones, it
<table><caption>Table B.1: SDC1 scores and related properties for source catalogs from different models and architectures.</caption><thead><tr><th>Method</th><th>M<sub>s</sub> (Score)</th><th>N<sub>det</sub></th><th>N<sub>match</sub></th><th>N<sub>false</sub></th><th>N<sub>bad</sub> &in; N<sub>false</sub></th><th>Purity</th><th>s&#772;</th></tr></thead><tbody><tr><td>darknet-19-regul-scratch</td><td>445093</td><td>688112</td><td>645626</td><td>42486</td><td>15070</td><td>93.83%</td><td>0.7552</td></tr><tr><td>darknet-19-base-pretrain</td><td>423077</td><td>665304</td><td>620685</td><td>44619</td><td>16003</td><td>93.29%</td><td>0.7535</td></tr><tr><td>darknet-19-regul-pretrain</td><td>411541</td><td>642153</td><td>600193</td><td>41960</td><td>13398</td><td>93.47%</td><td>0.7556</td></tr><tr><td>darknet-19-base-scratch</td><td>386395</td><td>644371</td><td>591039</td><td>53332</td><td>15020</td><td>91.72%</td><td>0.7440</td></tr></tbody></table>

is necessary to cut the end part of the darknet-19 architecture before it reaches a reduction factor of 32.

We compare two slightly different architectures. The first one is obtained by taking the first 13 convolution layers of our darknet architecture pretrained on the COCO dataset and adding three new convolutional layers with 1024 filters of size 3×3, each followed by a group normalization. We then add our detection layer. This first architecture is referred to as darknet-19-base. The second one uses the same pretrained part but then adds layers to recreate the detection head structure of our custom architecture consisting of the last four layers in Fig. 11. This architecture has a more progressive increase in size and includes dropout regularization. This second architecture is referred to as darknet-19-regul. It is essential to note the darknet-19-regul architecture is composed of 14.4 million parameters, which is very similar to our custom architecture. In contrast, the darknet-19-base is almost twice the size with a total of 28.3 million parameters, which is explained by the differences in the last four layers. Regarding computing performances, the darknet-19-regul architecture has almost the same performances as our custom architecture, while the darknet-19-base is around 20% slower.

We performed two independent training for each architecture, the first using the pretrained COCO weights for the corresponding layers (-pretrain) and the second from scratch using classical random weight initialization for all layers (-scratch). Therefore, we have a total of four trained models to compare. We use the same prediction pipeline as our reference model for all of them, following the description in Sect. 3.9.

## B.2. Results and discussion

The best score results for each of the four models are presented in Table B.1. We can first observe that the best one has a score 7% lower than our reference model from Table 5, which reaches better scores after only 400 iterations (Fig. 13). We stress that the results are reproducible and stable over multiple training with different initial weight values. In addition, the difference in score between models is significant as it is higher than the typical score fluctuation observed over multiple training of the same setup. From these results, we see that for the darknet-19-base architecture, pretraining improves the detection results, while it degrades it for the lighter darknet-19-regul architecture. The apparent flux distribution for these four models is very similar to our reference model. The main difference between these models is their completeness at a given purity, allowing some of them to detect more sources. We also note that models that achieve the best score have the highest characterization accuracy. This is expected, as the predicted flux accuracy is one of the match criteria.

Our interpretation is that the truncated darknet-19 architecture is not adapted to our application and encapsulates too much expressivity to be properly constrained by our training data. It appears that the pretrained weights do not encapsulate relevant information but still act as a startup regularization by reducing the accessible parameter space, preventing the network from over-fitting. The training of the darknet-19-base-scratch model is

very unstable as we observe variations of about 100000 points between successive control steps when continuing the training after the best score iteration, which is a striking proof of overfitting. This model exhibits the poor results of an unconstrained network, while the darknet-19-regul-scratch demonstrates that adding a small amount of structural regularization solves this issue better than pretraining. In our opinion, the most robust demonstration of the irrelevance of the features learned on COCO for our problem is that the darknet-19-regul-scratch model significantly outperforms the darknet-19-regul-pretrain model. In addition, we tested a variety of alternative setups around our darknet-19-regul architecture by changing the number of layers that start from their pretrained weights, the rest being initialized from scratch. We observed that the best achievable score degrades as the number of pretrained layers increases. In this regard, we consider the common empirical observation about obtaining better results using pretrained models as incomplete and possibly misleading regarding the relevance of low-level features learned from everyday-life images for astronomical datasets (e.g., Sortino et al. 2023; Wu et al. 2019). In addition, pretrained models do not necessarily train faster than the others on this specific application, which is another sign of the nonrelevance of the features they are starting from.

