How to go around truncating long sentences with Hugginface Tokenizers? - nlp
I am new to tokenizers. My understanding is that the truncate attribute just cuts the sentences. But I need the whole sentence for context.
For example, my sentence is :
"Ali bin Abbas'ın Kitab Kamilü-s Sina adlı eseri daha sonra 980 yılında nasıl adlandırılmıştır? Ali bin Abbas'ın eseri Rezi'nin hangi isimli eserinden daha özlü ve daha sistematikdir? Ali bin Abbas'ın Kitab Kamilü-s Sina adlı eseri İbn-i Sina'nın hangi isimli eserinden daha uygulamalı bir biçimde yazılmıştır? Kitab el-Maliki Avrupa'da Constantinus Africanus tarafından hangi dile çevrilmiştir? Kitab el-Maliki'nin ilk bölümünde neye ağırlık verilmiştir?
But when I use max_length=64, truncation=True and pad_to_max_length=True for my encoder(as suggested in the internet), half of sentence is being gone:
▁Ali', '▁bin', '▁Abbas', "'", 'ın', '▁Kitab', '▁Kami', 'lü', '-', 's', '▁Sina', '▁ad', 'lı', '▁es', 'eri', '▁daha', '▁sonra', '▁980', '▁yıl', 'ında', '▁na', 'sıl', '▁adlandır', 'ılmıştır', '?', '▁', '<sep>', '▁Ali', '▁bin', '▁Abbas', "'", 'ın', '▁es', 'eri', '▁Rez', 'i', "'", 'nin', '▁', 'hangi', '▁is', 'imli', '▁es', 'erinden', '▁daha', '▁', 'özlü', '▁ve', '▁daha', '▁sistema', 'tik', 'dir', '?', '▁', '<sep>', '▁Ali', '▁bin', '▁Abbas', "'", 'ın', '▁Kitab', '▁Kami', 'lü', '</s>']
And when I increase max length, CUDA is running out of memory of course. What should be my approach for long texts in the dataset?
My code for encoding:
input_encodings = tokenizer.batch_encode_plus(
example_batch['context'],
max_length=512,
add_special_tokens=True,
truncation=True,
pad_to_max_length=True)
target_encodings = tokenizer.batch_encode_plus(
example_batch['questions'],
max_length=64,
add_special_tokens=True,
truncation=True,
pad_to_max_length=True)
Yes, the truncate attribute just keeps the given number of subwords from the left. The workaround depends on the task you are solving and the data that you use.
Are the long sequence frequent in your data? If not, you can just safely throw away the instances because it is unlikely that the model would learn to generalize for long sequences anyway.
If you really need the long context, you have plenty of options:
Decrease the batch size (and perhaps do updates once after several batches).
Make the model smaller: use either a smaller dimension or fewer layers.
Use a different architecture: Transformers need quadratic memory w.r.t sequence length. Wouldn't an LSTM or CNN do the job? What architectures for long sequences (e.g., Reformer, Longformer).
If you need to use a pre-trained BERT-like model and there is no model of the size that would fit your needs, you can distill a smaller model or a model with a more suitable architecture yourself.
Perhaps you can split the input. In tasks like answer span selection, you can split the text where you are looking for an answer into smaller chunks and search in the chunks independently.
Related
fasttext: why do aligned vectors contain only one value per word?
I was taking a look at the Fasttext aligned vectors of some languages and was surprised to find that each vectors consisted of one value only. I was expecting a Matrix witch multidimensional vectors belonging to each word, instead there is only one column of numbers. I'm very new to this field and was wondering if somebody could explain to me, how this single number belongig to each word came to be and wether I'm looking at a semantic space as I was expecting or something different (if so what is it and are alingend multidimensional semantic spaces available somewhere?)
