1 Introduction
2 Related work
2.1 Retrieval of legal information
2.2 Clustering-based approaches in the legal sector
3 Methodology
-
Training set \(\varvec{D_T}\): a collection of legal case judgments, represented as textual documents, adopted to train our models;
-
Reference set \(\varvec{D_R}\): a collection of legal case judgments, represented as textual documents, from which we are interested to identify paragraph regularities;
-
Target document \({\varvec{d}}\): a legal case judgment (possibly incomplete or under preparation) about which we are interested to identify paragraph regularities from the reference set.
-
Training phase (see Fig. 1 and Algorithm 1), during which PRILJ i) trains a document embedding model from \(D_T\), that is able to represent documents into a semantic feature space; ii) identifies k groups of documents in \(D_T\) according to their semantic representation, through a clustering method; iii) learns k paragraph embedding models, one for each cluster, that are able to represent paragraphs into a semantic feature space.
-
Paragraph embedding of the reference set (see Fig. 2 and Algorithm 2), that exploits both the document embedding model and the k paragraph embedding models learned during the training phase, to identify a semantic representation of all the paragraphs of the reference set.
-
Identification of paragraph regularities (see Fig. 3 and Algorithm 3), that exploits the identified document clusters, the document embedding model and the k paragraph embedding models to evaluate, through an efficient strategy, the similarity among paragraphs. The purpose is to identify paragraphs from the reference set that appear related to those of the target document (possibly under preparation).
3.1 Learning document and paragraph embedding models through Word2Vec
3.2 Learning document and paragraph embedding models through Doc2Vec
3.3 Approximated Nearest Neighbour Search (ANNS) for the identification of paragraph regularities
4 Experiments
4.1 Dataset
4.2 Experimental setting
-
LEGAL-BERT-BASE, that is the LEGAL-BERT model\({}^{3}\) fine-tuned by Chalkidis et al. (2020) using a wide set of legal documents related to EU, UK and US law;
-
LEGAL-BERT-SMALL, that is the LEGAL-BERT model\({}^{3}\) fine-tuned by Chalkidis et al. (2020) using the same set of documents adopted for LEGAL-BERT-BASE, but in a lower-dimensional embedding space;
4.3 Results
One-step model | |||||||
---|---|---|---|---|---|---|---|
Noise % | |||||||
10% | 20% | 30% | 40% | 50% | 60% | ||
p@5 | T | 0.753 | 0.722 | 0.660 | 0.540 | 0.338 | 0.114 |
D | 0.930 | 0.910 | 0.882 | 0.782 | 0.553 | 0.301 | |
W | 0.936 | 0.925 | 0.911 | 0.887 | 0.827 | 0.690 | |
p@10 | T | 0.758 | 0.701 | 0.604 | 0.450 | 0.244 | 0.075 |
D | 0.922 | 0.897 | 0.849 | 0.697 | 0.453 | 0.241 | |
W | 0.935 | 0.922 | 0.904 | 0.870 | 0.783 | 0.615 | |
p@15 | T | 0.742 | 0.657 | 0.534 | 0.368 | 0.189 | 0.058 |
D | 0.911 | 0.877 | 0.788 | 0.599 | 0.379 | 0.205 | |