Finally, achieving better results with our custom backbone indicates that architectures that have been proven efficient for everyday-life images are not necessarily suited for astronomical images. A striking difference between the two architectures is the absence of inter-layer normalization. We already identified in Sect. 3.6 that using group normalization between most layers in our custom architecture significantly reduces our best achievable score because it alters the absolute value of the input pixels, which contains information about the source flux and the input dynamic. Still, group normalization is not enough to explain the lower result of the darknet-19-regul-scratch model (Sect. B), highlighting that other architectural design choices matter.

# Appendix C: Alternative training area for the SDC1

## C.1. Reference architecture

We exposed in Sect. 3.5 the issues that arise from having access to only a small subpart of the full image to train our detector. This section explores an alternative definition for the training area that is more representative of the image field variations. We use the post-challenge access to the full True catalog and define a new training area that spans from the center of the image up to the right edge, representing a radius of the primary beam. We do not add extra noise-only regions since they should not be required anymore. To evaluate only the effect of the training region, we adjust the area around the selected radius so the number of selected sources remains similar to our reference case (Sect. 3.4). Our alternative training area is then a rectangular region with $-2.80 \le RA \le 0.00$ degrees and $-30.12 \le Dec \le -29.88$ degrees as illustrated in Fig. C.1, and that contains 34913
<table><caption>Table C.1: Scores and related properties based on the alternative training area for source catalogs from different models.</caption><thead><tr><th>Method</th><th>M<sub>s</sub> (Score)</th><th>N<sub>det</sub></th><th>N<sub>match</sub></th><th>N<sub>false</sub></th><th>N<sub>bad</sub> &in; N<sub>false</sub></th><th>Purity</th><th>s&#772;</th></tr></thead><tbody><tr><td>YOLO-CIANNA-alt-train-large-bootstrap</td><td>502656</td><td>723655</td><td>690894</td><td>32761</td><td>12991</td><td>95.47%</td><td>0.7750</td></tr><tr><td>YOLO-CIANNA-alt-train-large</td><td>486053</td><td>709689</td><td>674404</td><td>35285</td><td>14380</td><td>95.02%</td><td>0.7730</td></tr><tr><td>YOLO-CIANNA-alt-train</td><td>484145</td><td>708954</td><td>672906</td><td>36048</td><td>14988</td><td>94.91%</td><td>0.7731</td></tr></tbody></table>

<figure><img src="image_25.png" /><figcaption>Fig. C.1: Two-dimensional histogram of the central coordinates of the sources from the full True catalog that pass our selection function. The red box indicates our alternative training area.</figcaption></figure>

Alt. training region hand-made selection function

<figure><img src="image_26.png" /></figure>

Alt. training region bootstrap selection function

<figure><img src="image_27.png" /><figcaption>Fig. C.2: Source flux distribution histogram in log scale and using log-bins for the True catalog and the selected sources in our alternative training. The top frame represents the classical selection function, and the bottom frame represents the bootstrap selection function after a single iteration.</figcaption></figure>

selected sources. Figure C.2 represents the apparent flux distribution of the selected sources, which is similar to the distribution we obtained with the default training region.

We train our network using the same configuration as our reference model and only change the training sample, which results in the YOLO-CIANNA-alt-train model. The prediction pipeline remained unchanged, but we altered the SDC1 scorer code to modify the definition of the training area. We obtain the score presented in Table C.1 and a list of matching sources to produce the same diagnostics we did on our reference catalog. While the scores cannot be directly compared due to the different testing areas, the number of detected sources is relatively similar to our reference catalog. The purity is even slightly improved by 0.70%. The histogram of the apparent flux of the detected sources is presented in Fig. C.4, exhibiting a similar distribution to our reference result. The average source score is also slightly higher, thanks to the presence of sources from all the primary beam regimes in the training sample. Looking at individual fields, this new model produces results that are visually similar to our reference model. However, Fig. C.3 shows that the distribution of false positive detections over the full image field is more homogeneous. It demonstrates that this alternative training sample allows for better generalization without requiring extra noise regions.

