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<h1 class="title is-1 publication-title">Singular Values-Driven Automated Filter Pruning</h1>
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<a href="https://github.com/pvti" target="_blank">Van Tien Pham</a>,</span>
<span class="author-block">
<a href="https://yzniyed.blogspot.com/p/about-me.html" target="_blank">Yassine Zniyed</a>,</span>
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<a href="https://webusers.i3s.unice.fr/~tpnguyen/" target="_blank">Thanh Phuong Nguyen</a>
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<a href="https://www.univ-tln.fr/" target="_blank" style="font-style: italic; color: black;">Université
de Toulon</a>,
<a href="https://www.univ-amu.fr/" target="_blank" style="font-style: italic; color: black;">Université
d'Aix-Marseille</a>,
<a href="https://www.cnrs.fr/fr" target="_blank" style="font-style: italic; color: black;">CNRS</a>,
<a href="https://www.lis-lab.fr/" target="_blank" style="font-style: italic; color: black;">LIS, UMR
7020, France</a>
</span>
<span class="author-block">
<a href="https://univ-cotedazur.fr/" target="_blank"
style="font-style: italic; color: black;">Université Côte d'Azur </a>,
<a href="https://www.cnrs.fr/fr" target="_blank" style="font-style: italic; color: black;">CNRS</a>,
<a href="https://www.i3s.unice.fr/en/" target="_blank" style="font-style: italic; color: black;">I3S,
UMR 7271, France</a>
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<span>🤗 Models</span>
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<h2 class="title is-3">Abstract</h2>
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<p>
We present SLIMING (Singular vaLues-drIven autoMated filter prunING), an automated filter pruning method
that uses singular values to formalize the pruning process as an optimization problem over filter tensors.
Recognizing that this original formulation poses a combinatorial challenge, we propose to replace it with
a two-step process that consistently uses singular values in each phase: (\(i\)) determining the pruning
configuration, which specifies the number of filters to retain in each layer, and (\(ii\)) selecting the
filters themselves. We show that this approach ensures the preservation of the filters' multidimensional
structure throughout the pruning process. For each of these steps, we propose a straightforward algorithm
to solve them. To validate each part of our approach, we performed a numerical simulation on an
overparameterized synthetic toy example. Additionally, we conducted extensive simulations across eight
architectures, four benchmark datasets, and four vision tasks, validating the efficacy of our framework.
</p>
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<h2 class="title is-3">🔥 News</h2>
<ul>
<li><strong>01.01.2025:</strong> We compare SLIMING with
<a href="https://ieeexplore.ieee.org/document/10819307" target="_blank">HSC (TPAMI'25)</a>. Check out <a
href="#table2">Table 2</a>!
Stay tuned for more 📊 comparisons with SOTAs coming soon 💪!
</li>
<li><strong>13.11.2024:</strong> 🎬 Lights, Camera, Action! <a
href="https://www.youtube.com/watch?v=P0jVSO9LjPg"> Presentation Video Out Now!</a> 🍿 Kick back and enjoy!
</li>
<li><strong>01.11.2024:</strong> <a href="https://huggingface.co/sliming/models">Baseline and checkpoints are
released</a> 🤗. Get your 👋 dirty 💻!</li>
<li><strong>31.10.2024:</strong> The manuscript has been submitted to <a
href="https://www.sciencedirect.com/journal/neural-networks">Neural Networks</a>.</li>
</ul>
</div>
</section>
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<h2 class="title">🎮 Toy example</h2>
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<p>
This paper proposes a method that leverages tools from linear and multilinear algebra to provide a new
solution for automated filter pruning.
We propose to detect network redundancy hinging on the dynamics of singular values and the use of the
nuclear norm.
We illuminate the intricate relationship between filter redundancy within neural networks and the observable
variations in their singular values.
To illustrate the rationale of our proposed approaches, we create a synthetic dataset, dubbed as SVGG, which
includes an original model that mimics the architecture of the VGG network with \(L=5\), \(d_l= 3\) and
\(\{C_l\}_{l=1}^L = \{64, 128, 256, 512, 512\}\).
