Data, Code, and the supplementary document for the paper, Neural Reasoning for Sure through Constructing Explainable Models. AAAI-25.
$ git clone https://github.com/gnodisnait/HSphNN.git
$ cd HSphNN
Paremeters are set in params.json;
type following command to unzip hsphnn_runs.zip and move the data directory
$ unzip hsphnn_runs.zip
After that, move the hsphnn_runs directory under the directory data as follows.
--
|-/data/hsphnn_runs/
|-/HSphNN/
HSphNN achieves the symbolic-level of syllogistic reasoning with 1 epoch
$ python eval_exp1.py
The results are saved in the following files.
|--data
|--hsphnn_runs
|--ValidSyllogism_DIM2R1InitLoc0
|--ValidSyllogism_DIM3R1InitLoc0
|--ValidSyllogism_DIM15R1InitLoc0
|--ValidSyllogism_DIM30R1InitLoc0
|--ValidSyllogism_DIM100R1InitLoc0
|--ValidSyllogism_DIM200R1InitLoc0
|--ValidSyllogism_DIM1000R1InitLoc0
|--ValidSyllogism_DIM2000R1InitLoc0
|--ValidSyllogism_DIM3000R1InitLoc0
DIM3000 means that spheres have the 3000 dimensions.
R1 means that spheres are initialised with their centres being located at the surface of a sphere with the radius of 1.
InitLoc0 means that spheres are initialised as being co-incided.
When spheres are initialised being coincided, HSphNN successfully identified all 24 valid syllogistic reasoning in one epoch. The dimension of sphere ranges from 2 to 3000.
+---------------------+-------+-----------------------------+--------------+
| Dimension of HSphere | epoch | #Identified Valid Reasoning | Total Number |
+---------------------+-------+-----------------------------+--------------+
| 2 | 1 | 24 | 24 |
| 3 | 1 | 24 | 24 |
| 15 | 1 | 24 | 24 |
| 30 | 1 | 24 | 24 |
| 100 | 1 | 24 | 24 |
| 200 | 1 | 24 | 24 |
| 1000 | 1 | 24 | 24 |
| 2000 | 1 | 24 | 24 |
| 3000 | 1 | 24 | 24 |
+---------------------+-------+-----------------------------+--------------+
Experiments show that it took HSphNN more time to determine valid syllogistic reasoning than to determine an invalid one.
+-------------------+---------------------+----------------------------+---------+--------+----------+
| type of syllogism | number of syllogism | max time cost (in seconds) | min - | mean - | median - |
+-------------------+---------------------+----------------------------+---------+--------+----------+
| valid syllogism | 216 | 67.55 | 2.81 | 17.71 | 12.09 |
| invalid syllogism | 2088 | 66.29 | 0.00069 | 3.46 | 2.41 |
| all syllogism | 2304 | 67.55 | 0.00069 | 4.80 | 2.52 |
+-------------------+---------------------+----------------------------+---------+--------+----------+
HSphNN is scalable with the increase of the dimension.
create a config directory in the HSphNN directory, and create the openai_key.txt file to save your API key of openai.
--
|-/data/hsphnn_runs/
|-/HSphNN/
|--/config/
|--openai_key.txt
then, type
$ python eval_exp2.py
****************************************************************************************************
using GPT-3.5-turbo, maximum 2 time feedback
../data/hsphnn_runs/ChatGPT3tb_short2_SphNN_words/
_words at the end of the directory name means that syllogistic statements use meaningful words, such as all Greeks are human.
