=Paper=
{{Paper
|id=Vol-3900/Paper11
|storemode=property
|title=Computational Creativity by Heuristic Search and Machine Learning
|pdfUrl=https://ceur-ws.org/Vol-3900/Paper11.pdf
|volume=Vol-3900
|authors=Amit Konar,Sayantani Ghosh
|dblpUrl=https://dblp.org/rec/conf/dosier/KonarG24
}}
==Computational Creativity by Heuristic Search and Machine Learning ==
https://ceur-ws.org/Vol-3900/Paper11.pdf
Computational Creativity by Heuristic Search and
Machine Learning
Amit Konar, Sayantani Ghosh
Artificial Intelligence Laboratory, Electronics and Telecommunication Engineering Department, Jadavpur University,
India
Abstract
Computational creativity refers to synthesis of human-like creativity on machines. This paper aims
at synthesizing computational creativity by taking up an interesting problem to develop chapter-end
problems of mathematics and physics using Artificial Intelligence techniques. The methodology employed
to address the problem includes traditional random search and heuristic search, and modern techniques
including Generative Adversarial Networks and Large Language Models. The true spirit of these models
is to autonomously enhance diversity of problems by random exploration, structured search and learning.
In addition, the paper demonstrates the scope of inductive learning to learn problem-solving from
analogous problems, and to employ it to solve or generate similar problems. A set of metrics is proposed
to compare the relative merits of the proposed and existing algorithms with a view to a have a uniform
framework of comparison for the present and future research.
Keywords
Computational creativity, diversity, problem generation, scientific domain
1. Introduction
Computational creativity (CC) [1, 2] deals with artificial modality of synthesis of creativity
by intelligent computational models. It has wide scope in diverse disciplines of knowledge,
covering linguistics, music, poetry, and even hard science like physics and mathematics. With
the advent of Large Language Models (LLMs) [3] the scope of CC has enhanced significantly as
scientific and literary ideas now can be presented in a human-like fashion. For instance, the
poems of Lord Byron, which convey strong emotion of love, have now been captured by modern
LLM, such as ChatGPT-3.5 [4]. It is indeed important to note that the re-discovered narration of
ChatGPT-3.5, which writes: "She walks the earth with grace and pride, a beauty that cannot be
denied...", conveys a more realistic thoughts of a lover that a machine could hardly generate in
the history of science. The above example demonstrates the computational power of LLMs in
perceiving real-world thoughts and its representation in a natural language. Besides the power of
perception and linguistic skill, CC also has a great role to play in synthesis of scientific creativity,
including development of new mathematical theory [5, 6], raising interesting problems in a
selected scientific domain [7], and many others.
The 2024 Sixth Doctoral Symposium on Intelligence Enabled Research (DoSIER 2024), November 28–29, 2024, Jalpaiguri,
India
$ konaramit@yahoo.co.in (A. Konar); sayantani.sonrisa25@gmail.com (S. Ghosh)
0000-0002-9474-5956 (A. Konar); 0000-0002-3156-9772 (S. Ghosh)
© 2025 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR
ceur-ws.org
Workshop ISSN 1613-0073
Proceedings
The present work focuses on designing innovative approaches to generate chapter-end
problems in science, particularly in mathematics and physics, by leveraging both classical and
modern AI techniques. Classical methods for fostering creativity include random search and
heuristic search while modern techniques involve Generative Adversarial Networks (GANs) [8]
LLMs. The study also explores the potential of inductive learning for developing computational
creative systems by drawing insights from analogous problems and applying them to solve
or generate similar ones. The methodologies for problem synthesis and problem-solving are
demonstrated through illustrative examples. Furthermore, a set of metrics is proposed to
evaluate and compare the effectiveness of the proposed generative algorithms against existing
state-of-the-art (SOTA) techniques. While this work provides a foundation for achieving
scientific creativity through machines, it acknowledges the limitations of the current models
and emphasizes the need for future advancements in integrating contextual and environmental
understanding to enhance the diversity and/or quality of generated problems, making them
comparable to those created by humans.