We choose the redundant rates (the ratio of the number of redundant filters to the total number of filters,
<em>i.e.</em>, \(\frac{C_l-N_l}{C_l}\)) of these layers sequentially as \(\{0.25, 0.3, 0.35, 0.4, 0.45\}\),
thus \(\{N_l\}_{l=1}^L = \{48, 90, 166, 307, 282\}\), and the number of retained filters \(N=893\).
In the \(l\)-th layer, we init \(N_l\) core filters with the standard normal distribution while the
remaining redundant filters are copied from the core filters with a small noise of variance \(\epsilon =
0.01\).
The "multilinear" singular values are visualized as follows.
One should note that the overparameterized model contains many near-zero singular values, indicating
redundancy.
The random search approach, CHIP, FPC, and SPSRC yield suboptimal results, whereas GEM successfully
identifies all unique filters, achieving 100% accuracy comparable to the complete search, with reduced
computational overhead.
</p>
</div>
<div class="has-text-centered">
<figure>
<img src="./static/images/svgg.png" alt="fig1" style="width: 100%; height: auto;">
<figcaption><b>Figure 1:</b> Distribution of singular values <i>(left)</i>. Non-redundant selected filters
<i>(right)</i>.
</figcaption>
</figure>
</div>
</div>
</section>
<section class="section" id="results">
<div class="container is-max-desktop">
<h2 class="title">🚩 Main results</h2>
<div class="content has-text-justified">
<p>
To showcase SLIMING's adaptability, we evaluate it on five architectures: VGG-16-BN, GoogLeNet with inception
modules, ResNet-20/32/56/110 with residual blocks, DenseNet-40 with dense blocks, and MobileNetV2 with
inverted residual blocks. These models are tested on the CIFAR-10/100 datasets. To further validate SLIMING's
scalability, we perform experiments on the ImageNet dataset using ResNet-50 and MobileNetV2 architectures.
Additionally, the compressed ResNet-50 model is used as the backbone for Faster R-CNN-FPN, Mask R-CNN, and
Keypoint R-CNN on the COCO-2017 dataset. We compare SLIMING with 56 related works, as detailed in the paper,
and present ResNet-50 results on ImageNet in <a href="#table1">Table 1</a> for clarity. Furthermore, the
compression results of ResNet-110 on CIFAR-10 are summarized in <a href="#table2">Table 2</a>. Our method
consistently surpasses other approaches across all compression levels in terms of performance and complexity
reduction.
</p>
</div>
<table id="table1" class="table is-striped is-fullwidth">
<caption><b>Table 1.</b> Compression results of ResNet-50 on ImageNet</caption>
<thead>
<tr>
<th>Method</th>
<th>Auto</th>
<th>Top-1</th>
<th>Top-5</th>
<th>MACs (↓%)</th>
<th>Params (↓%)</th>
</tr>
</thead>
<tbody>
<tr>
<td><em>ResNet-50 <a href="https://ieeexplore.ieee.org/document/7780459" target="_blank">(CVPR'16)</a></em>
</td>
<td></td>
<td>76.15</td>
<td>92.87</td>
<td>4.12G (00)</td>
<td>25.56M (00)</td>
</tr>