## C.2. Larger architecture and bootstrap training

An interesting side effect of this alternative training area is that the network training is more stable. We tried providing a bit of extra expressivity with less regularization by replacing the

second last layer of our default architecture with two 1×1 convolutional layers, the first one with 3072 filters and a dropout of 30% and the second one with 2048 filters, constructing the YOLO-CIANNA-alt-train-large model. Training this new architecture with our alternative training area only modestly improves the score, as presented in Table C.1. This improvement can not be considered significant since it is of the same order as our typical multiple-training-identical-setup variability.

The combination of a more representative training sample and a stronger network makes it possible to use a bootstrap approach for refining our selection function. Instead of deciding which objects from the True catalog should be considered detectable, we land this decision on the detector itself. Using a model trained with a hand-made selection function for a few hundred epochs, we can produce a catalog of predicted sources with an objectness score over the training region. This catalog can then be cross-matched with the underlying list of target objects
<figure><img src="image_28.png" /><figcaption>Fig. C.3: Two-dimensional histograms of various kinds of “objects” representing their distribution over the full SDC1 field for the YOLO-CIANNA-alt-train model. The training area is masked when necessary. All densities are binned using the same 200x200 grid. The match and false detections are made using the DIoU-based matching metric, while the missed ones are based on our selection function. The central coordinates of the field are RA = 0 deg, Dec = −30 deg.</figcaption></figure>

<figure><img src="image_29.png" /><figcaption>Fig. C.4: Histograms of the sources as a function of their apparent flux using logarithmic bins for the underlying True catalog and predicted sources in our modified testing area. The bottom part of each frame represents the purity and completeness of each bin of the histograms. Top and bottom frames represents the alt-train and alt-train-large-bootstrap models respectively.</figcaption></figure>

from the simulation to construct a new training sample. Targets that the detector fails to detect can be removed from the training sample, and targets that are detected outside our hand-made selection function can be added back. We stress that this process is never used to directly inject a detector prediction as a new target. The properties from the True catalog sources that were successfully detected are used to define the new training sample. This approach requires stable training, as selecting a prediction before network convergence or when the network overtrains can harm the self-constrained selection function. This approach can be repeated several times using the successively trained detectors to refine the selection function for the next training.

We tested this approach with our reference architecture using the default SDC1 training area, but it did not improve the result significantly. With the default training area, any change in our hand-made selection function results in significant variations in the best achievable score. This variability mainly comes from the intermediate primary beam regime in which the detector has to interpolate from the discontinuous training area. This effect is corrected with the alternative training area, and the bootstrap training approach actually becomes useful. It is especially relevant in this context where the visibility of a source is strongly dependent on the beam regime, which was less the case for the central training area with less sensitivity variation. In such a context, having the detector provide information on which sources should be detectable is especially useful.

Using our alternative training area and our larger architecture alternative, the bootstrap approach significantly improves the results after only a single step. We present the resulting selection function over the apparent flux histogram in Fig. C.2. Compared to our handmade custom function, it removes targets for almost all apparent flux values. The most plausible explanation is that it removes blended sources that the detector cannot separate. Another effect is to smooth the low-cut flux in a wider flux interval. The score of the resulting model is indicated in Table C.1, and the predicted sources flux distribution in Fig. C.4. While all the diagnostics show results that are very similar to what we obtain with our reference architecture on our alternative training sample, we observe a significative score improvement of more than 3%, correlated with a better flux characterization score with $\bar{\epsilon}_{flux} = 0.680$. More improvement would likely be achievable by searching the optimum architecture and hyperparameters setup with this new training sample.

Overall, this approach removes the necessity for a well-defined selection function. This could be useful in a highly dimensional input space where defining a selection function can
be difficult. With this approach, the starting selection function could be the catalog of a less performant detection method. Still, it requires access to all the possible targets regardless of their visibility, so only real detections are kept at each step. While a simulated dataset is a best-case scenario for this approach, it could still be employed on observed datasets by confirming the proposed new detections with additional observations.