The rest of the paper is organized as follows. Section 2 covers computational creativity using
random search techniques, while Section 3 focuses on heuristic-guided algorithms for generating
trigonometric identity problems. Section 4 explores inductive learning in mathematical creativity,
and Sections 5 and 6 discuss scientific problem generation using GANs and LLMs. Section 7
presents the performance analysis of the proposed algorithms in comparison to SOTA methods.
Section 8 addresses limitations and future directions, and Section 9 concludes the paper.
2. Creativity by Random Search and Experiments
Random experimentation refers to the process of conducting experiments in which certain
variables or conditions are assigned randomly. This approach often leads to unexpected dis-
coveries by enabling researchers to explore outcomes without preconceived notions or biases,
fostering an environment of genuine exploration and creativity. History demonstrates that
random experimentation can yield groundbreaking results, serving as a quintessential example
of innovation in science.
Many revolutionary breakthroughs have stemmed from the process of random experimen-
tation, where unexpected outcomes have paved the way for transformative insights [9]. For
instance, Faraday’s Law of Electromagnetic Induction resulted from simple experimental setups
that, through systematic and open-ended exploration, fundamentally reshaped our understand-
ing of electromagnetism. Similarly, the discovery of carbon’s atomic structure and its various
allotropes including graphite, diamond, and graphene, underscores how randomness and curios-
ity in experimental approaches can lead to groundbreaking findings. Another striking example
is the discovery of DNA’s double-helix structure by Watson and Crick. Their work was guided
by experimental data and serendipitous results, where seemingly random but insightful obser-
vations played a crucial role in unraveling the mysteries of genetic inheritance, revolutionizing
biology in the process.
To demonstrate the power of random search, let us instantiate the simple identity, often
taught in middle schools:
(𝑎 − 𝑏)2 = 𝑎2 + 𝑏2 − 2𝑎𝑏 (1)
√ √
where 𝑎 and 𝑏 are real numbers. Let us randomly select 𝑎 = 𝑥 and 𝑏 = 𝑦. The above
substitution yields,
√ √ √
( 𝑥 − 𝑦)2 = 𝑥 + 𝑦 − 2 𝑥𝑦 ≥ 0, as a whole-square of a real number is always positive or
zero.
𝑥+𝑦 √
⇒ ≥ 𝑥𝑦 (2)
2
⇒ arithmetic mean of 2 numbers: 𝑥 and 𝑦 ≥ geometric mean of the same numbers.
The above result indeed is an innovative outcome that unexpectedly follows as a result of
random substitution for 𝑎 and 𝑏. Now let us substitute 𝑎 = 𝑟𝑒𝑗𝜐 , 𝑏 = 𝑟𝑒−𝑗𝜐 in (1) just as a
random selection. The substitution yields:
(𝑟𝑒𝑗𝜃 − 𝑟𝑒−𝑗𝜃 )2 = 𝑟2 𝑒2𝑗𝜃 + 𝑟2 𝑒−2𝑗𝜃 − 2𝑟2 𝑒𝑗𝜃 𝑒−𝑗𝜃 (3)
⇒ (2𝑗𝑟 sin 𝜃)2 = 𝑟2 (2 cos 2𝜃 − 2)
⇒ −4𝑟2 sin2 𝜃 = 2𝑟2 (cos 2𝜃 − 1)
⇒ cos 2𝜃 = 1 − 2 sin2 𝜃 (4)
It is noteworthy that the expression (4) is an important identity in trigonometry. However,
its sudden appearance makes us rethink that random substitution may give rise to interesting
and often unexpected results. Can we enhance the random search by adding structures to the
search process? This will be undertaken in our next problem by exploring search and pruning
unwanted search space by a heuristic algorithm. To guide the exploration process, we add a
new term: diversity cost in the estimation of the diversity of a generated trial solution with
respect to an initial trial solution, called root node in a search-tree.