<tr>
<td>REAF <a href="https://ieeexplore.ieee.org/document/10181132" target="_blank">(TIP'23)</a></td>
<td>✅</td>
<td>75.17</td>
<td>92.44</td>
<td>2.16G (48)</td>
<td>14.57M (43)</td>
</tr>
<tr>
<td>RGP <a href="https://ieeexplore.ieee.org/document/10149178" target="_blank">(TNNLS'24)</a></td>
<td>❌</td>
<td>75.30</td>
<td>92.55</td>
<td>2.30G (44)</td>
<td>14.34M (44)</td>
</tr>
<tr>
<td>Chen <em>et al.</em> <a href="https://ieeexplore.ieee.org/document/10177916"
target="_blank">(TNNLS'23)</a></td>
<td>❌</td>
<td>75.60</td>
<td>92.58</td>
<td>2.21G (46)</td>
<td>N/A</td>
</tr>
<tr>
<td>C-SGD <a href="https://ieeexplore.ieee.org/document/10283855" target="_blank">(TNNLS'23)</a></td>
<td>❌</td>
<td>75.80</td>
<td>92.65</td>
<td>2.19G (47)</td>
<td>14.58M (43)</td>
</tr>
<tr>
<td>CHIP <a href="https://arxiv.org/abs/2110.13981" target="_blank">(NeurIPS'21)</a></td>
<td>❌</td>
<td>76.15</td>
<td>92.91</td>
<td>2.10G (49)</td>
<td>14.23M (44)</td>
</tr>
<tr>
<td>SFI-FP <a href="https://www.sciencedirect.com/science/article/pii/S0031320324002395"
target="_blank">(Pattern Recognition'24)</a></td>
<td>❌</td>
<td>76.29</td>
<td>93.08</td>
<td>2.10G (49)</td>
<td>14.23M (44)</td>
</tr>
<tr>
<td>PEEL <a href="https://www.sciencedirect.com/science/article/pii/S0031320323005848"
target="_blank">(Pattern Recognition'24)</a></td>
<td>❌</td>
<td>76.50</td>
<td>N/A</td>
<td>2.20G (46)</td>
<td>N/A</td>
</tr>
<tr>
<td><strong>SLIMING (Ours)</strong></td>
<td>✅</td>
<td><strong>76.74</strong></td>
<td><strong>93.43</strong></td>
<td><strong>2.09G (49)</strong></td>
<td><strong>13.27M (48)</strong></td>
</tr>
<tr>
<td>CIE <a href="https://www.sciencedirect.com/science/article/pii/S0893608024004209"
target="_blank">(Neural Networks'24)</a></td>
<td>✅</td>
<td>74.06</td>
<td>91.87</td>
<td>1.56G (62)</td>
<td>9.98M (61)</td>
</tr>
<tr>
<td>RGP <a href="https://ieeexplore.ieee.org/document/10149178" target="_blank">(TNNLS'24)</a></td>
<td>❌</td>
<td>74.58</td>
<td>92.09</td>
<td>1.92G (53)</td>
<td>11.99M (53)</td>
</tr>
<tr>
<td>MFP <a href="https://ieeexplore.ieee.org/document/9716788" target="_blank">(TNNLS'23)</a></td>
<td>❌</td>
<td>74.86</td>
<td>92.43</td>
<td>1.88G (54)</td>
<td>N/A</td>
</tr>
<tr>
<td>FPWT <a href="https://www.sciencedirect.com/science/article/pii/S089360802400501X"
target="_blank">(Neural Networks'24)</a></td>
<td>❌</td>
<td>75.01</td>
<td>92.45</td>
<td>1.89G (54)</td>
<td>12.86M (50)</td>
</tr>
<tr>
<td>Torque <a href="https://ieeexplore.ieee.org/document/10484493" target="_blank">(WACV'24)</a></td>
<td>❌</td>
<td>75.07</td>
<td>N/A</td>
<td>1.99G (51)</td>
<td>9.68M (62)</td>
</tr>
<tr>
<td>OTOv2 <a href="https://arxiv.org/abs/2303.06862" target="_blank">(ICLR'23)</a></td>
<td>✅</td>
<td>75.20</td>
<td>92.22</td>
<td>1.53G (63)</td>
<td>N/A</td>
</tr>
<tr>
<td>FiltDivNet <a href="https://ieeexplore.ieee.org/document/9881223" target="_blank">(TNNLS'24)</a></td>