W | 0.932 | 0.917 | 0.894 | 0.841 | 0.726 | 0.543 | |
p@20 | T | 0.696 | 0.587 | 0.456 | 0.305 | 0.154 | 0.047 |
D | 0.885 | 0.815 | 0.687 | 0.510 | 0.327 | 0.180 | |
W | 0.927 | 0.904 | 0.861 | 0.780 | 0.648 | 0.475 | |
p@50 | T | 0.317 | 0.278 | 0.221 | 0.149 | 0.077 | 0.024 |
D | 0.383 | 0.367 | 0.330 | 0.266 | 0.186 | 0.113 | |
W | 0.390 | 0.387 | 0.380 | 0.362 | 0.322 | 0.254 | |
p@100 | T | 0.167 | 0.149 | 0.121 | 0.084 | 0.044 | 0.015 |
D | 0.194 | 0.189 | 0.177 | 0.151 | 0.114 | 0.075 | |
W | 0.197 | 0.196 | 0.194 | 0.188 | 0.173 | 0.145 |
Two-step model - \(k=\sqrt{|D_T |}/ 2\) | |||||||
---|---|---|---|---|---|---|---|
Noise % | |||||||
10% | 20% | 30% | 40% | 50% | 60% | ||
p@5 | T | 0.870 | 0.853 | 0.825 | 0.772 | 0.673 | 0.492 |
D | 0.946 | 0.933 | 0.921 | 0.905 | 0.873 | 0.786 | |
W | 0.952 | 0.945 | 0.935 | 0.920 | 0.891 | 0.829 | |
p@10 | T | 0.874 | 0.846 | 0.798 | 0.721 | 0.593 | 0.402 |
D | 0.940 | 0.925 | 0.910 | 0.886 | 0.831 | 0.703 | |
W | 0.951 | 0.942 | 0.930 | 0.911 | 0.871 | 0.784 | |
p@15 | T | 0.867 | 0.821 | 0.753 | 0.653 | 0.514 | 0.338 |
D | 0.933 | 0.915 | 0.893 | 0.853 | 0.765 | 0.615 | |
W | 0.949 | 0.938 | 0.924 | 0.897 | 0.839 | 0.726 | |
p@20 | T | 0.835 | 0.764 | 0.678 | 0.573 | 0.444 | 0.291 |
D | 0.918 | 0.889 | 0.847 | 0.779 | 0.675 | 0.533 | |
W | 0.944 | 0.930 | 0.905 | 0.859 | 0.776 | 0.652 | |
p@50 | T | 0.369 | 0.353 | 0.328 | 0.290 | 0.235 | 0.165 |
D | 0.392 | 0.388 | 0.381 | 0.366 | 0.334 | 0.280 | |
W | 0.395 | 0.393 | 0.391 | 0.385 | 0.369 | 0.334 | |
p@100 | T | 0.189 | 0.184 | 0.175 | 0.160 | 0.136 | 0.103 |
D | 0.198 | 0.197 | 0.195 | 0.190 | 0.179 | 0.158 | |
W | 0.199 | 0.199 | 0.198 | 0.197 | 0.193 | 0.182 |
Two-step model - \(k=\sqrt{|D_T |}\) | |||||||
---|---|---|---|---|---|---|---|
Noise % | |||||||
10% | 20% | 30% | 40% | 50% | 60% | ||
p@5 | T | 0.886 | 0.871 | 0.846 | 0.800 | 0.715 | 0.559 |
D | 0.949 | 0.938 | 0.926 | 0.911 | 0.885 | 0.818 | |
W | 0.955 | 0.949 | 0.940 | 0.927 | 0.901 | 0.847 | |
p@10 | T | 0.890 | 0.866 | 0.824 | 0.755 | 0.642 | 0.470 |
D | 0.944 | 0.930 | 0.915 | 0.894 | 0.848 | 0.745 | |
W | 0.954 | 0.946 | 0.936 | 0.919 | 0.884 | 0.808 | |
p@15 | T | 0.884 | 0.843 | 0.782 | 0.692 | 0.566 | 0.402 |
D | 0.937 | 0.920 | 0.900 | 0.864 | 0.790 | 0.661 | |
W | 0.952 | 0.943 | 0.930 | 0.907 | 0.856 | 0.755 | |
p@20 | T | 0.854 | 0.789 | 0.709 | 0.611 | 0.492 | 0.349 |
D | 0.923 | 0.896 | 0.856 | 0.795 | 0.703 | 0.575 | |
W | 0.948 | 0.935 | 0.913 | 0.872 | 0.797 | 0.681 | |
p@50 | T | 0.375 | 0.361 | 0.340 | 0.308 | 0.262 | 0.199 |
D | 0.393 | 0.390 | 0.383 | 0.370 | 0.344 | 0.298 | |
W | 0.396 | 0.395 | 0.393 | 0.389 | 0.376 | 0.346 | |
p@100 | T | 0.192 | 0.187 | 0.180 | 0.168 | 0.149 | 0.121 |
D | 0.199 | 0.198 | 0.196 | 0.192 | 0.183 | 0.165 | |
W | 0.199 | 0.199 | 0.199 | 0.198 | 0.195 | 0.186 |
Two-step model - \(k=\sqrt{|D_T |} \cdot 2\) | |||||||
---|---|---|---|---|---|---|---|