3. Heuristic Search Approach to Computational Creativity
Consider the problem of generating trigonometric identities as the chapter-end problems of
a first learner of trigonometry. Here, an approach similar to A* algorithm [10] is proposed to
handle the afore-said identity generation problem. The rules utilized for generating identities
of trigonometric first course are provided in Table 1. We here try to maximize 𝐷(𝑛) − 𝑔(𝑛),
where 𝐷(𝑛) is the diversity cost of node 𝑛 with respect to the root node and 𝑔(𝑛) is the cost of
generation with respect to the root node. Diversity cost between a parent and child node = no.
of mismatched symbols in the left of the parent and child node + no. of mismatched symbols
in the right of the parent and child node. Diversity cost of a node 𝑛 = diversity cost of all the
nodes lying between the root node and the node 𝑛.
3.1. Computation of Diversity Cost
The diversity cost of a node 𝑞 with respect to its parent node 𝑝 is evaluated by (5)
𝑑(𝑞) = |𝐿𝑇𝑝 − 𝐿𝑇𝑞 | + |𝑅𝑇𝑝 − 𝑅𝑇𝑞 | (5)
Table 1
Some rules utilized for automatic trigonometric identity generation
No. Rules
R.1 𝑠𝑖𝑛 𝑥 + 𝑐𝑜𝑠2 𝑥 = 1
2
R.2 𝑠𝑒𝑐2 𝑥 − 𝑡𝑎𝑛2 𝑥 = 1
R.3 𝑐𝑜𝑠𝑒𝑐2 𝑥 − 𝑐𝑜𝑡2 𝑥 = 1
R.4 𝑠𝑖𝑛𝑥 = 1/𝑐𝑜𝑠𝑒𝑐𝑥
R.5 𝑐𝑜𝑠𝑥 = 1/𝑠𝑒𝑐𝑥
where,
𝐿𝑇𝑝 = set of terms (operands) in the left side of node 𝑝.
𝑅𝑇𝑝 = set of terms (operands) in the right side of node 𝑝. Similarly, 𝐿𝑇𝑞 and 𝑅𝑇𝑞 represent
the left and right hand terms of the node 𝑞 respectively. |𝐶| represents the number of elements
in a given set 𝐶. The diversity cost of the root node 𝑑(𝑟) is always 0. Now if the path from the
root node 𝑟 to node 𝑞 covers a sequence of nodes 𝑛1 , 𝑛2 , ...., 𝑛𝑙 then the diversity cost of node
𝑞 with respect to root is evaluated by (6)
𝑙
∑︁
𝐷(𝑞) = 𝑑(𝑞) + 𝑑(𝑛𝑖 ) (6)
𝑖=1
Let us now illustrate the computation of diversity cost of a node from the root node. Let the
node 𝑞 be the identity 1/𝑐𝑜𝑡𝑥 = 𝑠𝑖𝑛𝑥/𝑐𝑜𝑠𝑥 , its parent node 𝑝 be the identity 𝑡𝑎𝑛𝑥 = 𝑠𝑖𝑛𝑥/𝑐𝑜𝑠𝑥
and the root node 𝑟 is 1=1. Here, there is no mismatch between the right sides of the parent
and the current node i.e., 𝑅𝑇𝑝 ={𝑠𝑖𝑛𝑥, 𝑐𝑜𝑠𝑥}, 𝑅𝑇𝑞 ={𝑠𝑖𝑛𝑥, 𝑐𝑜𝑠𝑥} and thus, |𝑅𝑇𝑝 ˘𝑅𝑇𝑞 | = 0. But
there exists 2 mismatches in the left hand sides of the parent and child node, i.e., 𝐿𝑇𝑝 = {𝑡𝑎𝑛𝑥},
𝐿𝑇𝑞 ={1,𝑐𝑜𝑡𝑥} and so, |𝐿𝑇𝑝 ˘𝐿𝑇𝑞 | = 2. Thus, 𝑑(𝑞) = 0 + 2 = 2. Since, 𝑑(𝑟) = 0 and so
𝐷(𝑞) = 0 + 2 = 2.