The following table is the performance of ChatGPT gpt-3.5-turbo without the feedback from HSphNN.
no feedback
+---------------+----------+----------+----------+----------------+-------+------------------------+----------------------+
| #Correct+Expl | #HALLU 0 | #HALLU 1 | #HALLU 2 | #Inorrect+Expl | #Rest | #Ratio of Correct+Expl | #Irrationality ratio |
+---------------+----------+----------+----------+----------------+-------+------------------------+----------------------+
| 103 | 58 | 41 | 11 | 15 | 28 | 0.40234375 | 0.48828125 |
+---------------+----------+----------+----------+----------------+-------+------------------------+----------------------+
The following table is the performance of ChatGPT gpt-3.5-turbo with maximum two round of the feedback from HSphNN.
with maximum 2 times feedback
+---------------+----------+----------+----------+----------------+-------+------------------------+----------------------+
| #Correct+Expl | #HALLU 0 | #HALLU 1 | #HALLU 2 | #Inorrect+Expl | #Rest | #Ratio of Correct+Expl | #Irrationality ratio |
+---------------+----------+----------+----------+----------------+-------+------------------------+----------------------+
| 128 | 49 | 18 | 6 | 6 | 49 | 0.5 | 0.30859375 |
+---------------+----------+----------+----------+----------------+-------+------------------------+----------------------+
The following table lists the number of correct responses of ChatGPT gpt-3.5-turbo at the i-th feedback.
Number of correct decision and correct explanation vs. the number of feedbacks
+----------------------------------------------+-----+----+---+
| #Num of feedback | 0 | 1 | 2 |
+----------------------------------------------+-----+----+---+
| #Tasks with correct decision and explanation | 103 | 17 | 8 |
+----------------------------------------------+-----+----+---+
../data/hsphnn_runs/ChatGPT3tb_short2_SphNN_symbol/
_symbol at the end of the directory name means that syllogistic statements use simple symbols, such as all S are M0.
no feedback
+---------------+----------+----------+----------+----------------+-------+------------------------+----------------------+
| #Correct+Expl | #HALLU 0 | #HALLU 1 | #HALLU 2 | #Inorrect+Expl | #Rest | #Ratio of Correct+Expl | #Irrationality ratio |
+---------------+----------+----------+----------+----------------+-------+------------------------+----------------------+
| 120 | 0 | 73 | 33 | 14 | 16 | 0.46875 | 0.46875 |
+---------------+----------+----------+----------+----------------+-------+------------------------+----------------------+
with maximum 2 times feedback
+---------------+----------+----------+----------+----------------+-------+------------------------+----------------------+
| #Correct+Expl | #HALLU 0 | #HALLU 1 | #HALLU 2 | #Inorrect+Expl | #Rest | #Ratio of Correct+Expl | #Irrationality ratio |
+---------------+----------+----------+----------+----------------+-------+------------------------+----------------------+
| 151 | 2 | 30 | 19 | 4 | 50 | 0.58984375 | 0.21484375 |
+---------------+----------+----------+----------+----------------+-------+------------------------+----------------------+
Number of correct decision and correct explanation vs. the number of feedbacks
+----------------------------------------------+-----+----+----+
| #Num of feedback | 0 | 1 | 2 |
+----------------------------------------------+-----+----+----+
| #Tasks with correct decision and explanation | 120 | 17 | 14 |
+----------------------------------------------+-----+----+----+
../data/hsphnn_runs/ChatGPT3tb_short2_SphNN_random/
_random at the end of the directory name means that syllogistic statements use random symbols, such as All HWsF1eq9 are hONvNxop.
no feedback
+---------------+----------+----------+----------+----------------+-------+------------------------+----------------------+
| #Correct+Expl | #HALLU 0 | #HALLU 1 | #HALLU 2 | #Inorrect+Expl | #Rest | #Ratio of Correct+Expl | #Irrationality ratio |
+---------------+----------+----------+----------+----------------+-------+------------------------+----------------------+
| 106 | 1 | 45 | 38 | 17 | 49 | 0.4140625 | 0.39453125 |
+---------------+----------+----------+----------+----------------+-------+------------------------+----------------------+
with maximum 2 times feedback
+---------------+----------+----------+----------+----------------+-------+------------------------+----------------------+
| #Correct+Expl | #HALLU 0 | #HALLU 1 | #HALLU 2 | #Inorrect+Expl | #Rest | #Ratio of Correct+Expl | #Irrationality ratio |
+---------------+----------+----------+----------+----------------+-------+------------------------+----------------------+
| 138 | 4 | 20 | 19 | 1 | 74 | 0.5390625 | 0.171875 |
+---------------+----------+----------+----------+----------------+-------+------------------------+----------------------+
Number of correct decision and correct explanation vs. the number of feedbacks
+----------------------------------------------+-----+----+----+
| #Num of feedback | 0 | 1 | 2 |
+----------------------------------------------+-----+----+----+
| #Tasks with correct decision and explanation | 106 | 20 | 12 |
+----------------------------------------------+-----+----+----+
The following tables were the performances of ChatGPT-4o.