## Appendix D: Impact of simultaneous detection and characterization on detection-only performances

In Sect. 5.1.4, we introduce the idea that merging the detection and characterization inside a single loss could result in suboptimal performances. In practice, it is possible to separate both tasks by having a pure object detector and a dedicated characterization network. We could even train an independent characterization network for each parameter to predict. However, we observed that predicting correlated parameters in a single network produces better results for both parameters. For this reason, we expect a combined detection and characterization network to achieve better results as long as the parameter to predict correlates with the detectability of the object. The aim of this section is to verify this point for our method over the SDC1.

To compare models on a detection-only task, we can use the purely geometrical metric defined in Sect. 5.1.4 based on DIoU matching criteria. To evaluate the results at different detection quality requirements we use multiple DIoU threshold values of 0.1, 0.5, and 0.9. To reduce the matching time, predictions below a too-small objectness threshold will be removed. This threshold depends on the detection units and is set to 0.1 for the six small-size regimes and 0.05 for the three intermediate and large-size regimes. This will result in lower AP values than in Sect. 5.1.4, but the respective performances of different models will remain comparable. The results are compiled in Table D.1.

One issue with a purely geometrical match is that it increases the chances of a random match compared to the SDC1 match criterium that accounts for the flux. Before training any model, we evaluate the chances of random matches. For this, we build a density map from the raw ~950000 detections from our reference model. This map is used as a prior for drawing an equivalent number of sources with a random position, size, and objectness score that all follow the distributions of our reference model. The resulting "random 950k" catalog is passed through the scoring pipeline, and the results are reported in the same table. The number of random matches for DIoU > 0.5 is near 3%. However, this is not a good representation of our detection catalog as it comprises many detections overlapping over the same object. As stated in Sect. 4.1, almost 80% of the detections are removed by the NMS process that expects interdependency between the detections. Therefore, we build a second random catalog with only 110000 random sources, corresponding to the typical number of objects from our catalog that are not removed and do not match at the end of the post-process pipeline for a DIoU threshold of 0.1. This time, the obtained AP values are likely good approximations of the uncertainty of the AP values over the detected sources catalogs at their respective thresholds.

All the metric scores are reported for our default model with the prediction of the extra parameters as a reference (With param. reference). Our first test deactivates the optimization of the extra-parameters part of the loss while keeping the same architecture and training process (No param.), which is just a toggle switch in our CIANNA framework. As expected, the geometrical score decreases for all DIoU matching values, and the

number of detected sources is also reduced. One alternative explanation would be that the network expressivity is now too high for the simplified task, which would also explain why the optimal epoch is found earlier than for our reference model. To test this hypothesis, we train two new models that slightly alter our reference architecture: one where we increase the dropout rate on the before-last layer (No param. more regular), and a second where we reduce the number of filters in the same layer by about 30% (No param. light). Both models perform lower than the simple "No param" case at most DIoU thresholds. This indicates that predicting the extra parameters does have a direct positive impact. Still, we must verify if this effect is generic or if we mitigated the possible negative impact with our quality conditional fitting that results in the extra-parameter cascading loss (Sect. 2.7). We test this hypothesis by retraining our reference model with the extra-parameter prediction activated but setting $L_p^{\text{fIoU}} = -1$ (With param. no cascade). The results are lower than with the parameter deactivated, so predicting parameters for poorly detected sources has a negative impact. In summary, we conclude that extra-parameters can have a positive impact when predicting correlated quantities but only when the negative contribution from unreliable detection is mitigated in the corresponding loss subpart.

Finally, we perform a few extra tests to verify if the lower performance observed when not predicting the extra parameters was only caused by a bad input normalization or augmentation design. For this, we use a per-input patch normalization instead of our global normalization. We train two models with (With param. patch norm) and without (No param. patch norm) the parameter prediction enabled. As expected, the performance of the model with the parameter prediction is lowered, while the performance of the model without the parameter prediction is improved. However, our reference model, which combines parameter prediction and global normalization, remains better. As a last test, we use two input channels corresponding to the two normalization types and train new models with and without the parameter prediction (With param. dual norm. and No param. dual norm.). The detection performances are improved for both models and even surpass our reference model on the detection-only metric, but again, keeping the parameter prediction is better. Still, from the SDC1 metric perspective, our reference score remains higher than with the dual normalization input. This is likely the result of a lack of expressivity in the upper layers of the network that now have to handle two inputs with a limited number of parameters, negatively impacting the source characterization. These results strongly demonstrate that simultaneously predicting correlated parameters with a dynamic loss is a viable approach for improving detection-only performances.