<td>✅</td>
<td>75.23</td>
<td>92.50</td>
<td>1.66G (59)</td>
<td>15.62M (39)</td>
</tr>
<tr>
<td>ASTER <a href="https://ieeexplore.ieee.org/document/10064249" target="_blank">(TNNLS'24)</a></td>
<td>✅</td>
<td>75.27</td>
<td>92.47</td>
<td>1.51G (63)</td>
<td>N/A</td>
</tr>
<tr>
<td>C-SGD <a href="https://ieeexplore.ieee.org/document/10283855" target="_blank">(TNNLS'23)</a></td>
<td>❌</td>
<td>75.29</td>
<td>92.39</td>
<td>1.82G (55)</td>
<td>12.37M (52)</td>
</tr>
<tr>
<td>Hu <em>et al.</em> <a href="https://doi.org/10.1016/j.patcog.2024.110546" target="_blank">(Pattern
Recognition'24)</a></td>
<td>❌</td>
<td>75.30</td>
<td>92.40</td>
<td>1.81G (56)</td>
<td>17.86M (30)</td>
</tr>
<tr>
<td>HSC</em> <a href="https://ieeexplore.ieee.org/document/10819307" target="_blank">(TPAMI'25)</a></td>
<td>❌</td>
<td>75.46</td>
<td>92.40</td>
<td>1.57G (62)</td>
<td>N/A</td>
</tr>
<tr>
<td>DCFF <a href="https://ieeexplore.ieee.org/document/10078845" target="_blank">(TPAMI'23)</a></td>
<td>❌</td>
<td>75.60</td>
<td>92.55</td>
<td>1.52G (63)</td>
<td>11.05M (57)</td>
</tr>
<tr>
<td>HTP-URC <a href="https://ieeexplore.ieee.org/document/10103912" target="_blank">(TNNLS'24)</a></td>
<td>✅</td>
<td>75.81</td>
<td>N/A</td>
<td>1.88G (54)</td>
<td>15.81M (38)</td>
</tr>
<tr>
<td><strong>SLIMING (Ours)</strong></td>
<td>✅</td>
<td><strong>75.96</strong></td>
<td><strong>93.29</strong></td>
<td><strong>1.51G (63)</strong></td>
<td><strong>9.68M (62)</strong></td>
</tr>
<tr>
<td>HBFP <a href="https://www.sciencedirect.com/science/article/pii/S0925231224000286"
target="_blank">(Neurocomputing'24)</a></td>
<td>❌</td>
<td>69.17</td>
<td>N/A</td>
<td>0.94G (76)</td>
<td>8.09M (68)</td>
</tr>
<tr>
<td>CHIP <a href="https://arxiv.org/abs/2110.13981" target="_blank">(NeurIPS'21)</a></td>
<td>❌</td>
<td>72.30</td>
<td>90.74</td>
<td>0.95G (77)</td>
<td>8.01M (69)</td>
</tr>
<tr>
<td>SNACS <a href="https://ieeexplore.ieee.org/document/9866022" target="_blank">(TNNLS'24)</a></td>
<td>✅</td>
<td>72.60</td>
<td>N/A</td>
<td>1.98G (52)</td>
<td>7.92M (69)</td>
</tr>
<tr>
<td>RGP <a href="https://ieeexplore.ieee.org/document/10149178" target="_blank">(TNNLS'24)</a></td>
<td>❌</td>
<td>72.68</td>
<td>91.06</td>
<td>0.94G (77)</td>
<td>8.13M (68)</td>
</tr>
<tr>
<td>FPWT <a href="https://www.sciencedirect.com/science/article/pii/S089360802400501X"
target="_blank">(Neural Networks'24)</a></td>
<td>❌</td>
<td>72.82</td>
<td>91.14</td>
<td>1.02G (75)</td>
<td>6.38M (75)</td>
</tr>
<tr>
<td>SFI-FP <a href="https://www.sciencedirect.com/science/article/pii/S0031320324002395"
target="_blank">(Pattern Recognition'24)</a></td>
<td>❌</td>
<td>73.48</td>
<td>92.87</td>
<td>0.96G (77)</td>
<td>8.03M (69)</td>
</tr>
<tr>
<td>ACSC <a href="https://www.sciencedirect.com/science/article/pii/S0925231224004697"
