oroikono/SIGS-GrammarVAE
6.13M • Updated • 4
Datasets:
id int32 0 23.7k | expression stringlengths 1 124 | math_class stringclasses 6
values | has_x bool 2
classes | has_t bool 2
classes | has_y bool 2
classes | latent_mu list | latent_log_sigma list |
|---|---|---|---|---|---|---|---|
0 | (x+1)*exp(x) | SPATIAL_1D | true | false | false | [
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2.559635877609253,
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-4.48... |
1 | cos(x/9) | SPATIAL_1D | true | false | false | [
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... | [
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-3... |
2 | -1*1 | CONSTANT | false | false | false | [
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... | [
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... |
3 | 0.143*x | SPATIAL_1D | true | false | false | [
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... | [
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-4... |
4 | log(x)+1 | SPATIAL_1D | true | false | false | [
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-1... | [
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... |
5 | exp(-x^2) | SPATIAL_1D | true | false | false | [
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6 | x | SPATIAL_1D | true | false | false | [
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... |
7 | -x+sin(x)-5 | SPATIAL_1D | true | false | false | [
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... | [
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-4... |
8 | exp(-8*x) | SPATIAL_1D | true | false | false | [
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... | [
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... |
9 | 7*90*x | SPATIAL_1D | true | false | false | [
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... | [
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... |
10 | 2*x | SPATIAL_1D | true | false | false | [
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-0... | [
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... |
11 | 2-2*x | SPATIAL_1D | true | false | false | [
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-2.... | [
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... |
12 | x^2/(x-1) | SPATIAL_1D | true | false | false | [
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1.046068549156189,
0.8733604550361633,
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-1.... | [
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-4.30... |
13 | cos(x^2) | SPATIAL_1D | true | false | false | [
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... |
14 | cos(x+8) | SPATIAL_1D | true | false | false | [
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... | [
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... |
15 | cos(x+7) | SPATIAL_1D | true | false | false | [
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-3.... |
16 | -10/x | SPATIAL_1D | true | false | false | [
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-3.... |
17 | cos(x) | SPATIAL_1D | true | false | false | [
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... | [
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18 | (x+7)/sin(x) | SPATIAL_1D | true | false | false | [
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2.659882068634033,
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... | [
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... |
19 | cos(x/4) | SPATIAL_1D | true | false | false | [
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0.9639368653297424,
-0.470493882894516,... | [
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... |
20 | -0.1*x | SPATIAL_1D | true | false | false | [
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... | [
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-4.01... |
21 | -x^2/(x-9) | SPATIAL_1D | true | false | false | [
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0.28842127323150635,
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2.105344772338867,
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1.340625524520874,
0.13053543865680695,
0.0076555232517421246,
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0.4871762990951538,
0.05015017837285995... | [
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-4.... |
22 | sin(x/8) | SPATIAL_1D | true | false | false | [
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0.015567733906209469,
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0.30151718854904175,
0.5129814743995667,
1.8224095106124878,
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1.7977359294891357,
-0.5061756372451782,... | [
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... |
23 | 0.5*x | SPATIAL_1D | true | false | false | [
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0.5892243385314941,
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0.03687017410993576,
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1.7072514295578003,
0.3297334313392639,
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0.2322399765253067,
0.01126713864505291,
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... | [
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-... |
24 | 9/(x-10) | SPATIAL_1D | true | false | false | [
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0.2004869133234024,
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1.8918015956878662,
1.0118271112442017,
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... | [
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-4.5... |
25 | x | SPATIAL_1D | true | false | false | [
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0.13438424468040466,
0.18126970529556274,
0.1430628001689911,
0.1279904842376709,
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0.03899820148944855,
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-1.289296269416809,... | [
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-3.0018556118011475... |
26 | sin(sin(x)) | SPATIAL_1D | true | false | false | [
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0.4517621397972107,
0.5335415601730347,
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0.6444848775863647,
1.6067173480987549,
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... | [
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-3.8758389949798584... |
27 | cos(exp(x)) | SPATIAL_1D | true | false | false | [
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0.8936548233032227,
0.8848678469657898,
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0.3446839451789856,
0.264396995306015,
1.549946665763855,
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... | [
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... |
28 | -x/6/x | SPATIAL_1D | true | false | false | [
0.41463786363601685,
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0.354117751121521,
0.2740035057067871,
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1.4284472465515137,
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... | [
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29 | exp(-x) | SPATIAL_1D | true | false | false | [
0.8526851534843445,
1.0177133083343506,
1.0500198602676392,
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0.5348461270332336,
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0.18711727857589722,
-1.4089428186416... | [
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... |
30 | exp(sin(x)) | SPATIAL_1D | true | false | false | [
1.3812775611877441,
0.7899171710014343,
0.9702498316764832,
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0.1621967852115631,
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0.2775445878505707,
1.3036617040634155,
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... | [
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... |
31 | x+sin(x) | SPATIAL_1D | true | false | false | [
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1.4855748414993286,
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1.0441445112228394,
0.9168866872787476,
2.01464581489563,
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... | [
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32 | -x^2+x+2 | SPATIAL_1D | true | false | false | [
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0.1401750147342682,
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1.6541701555252075,
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-... | [
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33 | 10*x^2 | SPATIAL_1D | true | false | false | [
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0.008308209478855133,
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-1.64075827598571... | [