Still, all these results were obtained for a single architecture with only small variations, a single set of hyperparameters, and one dataset. Empirical verification on a per-application basis is advised. Also, we acknowledge that global normalization is only possible in the context of a constant noise image from a single acquisition on a unique instrument. If the objective were to construct a generic source-detector, we would either have to i) input more context information about the instrumental setup or ii) adopt the per-input-patch normalization that forces the detector to base its detection on morphological contrast between the objects and the noise structure or artifacts. The resulting model would likely lose performances in a specific setup but would be more generic and resilient to new structures in the images.
<table><caption>Table D.1: Detection-only score metrics for various approaches with and without the extra-parameter part of the loss.</caption><thead><tr><th>Approach</th><th>Epoch</th><th>AP<sub>0.1</sub></th><th>AP<sub>0.5</sub></th><th>AP<sub>0.9</sub></th><th>N<sup>m</sup><sub>0.1</sub></th><th>N<sup>m</sup><sub>0.5</sub></th><th>N<sup>m</sup><sub>0.9</sub></th><th>Score</th><th>AP<sub>SDC1</sub></th><th>N<sup>m</sup><sub>SDC1</sub></th></tr></thead><tbody><tr><td>With param. reference</td><td>3000</td><td>15.71</td><td>13.57</td><td>0.70</td><td>835789</td><td>737056</td><td>120467</td><td>480439</td><td>14.47</td><td>679778</td></tr><tr><td>With param. no cascade</td><td>4200</td><td>14.94</td><td>13.12</td><td>0.69</td><td>791421</td><td>708597</td><td>117005</td><td>476943</td><td>14.24</td><td>676288</td></tr><tr><td>With param. patch norm.</td><td>3200</td><td>15.25</td><td>13.05</td><td>0.71</td><td>811351</td><td>711355</td><td>117859</td><td>461417</td><td>14.08</td><td>654838</td></tr><tr><td>With param. dual norm.</td><td>3600</td><td>15.96</td><td>13.74</td><td>0.73</td><td>857652</td><td>751529</td><td>126662</td><td>473758</td><td>14.35</td><td>657853</td></tr><tr><td>No param.</td><td>2600</td><td>15.12</td><td>13.05</td><td>0.58</td><td>801494</td><td>709853</td><td>108664</td><td>N/A</td><td>N/A</td><td>N/A</td></tr><tr><td>No param. more regul.</td><td>3000</td><td>14.91</td><td>13.06</td><td>0.73</td><td>789935</td><td>707086</td><td>119189</td><td>N/A</td><td>N/A</td><td>N/A</td></tr><tr><td>No param. light</td><td>3000</td><td>14.93</td><td>12.89</td><td>0.67</td><td>791478</td><td>699148</td><td>114422</td><td>N/A</td><td>N/A</td><td>N/A</td></tr><tr><td>No param. patch norm.</td><td>2600</td><td>15.62</td><td>13.18</td><td>0.64</td><td>836355</td><td>723201</td><td>113519</td><td>N/A</td><td>N/A</td><td>N/A</td></tr><tr><td>No param. dual norm.</td><td>2600</td><td>15.84</td><td>13.52</td><td>0.62</td><td>847780</td><td>740967</td><td>116617</td><td>N/A</td><td>N/A</td><td>N/A</td></tr><tr><td>Random 950k</td><td>N/A</td><td>0.40</td><td>0.01</td><td>0.00</td><td>137877</td><td>26416</td><td>633</td><td>N/A</td><td>N/A</td><td>N/A</td></tr><tr><td>Random 110k</td><td>N/A</td><td>0.05</td><td>0.00</td><td>0.00</td><td>17152</td><td>3306</td><td>75</td><td>N/A</td><td>N/A</td><td>N/A</td></tr></tbody></table>