target="_blank">(Neurocomputing'24)</a></td>
<td>✅</td>
<td>73.68</td>
<td>N/A</td>
<td>1.03G (75)</td>
<td>6.31M (75)</td>
</tr>
<tr>
<td>DCFF <a href="https://ieeexplore.ieee.org/document/10078845" target="_blank">(TPAMI'23)</a></td>
<td>❌</td>
<td>73.81</td>
<td>91.59</td>
<td>1.02G (75)</td>
<td>6.56M (74)</td>
</tr>
<tr>
<td>Guo <em>et al.</em> <a href="https://link.springer.com/article/10.1007/s11263-023-01972-x"
target="_blank">(IJCV'24)</a></td>
<td>✅</td>
<td>73.84</td>
<td>92.07</td>
<td>1.19G (71)</td>
<td>6.25M (75)</td>
</tr>
<tr>
<td><strong>SLIMING (Ours)</strong></td>
<td>✅</td>
<td><strong>73.88</strong></td>
<td><strong>92.07</strong></td>
<td><strong>0.87G (79)</strong></td>
<td><strong>5.68M (78)</strong></td>
</tr>
</tbody>
</table>
<table id="table2" class="table is-striped is-fullwidth">
<caption><b>Table 2.</b> Compression results of ResNet-110 on CIFAR-10</caption>
<thead>
<tr>
<th>Method</th>
<th>Auto</th>
<th>Top-1</th>
<th>MACs (↓%)</th>
<th>Params (↓%)</th>
</tr>
</thead>
<tbody>
<tr>
<td><em>ResNet-110 <a href="https://ieeexplore.ieee.org/document/7780459" target="_blank">(CVPR'16)</a></em>
</td>
<td></td>
<td>93.50</td>
<td>256.04M (00)</td>
<td>1.73M (00)</td>
</tr>
<tr>
<td>HSC</em> <a href="https://ieeexplore.ieee.org/document/10819307" target="_blank">(TPAMI'25)</a></td>
<td>❌</td>
<td>94.01</td>
<td>88.26M (65)</td>
<td>0.69M (60)</td>
</tr>
<tr>
<td><strong>SLIMING (Ours)</strong></td>
<td>✅</td>
<td><strong>94.52</strong></td>
<td><strong>87.59M (66)</strong></td>
<td><strong>0.61M (65)</strong></td>
</tr>
<tr>
<td>HSC</em> <a href="https://ieeexplore.ieee.org/document/10819307" target="_blank">(TPAMI'25)</a></td>
<td>❌</td>
<td>93.56</td>
<td>71.31M (72)</td>
<td>0.51M (70)</td>
</tr>
<tr>
<td><strong>SLIMING (Ours)</strong></td>
<td>✅</td>
<td><strong>93.64</strong></td>
<td><strong>54.50M (79)</strong></td>
<td><strong>0.28M (84)</strong></td>
</tr>
</tbody>
</table>
</div>
</section>
<section class="section" id="downstream">
<div class="container is-max-desktop">
<h2 class="title">🚀 Throughput acceleration</h2>
<div class="content has-text-justified">
<p>
To emphasize the practical benefits of SLIMMING, we meticulously conducted an experiment comparing a baseline
model with a compressed model, both designed for object detection tasks. Using the FasterRCNN_ResNet50_FPN
architecture on an RTX 3060 GPU, the experiment robustly demonstrates the significant performance improvement
achieved by SLIMMING. Accompanying GIFs provide a clear visual representation: the baseline model achieves an
inference speed of approximately 9 FPS, while the SLIMMING-compressed model achieves a remarkable twofold
increase in throughput. This substantial difference effectively demonstrates SLIMMING's effectiveness and
scalability, firmly establishing its relevance and usefulness across various deployment scenarios.