Noise % | |||||||
10% | 20% | 30% | 40% | 50% | 60% | ||
p@5 | T | 0.899 | 0.884 | 0.862 | 0.822 | 0.746 | 0.611 |
D | 0.953 | 0.943 | 0.931 | 0.916 | 0.891 | 0.835 | |
W | \({{\underline{\varvec{0.959}}}}\) | \({{\underline{\varvec{0.953}}}}\) | \({{\underline{\varvec{0.945}}}}\) | \({{\underline{\varvec{0.934}}}}\) | \({{\underline{\varvec{0.912}}}}\) | \({{\underline{\varvec{0.866}}}}\) | |
p@10 | T | 0.902 | 0.880 | 0.842 | 0.780 | 0.679 | 0.526 |
D | 0.948 | 0.935 | 0.920 | 0.899 | 0.857 | 0.768 | |
W | \({{\underline{\varvec{0.958}}}}\) | \({{\underline{\varvec{0.951}}}}\) | \({{\underline{\varvec{0.942}}}}\) | \({{\underline{\varvec{0.928}}}}\) | \({{\underline{\varvec{0.898}}}}\) | \({{\underline{\varvec{0.831}}}}\) | |
p@15 | T | 0.896 | 0.859 | 0.803 | 0.721 | 0.605 | 0.456 |
D | 0.942 | 0.925 | 0.904 | 0.870 | 0.803 | 0.688 | |
W | \({{\underline{\varvec{0.956}}}}\) | \({{\underline{\varvec{0.948}}}}\) | \({{\underline{\varvec{0.937}}}}\) | \({{\underline{\varvec{0.917}}}}\) | \({{\underline{\varvec{0.873}}}}\) | \({{\underline{\varvec{0.782}}}}\) | |
p@20 | T | 0.868 | 0.808 | 0.732 | 0.641 | 0.530 | 0.399 |
D | 0.928 | 0.901 | 0.862 | 0.804 | 0.718 | 0.601 | |
W | \({{\underline{\varvec{0.952}}}}\) | \({{\underline{\varvec{0.941}}}}\) | \({{\underline{\varvec{0.922}}}}\) | \({{\underline{\varvec{0.885}}}}\) | \({{\underline{\varvec{0.817}}}}\) | \({{\underline{\varvec{0.710}}}}\) | |
p@50 | T | 0.379 | 0.368 | 0.350 | 0.322 | 0.281 | 0.227 |
D | 0.395 | 0.391 | 0.385 | 0.373 | 0.349 | 0.309 | |
W | \({{\underline{\varvec{0.397}}}}\) | \({{\underline{\varvec{0.397}}}}\) | \({{\underline{\varvec{0.395}}}}\) | \({{\underline{\varvec{0.392}}}}\) | \({{\underline{\varvec{0.382}}}}\) | \({{\underline{\varvec{0.357}}}}\) | |
p@100 | T | 0.193 | 0.190 | 0.184 | 0.174 | 0.159 | 0.136 |
D | 0.199 | 0.198 | 0.196 | 0.193 | 0.185 | 0.170 | |
W | \({{\underline{\varvec{0.200}}}}\) | \({{\underline{\varvec{0.200}}}}\) | \({{\underline{\varvec{0.200}}}}\) | \({{\underline{\varvec{0.199}}}}\) | \({{\underline{\varvec{0.197}}}}\) | \({{\underline{\varvec{0.190}}}}\) |
One-step model | |||||||
---|---|---|---|---|---|---|---|
Noise % | |||||||
10% | 20% | 30% | 40% | 50% | 60% | ||
r@5 | T | 0.188 | 0.181 | 0.165 | 0.135 | 0.085 | 0.028 |
D | 0.233 | 0.228 | 0.220 | 0.195 | 0.138 | 0.075 | |
W | 0.234 | 0.231 | 0.228 | 0.222 | 0.207 | 0.172 | |
r@10 | T | 0.379 | 0.350 | 0.302 | 0.225 | 0.122 | 0.038 |
D | 0.461 | 0.449 | 0.424 | 0.348 | 0.227 | 0.121 | |
W | 0.467 | 0.461 | 0.452 | 0.435 | 0.391 | 0.307 | |
r@15 | T | 0.557 | 0.493 | 0.401 | 0.276 | 0.142 | 0.043 |
D | 0.683 | 0.658 | 0.591 | 0.449 | 0.285 | 0.154 | |
W | 0.699 | 0.688 | 0.670 | 0.631 | 0.544 | 0.408 | |
r@20 | T | 0.696 | 0.587 | 0.456 | 0.305 | 0.154 | 0.047 |
D | 0.885 | 0.815 | 0.687 | 0.510 | 0.327 | 0.180 | |
W | 0.927 | 0.904 | 0.861 | 0.780 | 0.648 | 0.475 | |
r@50 | T | 0.794 | 0.695 | 0.552 | 0.373 | 0.191 | 0.061 |