3.2. Algorithm for Heuristic Guided Search
The algorithm for the automatic generation of trigonometric identifies utilizing the heuristic
guided search is outlined in Algorithm 1. For the present context, the terminating condition is
imposed on number of selection of nodes for expansion. An illustration of the heuristic guided
search tree is provided in Figure 1 for a branching factor of 2 and pre-defined search depth of 3.
The value of the cost function (i.e., 𝐷(𝑛) − 𝑔(𝑛)) is provided in {·} beside each generated node.
4. Inductive Learning Approach to Computational Creativity
An alternative modality of problem generation is through inductive learning [11, 12]. Here,
the program learns a theme from examples and the learnt knowledge is utilized to develop
a new problem. As a simple example, suppose a program learns the rule: um → a to
transform the plural form: bacteria from the singular form: bacterium, and employs the
derived knowledge to compute the plural form of penicillium. Similar examples hold for
Algorithm 1 : Heuristic guided search algorithm for automatic trigonometric identity
generation
1. Initialize a list 𝐿 with a start-up element 𝑒: 1=1.
2. While terminating condition is not reached do
Begin
a) Expand 𝑒 by using the rules 1 to 5 𝑘 times randomly to generate 𝑘 offspring of 𝑒,
called 𝑛𝑖 , 𝑖=1 to 𝑘.
b) Add them in descending order of their 𝐷(𝑛𝑖 ) − 𝑔(𝑛𝑖 ), 𝑖=1 to 𝑘. Delete 𝑒 from list.
c) Rename the first element of the list as 𝑒.
End-While
Figure 1: Illustration of the heuristic guided search tree for trigonometric identity generation for a
branching factor of 2 and user-defined depth of 3.
learning the knowledge us → i for transformation of the singular form alumnus to alumni,
and uses it to derive fungi from its singular form fungus. Naturally, the question arises:
can we utilize similar inductive knowledge for the generation of new problems? The an-
swer to this question is illustrated though an example from integration problems in mathematics.
Suppose a machine learns some examples of solving integrals which include:
Example ∫︀1: 𝑥1 𝑑𝑥 = ln(𝑥) + 𝑐
∫︀
Example 2: 𝑥22𝑥+1 𝑑𝑥 = ln(𝑥2 + 1) + 𝑐
If the machine can accidently identify that the generalization of the above integrals is
Table 2
Table for 𝑓 (𝑛) and 𝑓 ′ (𝑛)
f (n) f ′ (n)
𝑓1 (𝑛) + 𝑓2 (𝑛) 𝑓1′ (𝑛) + 𝑓2′ (𝑛)
𝑥𝑛 , 𝑛 ≥ 1 𝑛𝑥𝑛
𝑓 ′ (𝑥)
∫︁
𝑑𝑥 = ln 𝑓 (𝑥) + 𝑐 (7)
𝑓 (𝑥)
which can be learnt by random experiments with known tables of 𝑓 (𝑛) and 𝑓 ′ (𝑛) (Table 2),
then using the acquired knowledge (7), the machine can generate several problems on integrals
using (7) such as
∫︁
2𝑥 + 5
2
𝑑𝑥 = ln(𝑥2 + 5𝑥 + 2) + 𝑐 (8)
𝑥 + 5𝑥 + 2
5. Computational Creativity by Generative Adversarial Network
A GAN [8] is a deep learning framework consisting of two primary components: a generator
and a discriminator. These components work in a competitive setup to enable the creation of
realistic outputs. The generator is tasked with producing synthetic data, while the discriminator
acts as a classifier that evaluates the authenticity of the generated data. The competition arises
as the generator simultaneously tries to fool the discriminator by improving the quality of its
outputs. This adversarial process continues until the generator produces outputs so realistic that
the discriminator fails to identify them as fake. The LeakGAN (Generative Adversarial Network
with leaked Information) [2] is an advanced variant of GAN designed for text generation, where,
in addition to the adversarial setup, the discriminator leaks high-level features of partially
generated sequences to guide the generator, improving coherence and diversity in the generated
text outputs. This feedback mechanism allows LeakGAN to produce more structured and
meaningful sequences compared to standard GANs. The present work utilizes the LeakGAN
framework for generating trigonometric identity problems.