I think you may be misinterpreting those files. When I look at one of those files – for example wiki.en.align.vec – each line is a word-token, then 300 different values (to provide a 300-dimensional word-vector). For example, the 4th line of the file is: the -0.0324 -0.0462 -0.0087 0.0994 0.0147 -0.0198 -0.0811 -0.0362 0.0445 0.0402 -0.0199 -0.1173 0.0906 -0.0304 -0.0320 -0.0374 -0.0249 -0.0099 0.0017 0.0719 -0.0834 0.0382 -0.1141 -0.0288 -0.0666 -0.0365 -0.0006 0.0098 0.0282 0.0310 -0.0773 0.0755 -0.0528 0.1225 -0.0138 -0.0879 0.0036 -0.0593 0.0416 -0.0588 0.0266 -0.0011 -0.0419 0.0141 0.0388 -0.0597 -0.0203 0.0444 0.0253 -0.0316 0.0352 -0.0318 -0.0473 0.0347 -0.0250 0.0289 0.0426 0.0218 -0.0254 0.0486 -0.0252 -0.0904 0.1607 -0.0379 0.0231 -0.0988 -0.1213 -0.0926 -0.1116 0.0345 -0.1856 -0.0409 0.0306 -0.0653 -0.0377 -0.0301 0.0361 0.1212 0.0105 -0.0354 0.0552 0.0363 -0.0427 0.0555 -0.0031 -0.0830 -0.0325 0.0415 -0.0461 -0.0615 -0.0412 0.0060 0.1680 -0.1347 0.0271 -0.0438 0.0364 0.0121 0.0018 -0.0138 -0.0625 -0.0161 -0.0009 -0.0373 -0.1009 -0.0583 0.0038 0.0109 -0.0068 0.0319 -0.0043 -0.0412 -0.0506 -0.0674 0.0426 -0.0031 0.0788 0.0924 0.0559 0.0449 0.1364 0.1132 -0.0378 0.1060 0.0130 0.0349 0.0638 0.1020 0.0459 0.0634 -0.0870 0.0447 -0.0124 0.0167 -0.0603 0.0297 -0.0298 0.0691 -0.0280 0.0749 0.0474 0.0275 0.0255 0.0184 0.0085 0.1116 0.0233 0.0176 0.0327 0.0471 0.0662 -0.0353 -0.0387 -0.0336 -0.0354 -0.0348 0.0157 -0.0294 0.0710 0.0299 -0.0602 0.0732 -0.0344 0.0419 0.0773 0.0119 -0.0550 0.0377 0.0808 -0.0424 -0.0977 -0.0386 -0.0334 -0.0384 -0.0520 0.0641 0.0049 0.1226 -0.0011 -0.0131 0.0224 0.0138 -0.0243 0.0544 -0.0164 0.1194 0.0916 -0.0755 0.0565 0.0235 -0.0009 -0.0818 0.0953 0.0873 -0.0215 0.0240 -0.0271 0.0134 -0.0870 0.0597 -0.0073 -0.0230 -0.0220 0.0562 -0.0069 -0.0796 -0.0118 0.0059 0.0221 0.0509 0.1175 0.0508 -0.0044 -0.0265 0.0328 -0.0525 0.0493 -0.1309 -0.0674 0.0148 -0.0024 -0.0163 -0.0241 0.0726 -0.0165 0.0368 -0.0914 0.0197 0.0018 -0.0149 0.0654 0.0912 -0.0638 -0.0135 -0.0277 -0.0078 0.0092 -0.0477 0.0054 -0.0153 -0.0411 -0.0177 0.0874 0.0221 0.1040 0.1004 0.0595 -0.0610 0.0650 -0.0235 0.0257 0.1208 0.0129 -0.0086 -0.0846 0.1102 -0.0338 -0.0553 0.0166 -0.0602 0.0128 0.0792 -0.0181 0.0046 -0.0548 -0.0394 -0.0546 0.0425 0.0048 -0.1172 -0.0925 -0.0357 -0.0123 0.0371 -0.0142 0.0157 0.0442 0.1186 0.0834 -0.0293 0.0313 -0.0287 0.0095 0.0080 0.0566 -0.0370 0.0257 0.1032 -0.0431 0.0544 0.0323 -0.1076 -0.0187 0.0407 -0.0198 -0.0255 -0.0505 0.0827 -0.0650 0.0176 Thus every one of the 2,519,370 word-tokens has a 300-dimensional vector. If this isn't what you're seeing, you should explain further. If this is what you're seeing and you were expecting something else, you should explain further what you were expecting.