D | 0.957 | 0.919 | 0.826 | 0.665 | 0.465 | 0.282 | |
W | 0.976 | 0.968 | 0.950 | 0.906 | 0.804 | 0.635 | |
r@100 | T | 0.833 | 0.743 | 0.603 | 0.418 | 0.220 | 0.074 |
D | 0.972 | 0.945 | 0.884 | 0.756 | 0.571 | 0.374 | |
W | 0.985 | 0.980 | 0.969 | 0.941 | 0.867 | 0.724 |
Two-step model - \(k=\sqrt{|D_T |}/ 2\) | |||||||
---|---|---|---|---|---|---|---|
Noise % | |||||||
10% | 20% | 30% | 40% | 50% | 60% | ||
r@5 | T | 0.217 | 0.213 | 0.206 | 0.193 | 0.168 | 0.123 |
D | 0.236 | 0.233 | 0.230 | 0.226 | 0.218 | 0.197 | |
W | 0.238 | 0.236 | 0.234 | 0.230 | 0.223 | 0.207 | |
r@10 | T | 0.437 | 0.423 | 0.399 | 0.360 | 0.296 | 0.201 |
D | 0.470 | 0.463 | 0.455 | 0.443 | 0.415 | 0.352 | |
W | 0.475 | 0.471 | 0.465 | 0.456 | 0.435 | 0.392 | |
r@15 | T | 0.650 | 0.616 | 0.564 | 0.490 | 0.385 | 0.253 |
D | 0.700 | 0.686 | 0.670 | 0.640 | 0.574 | 0.461 | |
W | 0.711 | 0.704 | 0.693 | 0.673 | 0.629 | 0.545 | |
r@20 | T | 0.835 | 0.764 | 0.678 | 0.573 | 0.444 | 0.291 |
D | 0.918 | 0.889 | 0.847 | 0.779 | 0.675 | 0.533 | |
W | 0.944 | 0.930 | 0.905 | 0.859 | 0.776 | 0.652 | |
r@50 | T | 0.922 | 0.882 | 0.819 | 0.725 | 0.589 | 0.413 |
D | 0.979 | 0.970 | 0.952 | 0.914 | 0.835 | 0.701 | |
W | 0.987 | 0.984 | 0.978 | 0.964 | 0.923 | 0.835 | |
r@100 | T | 0.947 | 0.920 | 0.874 | 0.799 | 0.680 | 0.515 |
D | 0.990 | 0.985 | 0.974 | 0.951 | 0.895 | 0.789 | |
W | 0.994 | 0.993 | 0.990 | 0.984 | 0.964 | 0.908 |
Two-step model - \(k=\sqrt{|D_T |}\) | |||||||
---|---|---|---|---|---|---|---|
Noise % | |||||||
10% | 20% | 30% | 40% | 50% | 60% | ||
r@5 | T | 0.222 | 0.218 | 0.212 | 0.200 | 0.179 | 0.140 |
D | 0.237 | 0.234 | 0.232 | 0.228 | 0.221 | 0.205 | |
W | 0.239 | 0.237 | 0.235 | 0.232 | 0.225 | 0.212 | |
r@10 | T | 0.445 | 0.433 | 0.412 | 0.377 | 0.321 | 0.235 |
D | 0.472 | 0.465 | 0.458 | 0.447 | 0.424 | 0.373 | |
W | 0.477 | 0.473 | 0.468 | 0.460 | 0.442 | 0.404 | |
r@15 | T | 0.663 | 0.632 | 0.587 | 0.519 | 0.424 | 0.301 |
D | 0.703 | 0.690 | 0.675 | 0.648 | 0.592 | 0.496 | |
W | 0.714 | 0.707 | 0.697 | 0.680 | 0.642 | 0.566 | |
r@20 | T | 0.854 | 0.789 | 0.709 | 0.611 | 0.492 | 0.349 |
D | 0.923 | 0.896 | 0.856 | 0.795 | 0.703 | 0.575 | |
W | 0.948 | 0.935 | 0.913 | 0.872 | 0.797 | 0.681 | |
r@50 | T | 0.937 | 0.903 | 0.851 | 0.771 | 0.654 | 0.498 |
D | 0.983 | 0.974 | 0.958 | 0.926 | 0.860 | 0.745 | |
W | 0.989 | 0.987 | 0.983 | 0.972 | 0.940 | 0.865 | |
r@100 | T | 0.958 | 0.937 | 0.901 | 0.841 | 0.746 | 0.607 |
D | 0.993 | 0.989 | 0.979 | 0.959 | 0.914 | 0.826 | |
W | 0.996 | 0.996 | 0.995 | 0.991 | 0.976 | 0.932 |
Two-step model - \(k=\sqrt{|D_T |} \cdot 2\) | |||||||
---|---|---|---|---|---|---|---|
Noise % | |||||||
10% | 20% | 30% | 40% | 50% | 60% | ||
r@5 | T | 0.225 | 0.221 | 0.216 | 0.205 | 0.186 | 0.153 |
D | 0.238 | 0.236 | 0.233 | 0.229 | 0.223 | 0.209 | |
W | \({{\underline{\varvec{0.240}}}}\) | \({{\underline{\varvec{0.238}}}}\) | \({{\underline{\varvec{0.236}}}}\) | \({{\underline{\varvec{0.234}}}}\) | \({{\underline{\varvec{0.228}}}}\) | \({{\underline{\varvec{0.216}}}}\) | |