../data/hsphnn_runs/ChatGPT4o_short2_SphNN_words/
no feedback
+---------------+----------+----------+----------+----------------+-------+------------------------+----------------------+
| #Correct+Expl | #HALLU 0 | #HALLU 1 | #HALLU 2 | #Inorrect+Expl | #Rest | #Ratio of Correct+Expl | #Irrationality ratio |
+---------------+----------+----------+----------+----------------+-------+------------------------+----------------------+
| 191 | 15 | 8 | 20 | 17 | 5 | 0.74609375 | 0.234375 |
+---------------+----------+----------+----------+----------------+-------+------------------------+----------------------+
with maximum 2 times feedback
+---------------+----------+----------+----------+----------------+-------+------------------------+----------------------+
| #Correct+Expl | #HALLU 0 | #HALLU 1 | #HALLU 2 | #Inorrect+Expl | #Rest | #Ratio of Correct+Expl | #Irrationality ratio |
+---------------+----------+----------+----------+----------------+-------+------------------------+----------------------+
| 194 | 20 | 10 | 10 | 17 | 5 | 0.7578125 | 0.22265625 |
+---------------+----------+----------+----------+----------------+-------+------------------------+----------------------+
Number of correct decision and correct explanation vs. the number of feedbacks
+----------------------------------------------+-----+---+---+
| #Num of feedback | 0 | 1 | 2 |
+----------------------------------------------+-----+---+---+
| #Tasks with correct decision and explanation | 191 | 3 | 0 |
+----------------------------------------------+-----+---+---+
../data/hsphnn_runs/ChatGPT4o_short2_SphNN_symbol/
no feedback
+---------------+----------+----------+----------+----------------+-------+------------------------+----------------------+
| #Correct+Expl | #HALLU 0 | #HALLU 1 | #HALLU 2 | #Inorrect+Expl | #Rest | #Ratio of Correct+Expl | #Irrationality ratio |
+---------------+----------+----------+----------+----------------+-------+------------------------+----------------------+
| 196 | 3 | 13 | 20 | 19 | 5 | 0.765625 | 0.21484375 |
+---------------+----------+----------+----------+----------------+-------+------------------------+----------------------+
with maximum 2 times feedback
+---------------+----------+----------+----------+----------------+-------+------------------------+----------------------+
| #Correct+Expl | #HALLU 0 | #HALLU 1 | #HALLU 2 | #Inorrect+Expl | #Rest | #Ratio of Correct+Expl | #Irrationality ratio |
+---------------+----------+----------+----------+----------------+-------+------------------------+----------------------+
| 202 | 8 | 13 | 9 | 23 | 1 | 0.7890625 | 0.20703125 |
+---------------+----------+----------+----------+----------------+-------+------------------------+----------------------+
Number of correct decision and correct explanation vs. the number of feedbacks
+----------------------------------------------+-----+---+---+
| #Num of feedback | 0 | 1 | 2 |
+----------------------------------------------+-----+---+---+
| #Tasks with correct decision and explanation | 196 | 5 | 1 |
+----------------------------------------------+-----+---+---+
../data/hsphnn_runs/ChatGPT4o_short2_SphNN_random/
no feedback
+---------------+----------+----------+----------+----------------+-------+------------------------+----------------------+
| #Correct+Expl | #HALLU 0 | #HALLU 1 | #HALLU 2 | #Inorrect+Expl | #Rest | #Ratio of Correct+Expl | #Irrationality ratio |
+---------------+----------+----------+----------+----------------+-------+------------------------+----------------------+
| 211 | 1 | 4 | 16 | 18 | 6 | 0.82421875 | 0.15234375 |
+---------------+----------+----------+----------+----------------+-------+------------------------+----------------------+
with maximum 2 times feedback