Gradients vanishing despite using Kaiming initialization
I was implementing a conv block in pytorch with activation function(prelu). I used Kaiming initilization to initialize all my weights and set all the bias to zero. However as I tested these blocks (by stacking 100 such conv and activation blocks on top of each other), I noticed that the output I am getting values of the order of 10^(-10). Is this normal, considering I am stacking upto 100 layers. Adding a small bias to each layer fixes the problem. But in Kaiming initialization the biases are supposed to be zero. Here is the conv block code from collections import Iterable def convBlock( input_channels, output_channels, kernel_size=3, padding=None, activation="prelu" ): """ Initializes a conv block using Kaiming Initialization """ padding_par = 0 if padding == "same": padding_par = same_padding(kernel_size) conv = nn.Conv2d(input_channels, output_channels, kernel_size, padding=padding_par) relu_negative_slope = 0.25 act = None if activation == "prelu" or activation == "leaky_relu": nn.init.kaiming_normal_(conv.weight, a=relu_negative_slope, mode="fan_in") if activation == "prelu": act = nn.PReLU(init=relu_negative_slope) else: act = nn.LeakyReLU(negative_slope=relu_negative_slope) if activation == "relu": nn.init.kaiming_normal_(conv.weight, nonlinearity="relu") act = nn.ReLU() nn.init.constant_(conv.bias.data, 0) block = nn.Sequential(conv, act) return block def flatten(lis): for item in lis: if isinstance(item, Iterable) and not isinstance(item, str): for x in flatten(item): yield x else: yield item def Sequential(args): flattened_args = list(flatten(args)) return nn.Sequential(*flattened_args) This is the test Code ls=[] for i in range(100): ls.append(convBlock(3,3,3,"same")) model=Sequential(ls) test=np.ones((1,3,5,5)) model(torch.Tensor(test)) And the output I am getting is tensor([[[[-1.7771e-10, -3.5088e-10, 5.9369e-09, 4.2668e-09, 9.8803e-10], [ 1.8657e-09, -4.0271e-10, 3.1189e-09, 1.5117e-09, 6.6546e-09], [ 2.4237e-09, -6.2249e-10, -5.7327e-10, 4.2867e-09, 6.0034e-09], [-1.8757e-10, 5.5446e-09, 1.7641e-09, 5.7018e-09, 6.4347e-09], [ 1.2352e-09, -3.4732e-10, 4.1553e-10, -1.2996e-09, 3.8971e-09]], [[ 2.6607e-09, 1.7756e-09, -1.0923e-09, -1.4272e-09, -1.1840e-09], [ 2.0668e-10, -1.8130e-09, -2.3864e-09, -1.7061e-09, -1.7147e-10], [-6.7161e-10, -1.3440e-09, -6.3196e-10, -8.7677e-10, -1.4851e-09], [ 3.1475e-09, -1.6574e-09, -3.4180e-09, -3.5224e-09, -2.6642e-09], [-1.9703e-09, -3.2277e-09, -2.4733e-09, -2.3707e-09, -8.7598e-10]], [[ 3.5573e-09, 7.8113e-09, 6.8232e-09, 1.2285e-09, -9.3973e-10], [ 6.6368e-09, 8.2877e-09, 9.2108e-10, 9.7531e-10, 7.0011e-10], [ 6.6954e-09, 9.1019e-09, 1.5128e-08, 3.3151e-09, 2.1899e-10], [ 1.2152e-08, 7.7002e-09, 1.6406e-08, 1.4948e-08, -6.0882e-10], [ 6.9930e-09, 7.3222e-09, -7.4308e-10, 5.2505e-09, 3.4365e-09]]]], grad_fn=<PreluBackward>)
Amazing question (and welcome to StackOverflow)! Research paper for quick reference. TLDR Try wider networks (64 channels) Add Batch Normalization after activation (or even before, shouldn't make much difference) Add residual connections (shouldn't improve much over batch norm, last resort) Please check this out in this order and give a comment what (and if) any of that worked in your case (as I'm also curious). Things you do differently Your neural network is very deep, yet very narrow (81 parameters per layer only!) Due to above, one cannot reliably create those weights from normal distribution as the sample is just too small. Try wider networks, 64 channels or more You are trying much deeper network than they did Section: Comparison Experiments We conducted comparisons on a deep but efficient model with 14 weight layers (actually 22 was also tested in comparison with Xavier) That was due to date of release of this paper (2015) and hardware limitations "back in the days" (let's say) Is this normal? Approach itself is quite strange with layers of this depth, at least currently; each conv block is usually followed by activation like ReLU and Batch Normalization (which normalizes signal and helps with exploding/vanishing signals) usually networks of this depth (even of depth half of what you've got) use also residual connections (though this is not directly linked to vanishing/small signal, more connected to degradation problem of even deep networks, like 1000 layers)
How to estimate camera pose according to a projective transformation matrix of two consecutive frames?