r@10 | T | 0.451 | 0.440 | 0.421 | 0.390 | 0.339 | 0.263 |
D | 0.474 | 0.467 | 0.460 | 0.449 | 0.428 | 0.384 | |
W | \({{\underline{\varvec{0.479}}}}\) | \({{\underline{\varvec{0.476}}}}\) | \({{\underline{\varvec{0.471}}}}\) | \({{\underline{\varvec{0.464}}}}\) | \({{\underline{\varvec{0.449}}}}\) | \({{\underline{\varvec{0.416}}}}\) | |
r@15 | T | 0.672 | 0.645 | 0.602 | 0.541 | 0.454 | 0.342 |
D | 0.706 | 0.694 | 0.678 | 0.652 | 0.602 | 0.516 | |
W | \({{\underline{\varvec{0.717}}}}\) | \({{\underline{\varvec{0.711}}}}\) | \({{\underline{\varvec{0.703}}}}\) | \({{\underline{\varvec{0.688}}}}\) | \({{\underline{\varvec{0.655}}}}\) | \({{\underline{\varvec{0.587}}}}\) | |
r@20 | T | 0.868 | 0.808 | 0.732 | 0.641 | 0.530 | 0.399 |
D | 0.928 | 0.901 | 0.862 | 0.804 | 0.718 | 0.601 | |
W | \({{\underline{\varvec{0.952}}}}\) | \({{\underline{\varvec{0.941}}}}\) | \({{\underline{\varvec{0.922}}}}\) | \({{\underline{\varvec{0.885}}}}\) | \({{\underline{\varvec{0.817}}}}\) | \({{\underline{\varvec{0.710}}}}\) | |
r@50 | T | 0.947 | 0.919 | 0.874 | 0.805 | 0.704 | 0.568 |
D | 0.987 | 0.978 | 0.962 | 0.933 | 0.874 | 0.772 | |
W | \({{\underline{\varvec{0.993}}}}\) | \({{\underline{\varvec{0.992}}}}\) | \({{\underline{\varvec{0.989}}}}\) | \({{\underline{\varvec{0.981}}}}\) | \({{\underline{\varvec{0.956}}}}\) | \({{\underline{\varvec{0.893}}}}\) | |
r@100 | T | 0.965 | 0.948 | 0.919 | 0.871 | 0.793 | 0.678 |
D | 0.996 | 0.991 | 0.982 | 0.964 | 0.925 | 0.850 | |
W | \({{\underline{\varvec{0.999}}}}\) | \({{\underline{\varvec{0.999}}}}\) | \({{\underline{\varvec{0.998}}}}\) | \({{\underline{\varvec{0.996}}}}\) | \({{\underline{\varvec{0.986}}}}\) | \({{\underline{\varvec{0.952}}}}\) |
One-step model | |||||||
---|---|---|---|---|---|---|---|
Noise % | |||||||
10% | 20% | 30% | 40% | 50% | 60% | ||
f@5 | T | 0.301 | 0.289 | 0.264 | 0.216 | 0.135 | 0.046 |
D | 0.372 | 0.364 | 0.353 | 0.313 | 0.221 | 0.121 | |
W | 0.374 | 0.370 | 0.365 | 0.355 | 0.331 | 0.276 | |
f@10 | T | 0.506 | 0.467 | 0.403 | 0.300 | 0.163 | 0.050 |
D | 0.614 | 0.598 | 0.566 | 0.464 | 0.302 | 0.161 | |
W | 0.623 | 0.615 | 0.603 | 0.580 | 0.522 | 0.410 | |
f@15 | T | 0.636 | 0.563 | 0.458 | 0.315 | 0.162 | 0.049 |
D | 0.781 | 0.752 | 0.676 | 0.514 | 0.325 | 0.176 | |
W | 0.799 | 0.786 | 0.766 | 0.721 | 0.622 | 0.466 | |
f@20 | T | 0.696 | 0.587 | 0.456 | 0.305 | 0.154 | 0.047 |
D | 0.885 | 0.815 | 0.687 | 0.510 | 0.327 | 0.180 | |
W | 0.927 | 0.904 | 0.861 | 0.780 | 0.648 | 0.475 | |
f@50 | T | 0.454 | 0.397 | 0.316 | 0.213 | 0.109 | 0.035 |
D | 0.547 | 0.525 | 0.472 | 0.380 | 0.266 | 0.161 | |
W | 0.558 | 0.553 | 0.543 | 0.518 | 0.460 | 0.363 | |
f@100 | T | 0.278 | 0.248 | 0.201 | 0.139 | 0.073 | 0.025 |
D | 0.324 | 0.315 | 0.295 | 0.252 | 0.190 | 0.125 | |
W | 0.328 | 0.327 | 0.323 | 0.314 | 0.289 | 0.241 |
Two-step model - \(k=\sqrt{|D_T |}/ 2\) | |||||||