</p>
</div>
<table class="table is-bordered is-striped is-narrow is-hoverable is-fullwidth">
<tbody>
<tr>
<td><img src="static/videos/faster-baseline.gif" alt=""></td>
<td><img src="static/videos/faster-pruned.gif" alt=""></td>
</tr>
<tr>
<td><img src="static/videos/mask-baseline.gif" alt=""></td>
<td><img src="static/videos/mask-pruned.gif" alt=""></td>
</tr>
<tr>
<td><img src="static/videos/keypoint-baseline.gif" alt=""></td>
<td><img src="static/videos/keypoint-pruned.gif" alt=""></td>
</tr>
</tbody>
</table>
<div class="has-text-centered">
<p><b>Figure 2:</b> Baseline (<em>left</em>) vs Pruned (<em>right</em>) model inference.</p>
</div>
</div>
</section>
<section class="section" id="gradcam">
<div class="container is-max-desktop">
<h2 class="title">🌈 Visualizing feature preservation</h2>
<div class="content has-text-justified">
<p>
We present a qualitative evaluation of feature preservation, complementing the established efficiency
demonstrated through numerical results.
Our analysis involves a random selection of 5 images from the ImageNet validation dataset, examining three
compression levels applied to the original ResNet-50 model: 44%, 63%, and 79%.
Utilizing GradCAM for interpretation, we visually assess and analyze feature maps in both the original and
compressed models.
The visual representation underscores our framework's efficacy in retaining crucial features across a diverse
range of classes.
Noteworthy is its consistent robustness in capturing and preserving essential information at different CRs.
This resilience implies sustained effectiveness and reliability across varying scenarios and compression
levels, positioning our framework as a versatile choice for network compression across diverse applications
and datasets.
</p>
</div>
<table class="table is-bordered is-striped is-narrow is-hoverable is-fullwidth">
<thead>
<tr>
<th class="has-text-centered">Input</th>
<th class="has-text-centered">CR=0%</th>
<th class="has-text-centered">CR=44%</th>
<th class="has-text-centered">CR=63%</th>
<th class="has-text-centered">CR=79%</th>
</tr>
</thead>
<tbody>
<tr>
<td><img src="static/images/cam/ILSVRC2012_val_00003498.JPEG" alt=""></td>
<td><img src="static/images/cam/ILSVRC2012_val_00003498_[0.]*20.jpg" alt=""></td>
<td><img src="static/images/cam/ILSVRC2012_val_00003498_[0.255]*20.jpg" alt=""></td>
<td><img src="static/images/cam/ILSVRC2012_val_00003498_[0.4]*20.jpg" alt=""></td>
<td><img src="static/images/cam/ILSVRC2012_val_00003498_[0.55]*20.jpg" alt=""></td>
</tr>
<tr>
<td><img src="static/images/cam/ILSVRC2012_val_00009497.JPEG" alt=""></td>
<td><img src="static/images/cam/ILSVRC2012_val_00009497_[0.]*20.jpg" alt=""></td>
<td><img src="static/images/cam/ILSVRC2012_val_00009497_[0.255]*20.jpg" alt=""></td>
<td><img src="static/images/cam/ILSVRC2012_val_00009497_[0.4]*20.jpg" alt=""></td>
<td><img src="static/images/cam/ILSVRC2012_val_00009497_[0.55]*20.jpg" alt=""></td>
</tr>
<tr>
<td><img src="static/images/cam/ILSVRC2012_val_00018573.JPEG" alt=""></td>
<td><img src="static/images/cam/ILSVRC2012_val_00018573_[0.]*20.jpg" alt=""></td>
<td><img src="static/images/cam/ILSVRC2012_val_00018573_[0.255]*20.jpg" alt=""></td>
<td><img src="static/images/cam/ILSVRC2012_val_00018573_[0.4]*20.jpg" alt=""></td>
<td><img src="static/images/cam/ILSVRC2012_val_00018573_[0.55]*20.jpg" alt=""></td>
</tr>
<tr>
<td><img src="static/images/cam/ILSVRC2012_val_00044350.JPEG" alt=""></td>
<td><img src="static/images/cam/ILSVRC2012_val_00044350_[0.]*20.jpg" alt=""></td>
<td><img src="static/images/cam/ILSVRC2012_val_00044350_[0.255]*20.jpg" alt=""></td>