+---------------+----------+----------+----------+----------------+-------+------------------------+----------------------+
| #Correct+Expl | #HALLU 0 | #HALLU 1 | #HALLU 2 | #Inorrect+Expl | #Rest | #Ratio of Correct+Expl | #Irrationality ratio |
+---------------+----------+----------+----------+----------------+-------+------------------------+----------------------+
| 217 | 4 | 2 | 9 | 18 | 6 | 0.84765625 | 0.12890625 |
+---------------+----------+----------+----------+----------------+-------+------------------------+----------------------+
Number of correct decision and correct explanation vs. the number of feedbacks
+----------------------------------------------+-----+---+---+
| #Num of feedback | 0 | 1 | 2 |
+----------------------------------------------+-----+---+---+
| #Tasks with correct decision and explanation | 211 | 4 | 2 |
+----------------------------------------------+-----+---+---+
****************************************************************************************************
We increase the maximum number of feedback to 10 round and found that ChatGPT was not sensitive to the repetition.
no feedback
+---------------+----------+----------+----------+----------------+-------+------------------------+----------------------+
| #Correct+Expl | #HALLU 0 | #HALLU 1 | #HALLU 2 | #Inorrect+Expl | #Rest | #Ratio of Correct+Expl | #Irrationality ratio |
+---------------+----------+----------+----------+----------------+-------+------------------------+----------------------+
| 211 | 0 | 6 | 17 | 17 | 5 | 0.82421875 | 0.15625 |
+---------------+----------+----------+----------+----------------+-------+------------------------+----------------------+
with maximum 10 times feedback
+---------------+----------+----------+----------+----------------+-------+------------------------+----------------------+
| #Correct+Expl | #HALLU 0 | #HALLU 1 | #HALLU 2 | #Inorrect+Expl | #Rest | #Ratio of Correct+Expl | #Irrationality ratio |
+---------------+----------+----------+----------+----------------+-------+------------------------+----------------------+
| 218 | 6 | 6 | 4 | 18 | 4 | 0.8515625 | 0.1328125 |
+---------------+----------+----------+----------+----------------+-------+------------------------+----------------------+
Number of correct decision and correct explanation vs. the number of feedbacks
+----------------------------------------------+-----+---+---+---+---+---+---+---+---+---+----+
| #Num of feedback | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
+----------------------------------------------+-----+---+---+---+---+---+---+---+---+---+----+
| #Tasks with correct decision and explanation | 211 | 5 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 |
+----------------------------------------------+-----+---+---+---+---+---+---+---+---+---+----+
Decide the satisfiability of the three statements (log_data_33.json):
all S are M0. no M0 are P. some S are not P.
(i) HSphNN decides it satisiable.
(ii) ChatGPT (gpt-3.5-turbo) decides it satisiable and gives an explanation:
(circle S, inside, circle M0)
(circle M0, outside, circle P)
(circle S, outside, circle P)
Here, it is correct that all S are M0 can be explained as (circle S, inside, circle M0) and
no M0 are P can be explained as (circle M0, outside, circle P) and some S are not P can be explained as (circle S, outside, circle P).
(iii) HSphNN tries to construct a model for ChatGPT's explanation and finds the explanation is satisfiable.
(iv) Therefore, ChatGPT (gpt-3.5-turbo) gives a correct decision and correct explanations.
LLM may make a correct decisioin and gives a partial explanation that cannot lead to any conclusion.
Decide the satisfiability of the three statements (log_data_64.json):
some S are not M0. all M0 are P. all S are P.