---|---|---|---|---|---|---|---|
Noise % | |||||||
10% | 20% | 30% | 40% | 50% | 60% | ||
f@5 | T | 0.348 | 0.341 | 0.330 | 0.309 | 0.269 | 0.197 |
D | 0.378 | 0.373 | 0.368 | 0.362 | 0.349 | 0.314 | |
W | 0.381 | 0.378 | 0.374 | 0.368 | 0.356 | 0.332 | |
f@10 | T | 0.583 | 0.564 | 0.532 | 0.480 | 0.395 | 0.268 |
D | 0.627 | 0.617 | 0.606 | 0.591 | 0.554 | 0.469 | |
W | 0.634 | 0.628 | 0.620 | 0.608 | 0.580 | 0.523 | |
f@15 | T | 0.743 | 0.704 | 0.645 | 0.560 | 0.440 | 0.289 |
D | 0.800 | 0.784 | 0.766 | 0.731 | 0.656 | 0.527 | |
W | 0.813 | 0.804 | 0.792 | 0.769 | 0.719 | 0.623 | |
f@20 | T | 0.835 | 0.764 | 0.678 | 0.573 | 0.444 | 0.291 |
D | 0.918 | 0.889 | 0.847 | 0.779 | 0.675 | 0.533 | |
W | 0.944 | 0.930 | 0.905 | 0.859 | 0.776 | 0.652 | |
f@50 | T | 0.527 | 0.504 | 0.468 | 0.414 | 0.336 | 0.236 |
D | 0.560 | 0.554 | 0.544 | 0.522 | 0.477 | 0.401 | |
W | 0.564 | 0.562 | 0.559 | 0.551 | 0.528 | 0.477 | |
f@100 | T | 0.316 | 0.307 | 0.291 | 0.266 | 0.227 | 0.172 |
D | 0.330 | 0.328 | 0.325 | 0.317 | 0.298 | 0.263 | |
W | 0.331 | 0.331 | 0.330 | 0.328 | 0.321 | 0.303 |
Two-step model - \(k=\sqrt{|D_T |}\) | |||||||
---|---|---|---|---|---|---|---|
Noise % | |||||||
10% | 20% | 30% | 40% | 50% | 60% | ||
f@5 | T | 0.355 | 0.348 | 0.338 | 0.320 | 0.286 | 0.223 |
D | 0.380 | 0.375 | 0.370 | 0.365 | 0.354 | 0.327 | |
W | 0.382 | 0.380 | 0.376 | 0.371 | 0.360 | 0.339 | |
f@10 | T | 0.593 | 0.577 | 0.549 | 0.503 | 0.428 | 0.314 |
D | 0.629 | 0.620 | 0.610 | 0.596 | 0.565 | 0.497 | |
W | 0.636 | 0.631 | 0.624 | 0.613 | 0.589 | 0.538 | |
f@15 | T | 0.757 | 0.723 | 0.670 | 0.593 | 0.485 | 0.344 |
D | 0.803 | 0.789 | 0.771 | 0.740 | 0.677 | 0.566 | |
W | 0.816 | 0.808 | 0.797 | 0.777 | 0.734 | 0.647 | |
f@20 | T | 0.854 | 0.789 | 0.709 | 0.611 | 0.492 | 0.349 |
D | 0.923 | 0.896 | 0.856 | 0.795 | 0.703 | 0.575 | |
W | 0.948 | 0.935 | 0.913 | 0.872 | 0.797 | 0.681 | |
f@50 | T | 0.535 | 0.516 | 0.486 | 0.440 | 0.374 | 0.284 |
D | 0.562 | 0.557 | 0.548 | 0.529 | 0.491 | 0.425 | |
W | 0.565 | 0.564 | 0.562 | 0.555 | 0.537 | 0.494 | |
f@100 | T | 0.319 | 0.312 | 0.300 | 0.280 | 0.249 | 0.202 |
D | 0.331 | 0.330 | 0.326 | 0.320 | 0.305 | 0.275 | |
W | 0.332 | 0.332 | 0.332 | 0.330 | 0.325 | 0.311 |
Two-step model - \(k=\sqrt{|D_T |} \cdot 2\) | |||||||
---|---|---|---|---|---|---|---|
Noise % | |||||||
10% | 20% | 30% | 40% | 50% | 60% | ||
f@5 | T | 0.359 | 0.354 | 0.345 | 0.329 | 0.298 | 0.244 |
D | 0.381 | 0.377 | 0.372 | 0.366 | 0.356 | 0.334 | |
W | \({{\underline{\varvec{0.383}}}}\) | \({{\underline{\varvec{0.381}}}}\) | \({{\underline{\varvec{0.378}}}}\) | \({{\underline{\varvec{0.374}}}}\) | \({{\underline{\varvec{0.365}}}}\) | \({{\underline{\varvec{0.346}}}}\) | |
f@10 | T | 0.601 | 0.587 | 0.561 | 0.520 | 0.452 | 0.351 |
D | 0.632 | 0.623 | 0.613 | 0.599 | 0.571 | 0.512 | |
W | \({{\underline{\varvec{0.638}}}}\) | \({{\underline{\varvec{0.634}}}}\) | \({{\underline{\varvec{0.628}}}}\) | \({{\underline{\varvec{0.619}}}}\) | \({{\underline{\varvec{0.599}}}}\) | \({{\underline{\varvec{0.554}}}}\) | |