In LeakGAN, the discriminator, implemented as a Convolutional Neural Network (CNN), and the
generator, which employs Long Short-Term Memory (LSTM) units, are initially pre-trained on
a dataset of mathematical identities sourced from textbooks. During the pre-training phase, all
identity problems are tokenized and converted into embedding vectors, as detailed in Appendix
[13].
The generator consists of two LSTM modules: the manager and the worker. The generation
process begins with the selection of a random term, represented as an embedding vector, which
serves as the starting point for generating a new identity. This vector is first passed to the
discriminator, which produces a pooled vector. This pooled vector is then leaked to the manager
module. The manager (LSTM) generates a goal vector that predicts the next term being an
operand or an operator. This goal vector is concatenated with the initial vector and fed into the
Figure 2: Block diagram of LeakGAN for generating trigonometric identities
Figure 3: Correctness checking of newly generated identity by SymPy module
worker module, which comprises an LSTM and a Multi-Layer Perceptron (MLP). The worker
predicts the next term based on the above concatenated input. This iterative process continues
until the complete identity is generated. The detailed procedure for generating new identities
is described in Algorithm 2 and its schematic view is shown in Figure 2. Additionally, an
exemplar problem is included in Appendix [13] to demonstrate the generation process due to
space limitations.
Once an identity is generated, it is passed to the discriminator to classify it as either real or fake.
Identities classified as real are further evaluated for mathematical correctness using the SymPy
module (a Python library for equation solving) as shown in Figure 3. If an identity is verified as
correct, it is considered for inclusion as a chapter-end exercise; otherwise, it is discarded.
6. Large Language Models for Scientific Problem Generation
The Blackboard approach in AI [14] offers an effective framework for generating physics
problems by integrating symbolic reasoning with the capabilities of large language models
(LLMs). At the heart of this system is the blackboard manager. The blackboard serves as a
shared workspace (see Figure 4) that displays the initial variables, such as final velocity 𝑣, time
𝑡, and initial velocity 𝑢, making this information accessible to various agents for computation
and problem generation via LLMs. Suppose the blackboard manager displays the values of 𝑢, 𝑣,
Algorithm 2 : Generation of identity problems by LeakGAN
1. Initialize any random embedded vector as the start-up element.
2. While entire identity is not generated do
Begin
a) Transfer the current embedded vector to the discriminator that performs convolution
and pooling upon this vector.
b) Transfer the pooled vector to the manager module to generate a goal vector.
c) Concatenate the goal vector and the current embedded vector and feed to the worker
module to predict the next vector.
d) Append the next vector to the current vector. Also, update the current vector with
the next vector.
End-While
3. Return the completely generated trigonometric identity problem by decoding its embedded
vector.
Figure 4: Illustration of Blackboard approach for problem generation
and 𝑡. These values are passed to Agent 1, which calculates the value of acceleration 𝑎. Next,
this agent transfers the value of 𝑎 back to the blackboard manager. The blackboard manager
then displays the value of a along with 𝑢, 𝑣, and 𝑡. The values of 𝑢, 𝑣, and 𝑎 are then taken up
by Agent 2, which uses them to calculate the value of 𝑠.
The detailed procedure of this approach is provided in Algorithm 3. When 𝑢 = 5𝑚/𝑠, 𝑣 =
10𝑚/𝑠, 𝑡 = 5𝑠, find 𝑎 and 𝑠 is represented by LLM as: “A ball is thrown with an initial velocity
𝑢 = 5𝑚/𝑠 downwards. When the ball reaches a distance 𝑠, the velocity becomes 𝑣 = 10𝑚/𝑠.