<td><img src="static/images/cam/ILSVRC2012_val_00044350_[0.4]*20.jpg" alt=""></td>
<td><img src="static/images/cam/ILSVRC2012_val_00044350_[0.55]*20.jpg" alt=""></td>
</tr>
<tr>
<td><img src="static/images/cam/ILSVRC2012_val_00049750.JPEG" alt=""></td>
<td><img src="static/images/cam/ILSVRC2012_val_00049750_[0.]*20.jpg" alt=""></td>
<td><img src="static/images/cam/ILSVRC2012_val_00049750_[0.255]*20.jpg" alt=""></td>
<td><img src="static/images/cam/ILSVRC2012_val_00049750_[0.4]*20.jpg" alt=""></td>
<td><img src="static/images/cam/ILSVRC2012_val_00049750_[0.55]*20.jpg" alt=""></td>
</tr>
<!-- Add other rows similarly -->
</tbody>
</table>
<div class="has-text-centered">
<p><b>Figure 3:</b> Qualitative assessment of feature preservation in compressed models.</p>
</div>
</div>
</section>
<!--BibTex citation -->
<section class="section" id="BibTeX">
<div class="container is-max-desktop content">
<h2 class="title">🔖 Citation</h2>
<p>If the code and paper help your research, please kindly cite:</p>
<pre><code id="citation">
@misc{pham2024singular,
title={Singular Values-Driven Automated Filter Pruning},
author={Pham, Van Tien and Zniyed, Yassine and Nguyen, Thanh Phuong},
howpublished={\url{https://sliming-ai.github.io/}},
year={2024}
}
</code></pre>
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<section class="section" id="acknowledgements">
<div class="container is-max-desktop content">
<h2 class="title">👍 Acknowledgements</h2>
<p>
This work was granted access to the high-performance computing resources of <a
href="http://www.idris.fr/eng/info/missions-eng.html">IDRIS</a> under the allocation 2023-103147 made by <a
href="https://genci.fr/">GENCI</a>. Specifically, our experiments were conducted on <a
href="http: //www.idris.fr/eng/jean-zay/jean-zay-presentation-eng.html">the Jean Zay supercomputer</a>,
located at IDRIS, the national computing center for <a href="https://www.cnrs.fr/fr">the National Centre for
Scientific Research (CNRS)</a>.
</p>
<p>
We thank <a href="https://anr.fr/fr/">the Agence Nationale de la Recherche (ANR)</a> for partially supporting
our work through the ANR ASTRID ROV-Chasseur project (<a
href="https://anr.fr/Projet-ANR-21-ASRO-0003">ANR-21-ASRO-0003</a>).
</p>
<figure>
<img src="./static/images/JeanZay.jpg" alt="jean-zay" style="width: 100%; height: auto;">
<img src="./static/images/Nouveau_logo_ANR_2022.jpg" alt="jean-zay" style="width: 100%; height: auto;">
</figure>
</div>
</section>
<!--End Acknowledgements-->
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<h2 class="title">⏩ More & Moore 📈</h2>
<div id="results-carousel" class="carousel results-carousel" style="max-width: 720px; margin: 0 auto;">
<div class="item">
<img src="static/images/singularity/PPTMooresLawai.png" alt="Moore's Law visualization over time" />
</div>
<div class="item">
<img src="static/images/singularity/Moore's_Law_over_120_Years.png"
alt="Chart of Moore's Law over 120 years" />
</div>
<div class="item">
<img src="static/images/singularity/PPTExponentialGrowthof_Computing.jpg"
alt="Exponential growth of computing power" />
</div>
<div class="item">
<img src="static/images/singularity/Countdown_to_Singularity_-_Linear.svg"
alt="Countdown to singularity timeline" />
</div>
</div>
<div class="content has-text-justified">
<p>
<blockquote>
The ever-<b>accelerating</b> progress of technology… gives the appearance of approaching some essential
<b>singularity</b>. — <i>John von Neumann, 1958</i>
</blockquote>
<blockquote>
The singularity is nearer. — <i>Ray Kurzweil, 2024</i>
</blockquote>
</p>
</div>
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</section>
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