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34 | x-10 | SPATIAL_1D | true | false | false | [
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1.2798309326171875,
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-... | [
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... |
35 | -3.2*x | SPATIAL_1D | true | false | false | [
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1.526248812675476,
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-1... | [
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36 | 2.65*x+1.18 | SPATIAL_1D | true | false | false | [
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0.4733318090438843,
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-... | [
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37 | x^2 | SPATIAL_1D | true | false | false | [
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38 | 0.05-122.2*x | SPATIAL_1D | true | false | false | [
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0.9624903798103333,
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1.184474229812622,
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... | [
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39 | log(2*x) | SPATIAL_1D | true | false | false | [
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0.6410523056983948,
-1.1595735549926758... | [
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40 | 7*x | SPATIAL_1D | true | false | false | [
0.13718320429325104,
0.565278172492981,
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0.16809917986392975,
0.9302560687065125,
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-0... | [
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... |
41 | exp(x+2) | SPATIAL_1D | true | false | false | [
0.07467915117740631,
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0.004347487818449736,
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0.14546258747577667,
1.5958207845687866,
-0.84970551729202... | [
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-3... |
42 | x^2-exp(x) | SPATIAL_1D | true | false | false | [
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0.8325255513191223,
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43 | -log(x)+sin(x) | SPATIAL_1D | true | false | false | [
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44 | 0.2*x*(x+10) | SPATIAL_1D | true | false | false | [
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45 | cos(cos(x)) | SPATIAL_1D | true | false | false | [
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46 | x-1 | SPATIAL_1D | true | false | false | [
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47 | 0.2*x*(x+6) | SPATIAL_1D | true | false | false | [
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48 | log(x/3) | SPATIAL_1D | true | false | false | [
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49 | cos(x+6) | SPATIAL_1D | true | false | false | [
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50 | -0.707*x | SPATIAL_1D | true | false | false | [
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51 | exp(9-x) | SPATIAL_1D | true | false | false | [
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52 | 4*x^2 | SPATIAL_1D | true | false | false | [
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53 | exp(2*x) | SPATIAL_1D | true | false | false | [
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54 | cos(x) | SPATIAL_1D | true | false | false | [
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55 | x+1 | SPATIAL_1D | true | false | false | [
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56 | -10*x | SPATIAL_1D | true | false | false | [
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57 | 2*x+7 | SPATIAL_1D | true | false | false | [
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58 | cos(x+1) | SPATIAL_1D | true | false | false | [
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59 | -x^2 | SPATIAL_1D | true | false | false | [
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60 | cos(x+2) | SPATIAL_1D | true | false | false | [
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61 | -0*x | SPATIAL_1D | true | false | false | [
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62 | -9*x^2 | SPATIAL_1D | true | false | false | [
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63 | sin(log(x)) | SPATIAL_1D | true | false | false | [
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64 | x*(1-x) | SPATIAL_1D | true | false | false | [
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65 | 7.5*x | SPATIAL_1D | true | false | false | [
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66 | cos(x)+1.33 | SPATIAL_1D | true | false | false | [
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67 | 0.333*x^2 | SPATIAL_1D | true | false | false | [
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68 | 0.333*cos(x) | SPATIAL_1D | true | false | false | [
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69 | -6*x | SPATIAL_1D | true | false | false | [
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71 | -2/x | SPATIAL_1D | true | false | false | [
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72 | x^2*(-x-9) | SPATIAL_1D | true | false | false | [
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73 | 2-x | SPATIAL_1D | true | false | false | [
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75 | 6*x+4 | SPATIAL_1D | true | false | false | [
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76 | x-5 | SPATIAL_1D | true | false | false | [
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77 | (10-x)*cos(x) | SPATIAL_1D | true | false | false | [
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78 | 10+6/x | SPATIAL_1D | true | false | false | [
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79 | exp(x)+4/x | SPATIAL_1D | true | false | false | [
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80 | exp(-x-3) | SPATIAL_1D | true | false | false | [
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81 | 2.45*x^2 | SPATIAL_1D | true | false | false | [
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82 | x*(-x-1) | SPATIAL_1D | true | false | false | [
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83 | log(4-x) | SPATIAL_1D | true | false | false | [
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84 | x+1 | SPATIAL_1D | true | false | false | [
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End of preview. Expand in Data Studio
SIGS symbolic expression latent corpus
This dataset contains 23,695 grammar-generated symbolic expressions used by the SIGS Grammar-VAE, together with their 32-dimensional latent statistics and variable-based mathematical classes.
Dataset structure
Each row contains:
id: stable row index;expression: symbolic expression generated by the SIGS grammar;math_class: one ofCONSTANT,TEMPORAL_1D,SPATIAL_1D,SPATIAL_2D,SPATIOTEMPORAL_2D, orSPATIOTEMPORAL_3D;has_x,has_t,has_y: variables present in the expression;latent_mu: 32-dimensional encoder mean;latent_log_sigma: 32-dimensional encoder log-scale statistic stored by the original pipeline.
The data is exported to Parquet so it can be inspected with the Hugging Face dataset viewer and loaded without executing pickle code.
Usage
from datasets import load_dataset
dataset = load_dataset("oroikono/SIGS-symbolic-expressions", split="train")
print(dataset[0]["expression"])
print(dataset[0]["math_class"])
Source and generation
Expressions were generated from the context-free grammar in the SIGS repository. The latent statistics were produced by the trained SIGS Grammar-VAE. Mathematical classes are derived deterministically from whether x, y, and t occur as variables.
The included build_dataset.py script converts the original trusted SIGS artifact into a typed Parquet file. Because Python pickle can execute code, do not run the converter on artifacts from an untrusted source.
Intended use
This dataset supports research on grammar-guided representation learning, symbolic regression, and analytical differential-equation solution discovery. Latent proximity does not establish mathematical equivalence or physical validity.
Limitations
- The corpus reflects the fixed SIGS grammar and its expression-generation distribution.
- Variable-based classes describe symbol presence, not equation suitability.
- Expressions may be undefined on parts of a chosen domain.
- Users must independently verify PDE residuals, domains, and boundary conditions.
Related resources
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Models trained or fine-tuned on oroikono/SIGS-symbolic-expressions