f@15 | T | 0.768 | 0.737 | 0.689 | 0.618 | 0.518 | 0.391 |
D | 0.807 | 0.793 | 0.775 | 0.746 | 0.688 | 0.589 | |
W | \({{\underline{\varvec{0.819}}}}\) | \({{\underline{\varvec{0.813}}}}\) | \({{\underline{\varvec{0.803}}}}\) | \({{\underline{\varvec{0.786}}}}\) | \({{\underline{\varvec{0.748}}}}\) | \({{\underline{\varvec{0.671}}}}\) | |
f@20 | T | 0.868 | 0.808 | 0.732 | 0.641 | 0.530 | 0.399 |
D | 0.928 | 0.901 | 0.862 | 0.804 | 0.718 | 0.601 | |
W | \({{\underline{\varvec{0.952}}}}\) | \({{\underline{\varvec{0.941}}}}\) | \({{\underline{\varvec{0.922}}}}\) | \({{\underline{\varvec{0.885}}}}\) | \({{\underline{\varvec{0.817}}}}\) | \({{\underline{\varvec{0.710}}}}\) | |
f@50 | T | 0.541 | 0.525 | 0.499 | 0.460 | 0.402 | 0.324 |
D | 0.564 | 0.559 | 0.550 | 0.533 | 0.499 | 0.441 | |
W | \({{\underline{\varvec{0.567}}}}\) | \({{\underline{\varvec{0.567}}}}\) | \({{\underline{\varvec{0.565}}}}\) | \({{\underline{\varvec{0.561}}}}\) | \({{\underline{\varvec{0.546}}}}\) | \({{\underline{\varvec{0.510}}}}\) | |
f@100 | T | 0.322 | 0.316 | 0.306 | 0.290 | 0.264 | 0.226 |
D | 0.332 | 0.330 | 0.327 | 0.321 | 0.308 | 0.283 | |
W | \({{\underline{\varvec{0.333}}}}\) | \({{\underline{\varvec{0.333}}}}\) | \({{\underline{\varvec{0.333}}}}\) | \({{\underline{\varvec{0.332}}}}\) | \({{\underline{\varvec{0.329}}}}\) | \({{\underline{\varvec{0.317}}}}\) |
Noise % | |||||||
---|---|---|---|---|---|---|---|
10% | 20% | 30% | 40% | 50% | 60% | ||
f@5 | PRILJ | 0.383 | 0.381 | 0.378 | 0.374 | 0.365 | 0.346 |
LEGAL-BERT-BASE | 0.358 | 0.221 | 0.082 | 0.026 | 0.009 | 0.003 | |
LEGAL-BERT-SMALL | 0.370 | 0.243 | 0.095 | 0.034 | 0.014 | 0.006 | |
LEGAL-BERT-EURLEX | 0.365 | 0.235 | 0.099 | 0.038 | 0.015 | 0.006 | |
BERT-PLI | 0.243 | 0.052 | 0.017 | 0.008 | 0.004 | 0.002 | |
f@10 | PRILJ | 0.638 | 0.634 | 0.628 | 0.619 | 0.599 | 0.554 |
LEGAL-BERT-BASE | 0.592 | 0.347 | 0.122 | 0.037 | 0.013 | 0.005 | |
LEGAL-BERT-SMALL | 0.611 | 0.375 | 0.136 | 0.047 | 0.019 | 0.008 | |
LEGAL-BERT-EURLEX | 0.604 | 0.370 | 0.146 | 0.053 | 0.021 | 0.008 | |
BERT-PLI | 0.373 | 0.072 | 0.022 | 0.010 | 0.006 | 0.003 | |
f@15 | PRILJ | 0.819 | 0.813 | 0.803 | 0.786 | 0.748 | 0.671 |
LEGAL-BERT-BASE | 0.739 | 0.408 | 0.141 | 0.042 | 0.015 | 0.006 | |
LEGAL-BERT-SMALL | 0.773 | 0.440 | 0.154 | 0.054 | 0.021 | 0.009 | |
LEGAL-BERT-EURLEX | 0.757 | 0.433 | 0.166 | 0.060 | 0.024 | 0.010 | |
BERT-PLI | 0.428 | 0.078 | 0.024 | 0.011 | 0.006 | 0.004 | |
f@20 | PRILJ | 0.952 | 0.941 | 0.922 | 0.885 | 0.817 | 0.710 |
LEGAL-BERT-BASE | 0.798 | 0.422 | 0.147 | 0.044 | 0.016 | 0.006 | |
LEGAL-BERT-SMALL | 0.856 | 0.459 | 0.161 | 0.056 | 0.023 | 0.010 | |
LEGAL-BERT-EURLEX | 0.820 | 0.446 | 0.172 | 0.063 | 0.025 | 0.010 | |
BERT-PLI | 0.432 | 0.078 | 0.024 | 0.011 | 0.007 | 0.004 | |
f@50 | PRILJ | 0.567 | 0.567 | 0.565 | 0.561 | 0.546 | 0.510 |