I'm working on the kitti visual odometry dataset. I use projective transformation to register two 2D consecutive frames(see projective transformation example here ). I want to know how this 3*3 projective transformation matrix is related to the ground truth poses provided by the kitti dataset. This dataset gives the ground truth poses (trajectory) for the sequences, which is described below: Folder 'poses': The folder 'poses' contains the ground truth poses (trajectory) for the first 11 sequences. This information can be used for training/tuning your method. Each file xx.txt contains a N x 12 table, where N is the number of frames of this sequence. Row i represents the i'th pose of the left camera coordinate system (i.e., z pointing forwards) via a 3x4 transformation matrix. The matrices are stored in row aligned order (the first entries correspond to the first row), and take a point in the i'th coordinate system and project it into the first (=0th) coordinate system. Hence, the translational part (3x1 vector of column 4) corresponds to the pose of the left camera coordinate system in the i'th frame with respect to the first (=0th) frame. Your submission results must be provided using the same data format. Some samples of the given groud-truth poses: 1.000000e+00 9.043680e-12 2.326809e-11 5.551115e-17 9.043683e-12 1.000000e+00 2.392370e-10 3.330669e-16 2.326810e-11 2.392370e-10 9.999999e-01 -4.440892e-16 9.999978e-01 5.272628e-04 -2.066935e-03 -4.690294e-02 -5.296506e-04 9.999992e-01 -1.154865e-03 -2.839928e-02 2.066324e-03 1.155958e-03 9.999971e-01 8.586941e-01 9.999910e-01 1.048972e-03 -4.131348e-03 -9.374345e-02 -1.058514e-03 9.999968e-01 -2.308104e-03 -5.676064e-02 4.128913e-03 2.312456e-03 9.999887e-01 1.716275e+00 9.999796e-01 1.566466e-03 -6.198571e-03 -1.406429e-01 -1.587952e-03 9.999927e-01 -3.462706e-03 -8.515762e-02 6.193102e-03 3.472479e-03 9.999747e-01 2.574964e+00 9.999637e-01 2.078471e-03 -8.263498e-03 -1.874858e-01 -2.116664e-03 9.999871e-01 -4.615826e-03 -1.135202e-01 8.253797e-03 4.633149e-03 9.999551e-01 3.432648e+00 9.999433e-01 2.586172e-03 -1.033094e-02 -2.343818e-01 -2.645881e-03 9.999798e-01 -5.770163e-03 -1.419150e-01 1.031581e-02 5.797170e-03 9.999299e-01 4.291335e+00 9.999184e-01 3.088363e-03 -1.239599e-02 -2.812195e-01 -3.174350e-03 9.999710e-01 -6.922975e-03 -1.702743e-01 1.237425e-02 6.961759e-03 9.998991e-01 5.148987e+00 9.998890e-01 3.586305e-03 -1.446384e-02 -3.281178e-01 -3.703403e-03 9.999605e-01 -8.077186e-03 -1.986703e-01 1.443430e-02 8.129853e-03 9.998627e-01 6.007777e+00 9.998551e-01 4.078705e-03 -1.652913e-02 -3.749547e-01 -4.231669e-03 9.999484e-01 -9.229794e-03 -2.270290e-01 1.649063e-02 9.298401e-03 9.998207e-01 6.865477e+00 9.998167e-01 4.566671e-03 -1.859652e-02 -4.218367e-01 -4.760342e-03 9.999347e-01 -1.038342e-02 -2.554151e-01 1.854788e-02 1.047004e-02 9.997731e-01 7.724036e+00 9.997738e-01 5.049868e-03 -2.066463e-02 -4.687329e-01 -5.289072e-03 9.999194e-01 -1.153730e-02 -2.838096e-01 2.060470e-02 1.164399e-02 9.997198e-01 