Find the time of traversal of the ball and the distance traversed."
Algorithm 3 : Blackboard approach for problem generation in physics
1. Initialize Agent 1 to compute 𝑣 = 𝑢 + 𝑎𝑡, Agent 2 to compute 𝑣 2 = 𝑢2 + 2𝑎𝑠, Agent 3 to
compute 𝑠 = 𝑢𝑡 + 1/2𝑎𝑡2 , and iteration 𝑖 = 0.
2. For each agent do in parallel
a) If one but all parameter is unknown, evaluate the parameter using Agents.
b) Submit it to the blackboard manager for updating.
c) 𝑖 ←𝑖+1
End-For
3. The blackboard manager updates the newly recorded parameters on the blackboard.
4. a) If 𝑖 ≤ maximum number of parameters and 𝜏 ≤ user defined runtime, loop through Step 2.
b) If 𝑖 > run-time, stop.
5. If condition 1 holds and 𝑖= maximum number of parameters, then the blackboard manager
passes on the known parameters and unknown parameters to the LLM to prepare a question.
7. Experiments: Relative Performance Analysis
The performance of the proposed techniques in comparison to the existing ones is discussed
below.
7.1. Comparative Study of Search Based Methods for Identity Generation
Table 3 presents a comparative analysis of identity problems generated by SOTA methods and
the proposed approaches, evaluated using two key metrics: i) Mean Diversity per Unit Depth
(MDPUD), defined as the mean diversity of the best node normalized by its depth across 150
problems, and ii) average run-time complexity over 150 instances. For this comparative study,
the problems generated by SOTA methods were back-traced to the root, and the proposed
algorithms generated identities at the same depth within the search tree to ensure consistency.
The findings demonstrate that the proposed approaches outperform traditional methods by
producing more diverse and less predictable problems while achieving greater efficiency in
run-time performance.
Although the MDPUD for both the random and heuristic-based search methods are similar,
the random search method requires more time to generate identities. This is because the
random search explores a larger search space to find a solution (creative outcome). In contrast,
the heuristic-guided approach limits the depth of the search tree, resulting in lower runtime
complexity.
7.2. Comparative Study of Generative Neural Models for Identity Generation
Table 4 presents the performance comparison between the LeakGAN model and traditional
generative neural networks in generating 150 trigonometric identities. The metrics used for
comparison include the Bilingual Evaluation Understudy (BLEU) score (a commonly employed
to assess the quality of both text and equation generation [2]) and runtime complexity. The
BLEU score evaluates how closely a machine translation matches reference data by measuring
n-gram overlap between the generated and reference sequences. Common n-grams include
Table 3
Relative performance analysis of problems generated by the proposed approaches and the traditional
methods
Algorithm MDPUD Run-time (sec)
Polozov et al. [15] 27.33 90.23
Papasalouros [16] 25.87 82.14
Pearce et al. [17] 14.96 42.45
Liu et al. [18] 15.20 35.02
Tabuguia et al. [19] 10.88 43.15
Briggs et al. [20] 24.50 96.72
Proposed Random Search 30.74 56.43
Proposed Heuristic Guided Search 31.18 32.07
Table 4
Comparative study of the LeakGAN model with traditional algorithms
Algorithms BLEU-3 (%) BLEU-4 (%) BLEU-5 (%) Run-time Complexity (secs)
LSTM [21] 55.12 28.33 16.43 57.27
VAE [22] 65.04 30.10 19.78 104.20
SeqGAN [23] 70.56 39.74 31.22 247.06
RankGAN [24] 75.09 43.86 33.65 208.54
LeakGAN 86.52 74.81 60.32 353.23
tri-grams (3-grams), quadra-grams (4-grams), and penta-grams (5-grams). To avoid favoring
shorter outputs, a brevity penalty is applied. The final score is the geometric mean of n-gram
precisions, adjusted by this penalty.