LEGAL-BERT-BASE | 0.524 | 0.336 | 0.135 | 0.044 | 0.016 | 0.007 | |
LEGAL-BERT-SMALL | 0.544 | 0.358 | 0.143 | 0.053 | 0.023 | 0.010 | |
LEGAL-BERT-EURLEX | 0.532 | 0.350 | 0.154 | 0.060 | 0.025 | 0.011 | |
BERT-PLI | 0.325 | 0.065 | 0.022 | 0.011 | 0.008 | 0.005 | |
f@100 | PRILJ | 0.333 | 0.333 | 0.333 | 0.332 | 0.329 | 0.317 |
LEGAL-BERT-BASE | 0.318 | 0.233 | 0.107 | 0.037 | 0.014 | 0.006 | |
LEGAL-BERT-SMALL | 0.325 | 0.245 | 0.110 | 0.044 | 0.020 | 0.010 | |
LEGAL-BERT-EURLEX | 0.321 | 0.240 | 0.119 | 0.050 | 0.022 | 0.010 | |
BERT-PLI | 0.218 | 0.047 | 0.018 | 0.010 | 0.007 | 0.005 |
ANNS | |||||||
---|---|---|---|---|---|---|---|
Noise % | |||||||
10% | 20% | 30% | 40% | 50% | 60% | ||
f@5 | T | 0.361 | 0.355 | 0.346 | 0.330 | 0.301 | 0.253 |
D | 0.384 | 0.381 | 0.377 | 0.372 | 0.364 | 0.345 | |
W | 0.385 | 0.384 | 0.382 | 0.379 | 0.372 | 0.358 | |
f@10 | T | 0.604 | 0.589 | 0.562 | 0.521 | 0.454 | 0.364 |
D | 0.637 | 0.631 | 0.623 | 0.609 | 0.585 | 0.533 | |
W | 0.641 | 0.639 | 0.635 | 0.627 | 0.610 | 0.571 | |
f@15 | T | 0.771 | 0.738 | 0.687 | 0.617 | 0.522 | 0.407 |
D | 0.815 | 0.804 | 0.787 | 0.758 | 0.706 | 0.619 | |
W | 0.823 | 0.819 | 0.811 | 0.797 | 0.760 | 0.686 | |
f@20 | T | 0.869 | 0.805 | 0.727 | 0.639 | 0.534 | 0.417 |
D | 0.938 | 0.914 | 0.875 | 0.819 | 0.741 | 0.634 | |
W | 0.958 | 0.949 | 0.928 | 0.890 | 0.822 | 0.719 | |
f@50 | T | 0.544 | 0.527 | 0.500 | 0.462 | 0.408 | 0.341 |
D | 0.569 | 0.566 | 0.558 | 0.543 | 0.513 | 0.463 | |
W | 0.570 | 0.570 | 0.568 | 0.563 | 0.548 | 0.512 | |
f@100 | T | 0.322 | 0.317 | 0.307 | 0.292 | 0.269 | 0.236 |
D | 0.333 | 0.332 | 0.330 | 0.326 | 0.315 | 0.295 | |
W | 0.333 | 0.333 | 0.333 | 0.332 | 0.328 | 0.316 |
Cosine similarity | |||||||
---|---|---|---|---|---|---|---|
Noise % | |||||||
10% | 20% | 30% | 40% | 50% | 60% | ||
f@5 | T | 0.365 | 0.359 | 0.349 | 0.333 | 0.305 | 0.262 |
D | 0.384 | 0.381 | 0.377 | 0.372 | 0.364 | 0.346 | |
W | 0.385 | 0.384 | 0.382 | 0.379 | 0.372 | 0.359 | |
f@10 | T | 0.608 | 0.592 | 0.566 | 0.525 | 0.463 | 0.380 |
D | 0.637 | 0.631 | 0.623 | 0.609 | 0.585 | 0.536 | |
W | 0.641 | 0.639 | 0.635 | 0.627 | 0.610 | 0.573 | |
f@15 | T | 0.775 | 0.742 | 0.692 | 0.623 | 0.533 | 0.426 |
D | 0.815 | 0.804 | 0.787 | 0.758 | 0.708 | 0.622 | |
W | 0.824 | 0.819 | 0.812 | 0.797 | 0.761 | 0.689 | |
f@20 | T | 0.873 | 0.811 | 0.735 | 0.647 | 0.545 | 0.434 |
D | 0.938 | 0.914 | 0.875 | 0.819 | 0.743 | 0.637 | |
W | 0.958 | 0.949 | 0.929 | 0.892 | 0.825 | 0.724 | |
f@50 | T | 0.551 | 0.533 | 0.506 | 0.468 | 0.416 | 0.350 |
D | 0.569 | 0.566 | 0.558 | 0.543 | 0.514 | 0.464 | |
W | 0.571 | 0.570 | 0.568 | 0.564 | 0.549 | 0.514 | |
f@100 | T | 0.328 | 0.322 | 0.312 | 0.297 | 0.274 | 0.242 |
D | 0.333 | 0.332 | 0.330 | 0.326 | 0.316 | 0.295 | |
W | 0.333 | 0.333 | 0.333 | 0.332 | 0.328 | 0.317 |
ANNS | Cosine Similarity | |
---|---|---|
TF-IDF |
0.513
| 407.612 |
Doc2Vec |
0.551
| 580.842 |
Word2Vec |
0.610
| 668.040 |