8.582886e+00 9.997264e-01 5.527315e-03 -2.272922e-02 -5.155474e-01 -5.816781e-03 9.999025e-01 -1.268908e-02 -3.121547e-01 2.265686e-02 1.281782e-02 9.996611e-01 9.440275e+00 9.996745e-01 6.000540e-03 -2.479692e-02 -5.624310e-01 -6.345160e-03 9.998840e-01 -1.384246e-02 -3.405416e-01 2.471098e-02 1.399530e-02 9.995966e-01 1.029896e+01 9.996182e-01 6.468772e-03 -2.686440e-02 -6.093087e-01 -6.873365e-03 9.998639e-01 -1.499561e-02 -3.689250e-01 2.676374e-02 1.517453e-02 9.995266e-01 1.115757e+01 9.995562e-01 7.058450e-03 -2.894213e-02 -6.562052e-01 -7.530449e-03 9.998399e-01 -1.623192e-02 -3.973964e-01 2.882292e-02 1.644266e-02 9.994492e-01 1.201541e+01 9.995095e-01 5.595311e-03 -3.081450e-02 -7.018788e-01 -6.093682e-03 9.998517e-01 -1.610315e-02 -4.239119e-01 3.071983e-02 1.628303e-02 9.993953e-01 1.286965e+01
The common name for your "projective transformation" is homography. In a calibrated setup (i.e. if you know your camera's field of view or, equivalently, its focal length) a homography can be decomposed into 3D rotation and translation, the latter only up to scale. The decomposition algorithm additionally produces the normal to the 3D plane inducting the homography. The algorithm has up to 4 solutions, of which only one is feasible when you apply additional constraints, such as that the matched image points triangulate in front of the camera, and that the general direction of the translation match a known prior. More information about the method is in a well-known paper by Malis and Vargas. There is an implementation in OpenCV, under the name decomposeHomographyMat.
Why do mllib word2vec word vectors only have 100 elements?
I have a word2vec model that I created in PySpark. The model is saved as a .parquet file. I want to be able to access and query the model (or the words and word vectors) using vanilla Python because I am building a flask app that will allow a user to enter words of interest for finding synonyms. I've extracted the words and word vectors, but I've noticed that while I have approximately 7000 unique words, my word vectors have a length of 100. For example, here are two words "serious" and "breaks". Their vectors only have a length of 100. Why is this? How is it able to then reconstruct the entire vector space with only 100 values for each word? Is it simply only giving me the top 100 or the first 100 values? vectors.take(2) Out[48]: [Row(word=u'serious', vector=DenseVector([0.0784, -0.0882, -0.0342, -0.0153, 0.0223, 0.1034, 0.1218, -0.0814, -0.0198, -0.0325, -0.1024, -0.2412, -0.0704, -0.1575, 0.0342, -0.1447, -0.1687, 0.0673, 0.1248, 0.0623, -0.0078, -0.0813, 0.0953, -0.0213, 0.0031, 0.0773, -0.0246, -0.0822, -0.0252, -0.0274, -0.0288, 0.0403, -0.0419, -0.1122, -0.0397, 0.0186, -0.0038, 0.1279, -0.0123, 0.0091, 0.0065, 0.0884, 0.0899, -0.0479, 0.0328, 0.0171, -0.0962, 0.0753, -0.187, 0.034, -0.1393, -0.0575, -0.019, 0.0151, -0.0205, 0.0667, 0.0762, -0.0365, -0.025, -0.184, -0.0118, -0.0964, 0.1744, 0.0563, -0.0413, -0.054, -0.1764, -0.087, 