(i) HSphNN decides it satisiable.
(ii) ChatGPT (gpt-3.5-turbo) decides it satisiable and gives a partial explanation:
(circle S, inside, circle P)
(circle P, inside, circle M0)
(circle M0, inside, circle P)
In ChatGPT's explanation, the relation between S and M0 is missing.
(iii) Therefore, ChatGPT (gpt-3.5-turbo) hallucinated a correct decision based on a partial explanation.
Note: the relation (circle P, inside, circle M0)and (circle M0, inside, circle P) is not contradictory. The two relations will follow that M0 and P are coincided.
LLM may make a correct decisioin and gives an incorrect explanation for at least one single statement.
Decide the satisfiability of the three statements (log_data_168.json):
no M0 are S. no M0 are P. all S are P.
(i) HSphNN decides it satisiable.
(ii) ChatGPT (gpt-3.5-turbo) decides it satisiable and gives an explanation:
(circle P, inside, circle M0)
(circle M0, outside, circle S)
(circle S, inside, circle P)
Here, ChatGPT mistakenly interpreted no M0 are P as (circle P, inside, circle M0).
(iii) Therefore, ChatGPT (gpt-3.5-turbo) hallucinated a correct decision based on an incorrect explanation.
LLM may make a correct decisioin and gives correct explanation for each single statement, but the whole explanation is incorrect.
Decide the satisfiability of the three statements:
some M0 are not S. all M0 are P. some S are not P.
(i) HSphNN decides it satisiable.
(ii) ChatGPT (gpt-3.5-turbo) decides it satisiable and gives an explanation:
(circle M0, overlaps, circle S)
(circle M0, inside, circle P)
(circle S, outside, circle P)
Here, it is correct that some M0 are not S can be explained as (circle M0, overlaps, circle S) and
all M0 are P can be explained as (circle M0, inside, circle P) and some S are not P can be explained as (circle S, outside, circle P).
(iii) HSphNN tries to construct a model for ChatGPT's explanation and finds the explanation is unsatisfiable.
(iv) Therefore, ChatGPT (gpt-3.5-turbo) gives a correct decision and correct explanation for each statement, but with an incorrect explanation.
Decide the satisfiability of the three statements:
all S are M0. no M0 are P. all S are P.
(i) HSphNN decides it unsatisiable.
(ii) ChatGPT (gpt-3.5-turbo) decides it satisiable and gives an explanation:
(circle S, inside, circle M0)
(circle M0, outside, circle P)
(circle S, inside, circle P)
The explanation is correct for each single statement and for the whole.
(iii) Therefore, ChatGPT (gpt-3.5-turbo) gives an incorrect decision with a correct explanation.
Decide the satisfiability of the three statements (log_data_24.json):
all M0 are S. some M0 are not P. all S are P.
(i) HSphNN decides it unsatisiable.
(ii) ChatGPT (gpt-3.5-turbo) decides it satisiable and gives an explanation:
(circle M0, inside, circle S)
(circle S, overlaps, circle P)
(circle M0, inside, circle P)
Here, it is not correct that all S are P can be explained as (circle S, overlaps, circle P).
(iii) Therefore, ChatGPT (gpt-3.5-turbo) gives an incorrect decision with an incorrect explanation.
$ conda create --name hsphnn python=3.9
$ conda activate hsphnn
$ conda install pytorch::pytorch torchvision torchaudio -c pytorch
$ conda install conda-forge::openai==0.28
$ conda install conda-forge::matplotlib
$ conda install conda-forge::tensorboard
$ conda install conda-forge::prettytable
$ ./experiment1.sh
$ ./experiment2.sh
This repository can be used for non-commercial purposes only. Contact one of the three authors of the paper below, if you are interested in a commercial license.
@inproceedings{djl2025,
author = {Tiansi Dong and Mateja Jamnik and Pietro Liò},
title = {Neural Reasoning for Sure through Constructing Explainable Models},
booktitle = {AAAI},
year = {2025},
}