0.0747, -0.022, 0.0778, -0.0014, -0.1313, -0.1133, -0.0669, 0.0007, -0.0378, -0.1093, -0.0732, 0.1494, -0.0815, -0.0137, 0.1009, -0.0057, 0.0195, 0.0085, 0.025, 0.0064, 0.0076, 0.0676, 0.1663, -0.0078, 0.0278, 0.0519, -0.0615, -0.0833, 0.0643, 0.0032, -0.0882, 0.1033])), Row(word=u'breaks', vector=DenseVector([0.0065, 0.0027, -0.0121, 0.0296, -0.0467, 0.0297, 0.0499, 0.0843, 0.1027, 0.0179, -0.014, 0.0586, 0.06, 0.0534, 0.0391, -0.0098, -0.0266, -0.0422, 0.0188, 0.0065, -0.0309, 0.0038, -0.0458, -0.0252, 0.0428, 0.0046, -0.065, -0.0822, -0.0555, -0.0248, -0.0288, -0.0016, 0.0334, -0.0028, -0.0718, -0.0571, -0.0668, -0.0073, 0.0658, -0.0732, 0.0976, -0.0255, -0.0712, 0.0899, 0.0065, -0.04, 0.0964, 0.0356, 0.0142, 0.0857, 0.0669, -0.038, -0.0728, -0.0446, 0.1194, -0.056, 0.1022, 0.0459, -0.0343, -0.0861, -0.0943, -0.0435, -0.0573, 0.0229, 0.0368, 0.085, -0.0218, -0.0623, 0.0502, -0.0645, 0.0247, -0.0371, -0.0785, 0.0371, -0.0047, 0.0012, 0.0214, 0.0669, 0.049, -0.0294, -0.0272, 0.0642, -0.006, -0.0804, -0.06, 0.0719, -0.0109, -0.0272, -0.0366, 0.0041, 0.0556, 0.0108, 0.0624, 0.0134, -0.0094, 0.0219, 0.0164, -0.0545, -0.0055, -0.0193]))] Any thoughts on the best way to reconstruct this model in vanilla python?
Just to improve on the comment by zero323, for anyone else who arrives here. Word2Vec has a default setting to create word vectors of 100dims. To change this: model = Word2Vec(sentences, size=300) when initializing the model will create vectors of 300 dimensions.
I think the problem lays with your minCount parameter value for the Word2Vec model. If this value is too high, less words get used in the training of the model resulting in a words vector of only 100. 7000 unique words is not a lot. Try setting the minCount lower than the default 5. model.setMinCount(value) https://spark.apache.org/docs/latest/api/python/pyspark.ml.html?highlight=word2vec#pyspark.ml.feature.Word2Vec
Reducing Model file size in LIBSVM
I want to reduce the model file size . Can we reduce it by reducing the number of digits in the weights of the model file. The number of classes in my model file is around 3800 and the number of features is around 357000. Here is some excerpt from the model file. Can I reduce the number of digits in these weights. solver_type L2R_L2LOSS_SVC_DUAL nr_class 3821 nr_feature 357021 bias -1.000000000000000 w -0.6298615183549175 -0.6884816945277815 -0.9850473581929793 -0.2730180225739936 -0.4444522939544599 -0.3045368061994185 -0.6752904784743610 -0.4936186126242763 -0.8167435931134331 -0.8747648882598349 -0.4980187300672689 -0.8255372912521536 -0.3329812532124196 -0.1751416471640286 -0.7447656595877303 -0.4240569914873799 -0.9004909961812873 -0.9857813112641359 -0.3674085365663847 -0.4819407419877990 -0.3645238468547681 -0.5827397105860186 -0.7290781581209491 -0.8615229165775795 -0.3975308017493017 -0.6522787326004871 -0.9846626520798610 -0.5583216247458188 -0.9488816092738117 -0.6469158771901011 -0.2306256734853684 -0.2940612946888093 -0.6895719661937446 -0.3041407180695167 -0.5602587606930518 -0.4434458835686698 -0.3960629365410545 -0.7512211790407204 -0.6082476608695304 -1.336132842955273 -0.6057066303450040 -0.5726087731282288 -0.4918814547677718 -0.7606578865363953 -0.2951659264868926 -0.3881680788359501 -0.3109241231671961 -0.7078707491799914 -0.3623625688446360 -0.4430137729068305 -0.9279271098475936 -0.2290838088700753 -0.3870980678621480 -0.8000332693180561 -0.7964744879675550 -0.4950551119251316 -0.5201500981458075 -0.6654200978736288 -0.9037766341356712 -0.5921799507740539 -0.4552915755388566 -0.8048467444625557 -0.08638961422716016 -0.3175800991399296 -0.8889281355804046 -0.8889673432972257 0.009443893188055608 -0.3033030733905986 -0.6063958370642328 -0.7781676697747630 -0.9969339455729528 -0.7847641855193951 -0.3709450948897945 -0.9293821956430142 -0.6711216076980766 -0.6472048031763484 -0.2844660995208588 -0.4547657013618363 -0.3093274839631762 -0.8264594986328345 -0.2693948669009715 -0.5691246530468883 -0.5816949288414970 -0.7988407843132017 -0.5846410991542126 -0.6102733673192773 -0.9474472897104326 -0.4619018809588187 -0.6922626991585266 -0.8529509393486879 -0.9341690394723746 -0.2048861760333368 -0.5763255438056814 -0.4753823007333206 -0.9847858814169310 -0.6084670508904806 -0.6097889096385636 -0.1558026578670219 -0.5407452525949980 -0.8426597160875828 -0.5728578082647764 -0.6254655056167889 -0.5002570985981800 -0.5660289375686121 -0.6966970933117435 -0.3595184568720410 -0.8869769517170271 -0.8293060581021244 -0.7660244640066636 -0.9191108227612158 -0.7495472111112249 -0.3250789003708131 -0.8545862221106031 -0.9847863669982040 -0.9862358540926807 -0.9843872487122278 -0.3764841688606632 -0.6665806111063707 -0.6998869717621219 -0.8398491506346015 -0.7498849663083538 -0.2584536929034274 -0.8798094698402976 -0.8659064866640068 -0.8540212609217359 -0.4705628403387491 -0.9848057457322186 -0.5870303872290659 -0.9105115844147157 -0.6855534064105064 -0.7447256224770895 -0.9845164901161550 -0.9267803381073205 -0.6874399094864110 -0.9868490844056681 -0.9871049327408159 -0.9127271706215343 -0.8894132571749456 -0.7481430771200624 -0.7661512147794380 -0.4619076734386954 -0.3463253354355214 -0.7324122395130058 -0.7198934949704492 -0.3869971300152642 -0.3580173602243875 -0.8144411145869335 -0.4708508640578066 -0.7583061726079500 -0.6102585014526588 -0.2323551831668570 -0.7124730357532248 -0.6407019387626708 -0.8770555543363814 -0.7747723882503575 -0.8880529094965369 -0.5221765657051773 -0.8927103129537772 -0.8873570244928761 -0.6814118942525524 -0.4812414843861851 -0.07723442473878635 -0.3004215736435181 -0.7901826925719376 -0.6000050603345796 -0.9391488020802135 -0.6130019120301854 -0.6519260224181763 -0.6312423953207323 -0.6236684911320279 -0.8319901021019791 -0.9846585341126538 -0.8241847119432536 -0.9849733862258551 0.03619613868867930 -0.9402473523400392 -0.4963043182116479 -0.06988396609313940 -0.6160025364808686 -0.9485679374403244 -0.9552678112333591 -0.2951058860501357 -0.9871232492575841 -0.2801466899229405 -0.5623043303