The results in Table 4 show that the proposed approach significantly outperforms all tradi-
tional networks in terms of BLEU scores. However, the runtime complexity of the LeakGAN
model is higher than that of the traditional networks. This trade-off between improved quality
and increased complexity reflects a balance between performance and efficiency.
7.3. Comparative Study of Generative Neural Models for Identity Generation
Table 5 showcases the performance comparison between the Blackboard approach and traditional
LLMs in generating 100 physics problems. The evaluation is based on the same metrics outlined
in Section 7.2. The results clearly indicate that the proposed approach generates a more diverse
set of physics problems compared to established LLMs, as evidenced by its superior BLEU scores.
Additionally, the computational efficiency of the proposed method is noteworthy, making it a
practical solution for creating chapter-end exercises in physics.
8. Further Scope of Computational Creative Models
Existing computationally creative models offer numerous advantages but also face significant
limitations. One notable drawback is their inability to effectively contextualize problems within
Table 5
Comparative study of the Blackboard approach for physics problem generation
Algorithms BLEU-3 (%) BLEU-4 (%) BLEU-5 (%) Run-time Complexity (secs)
Google Gemini [25] 82.22 72.86 55.44 45.56
ChatGPT [3] 85.20 75.32 59.88 41.42
MetaLlama [26] 80.57 70.90 53.81 48.87
Black board Approch 87.03 76.27 61.05 41.72
environmental representations. For instance, in Figure 5 (a) and (b), there are 2 scenarios
illustrated which are as follows.
Scenario 1: A lotus of height 𝐻 + ℎ stands upright in a pond, where ℎ is above water and
𝐻 is submerged. A gust of wind bends the lotus, making its tip touch the water a units away
from its original position. Given ℎ and 𝑎, find 𝐻. The above scenario can be addressed using
Pythagoras theorem by equating (𝐻 + ℎ)2 = 𝐻 2 + 𝑎2 .
Scenario 2: An electric pole of height H has an electric wire attached to it at the top, with
the lower end initially free. Next, the wire is stretched to 𝐻 + 1 inches and fixed 2 inches from
the base. Find 𝐻. The above scenario can be addressed using Pythagoras theorem by equating
(𝐻 + 1)2 = 𝐻 2 + 22 .
A machine capable of understanding the concepts depicted in scenarios 1 and 2, recognizing
the Pythagorean theorem as the underlying principle across these problems, and tagging this
rule to generate a novel problem in a different scenario would demonstrate remarkable creative
reasoning. This type of learning mechanism is referred to as cross-domain learning [27]. The
afore-said novel problem generation in a different scenario is illustrated in Figure 5 (c) and is
described as follows.
Developed New Scenario: A coconut tree breaks and falls across a canal after a storm. A
goat, tied to a string held by a man, walks along the trunk to the other side. Determine the
canal’s width.
However, current CC models fall short of achieving this. This limitation stems from the lack
of perceptual knowledge about real-world entities, such as ponds or electric poles, and the
inability to grasp the physical and spatial relationships [28, 29] inherent in these objects and
their environments. In other words, these models are constrained by their limited capacity
for environmental context, perceptual reasoning [30], and spatial understanding. Addressing
this gap requires the development of more advanced computational frameworks that integrate
environmental context and reasoning capabilities. By incorporating a richer understanding of
the physical world and its representations, future models could enable spatial reasoning and
generate innovative solutions or problems across diverse domains.
9. Conclusions
The present study highlights the potential of CC to replicate human-like creative processes
within the scientific domain. By combining classical AI techniques, such as random experi-
mentation, heuristic search, and inductive learning, with modern approaches like GANs and
(a)
(b)
(c)
Figure 5: Illustration of application of cross-domain knowledge to generate new problems in another
domain (a) Scenario 1 depicting the lotus problem, (b) Scenario 2 depicting the electric pole problem (c)
Scenario 3 denotes the problem generated from Scenarios 1 and 2
LLMs, this work demonstrates innovative methodologies for generating complex chapter-end
problems in mathematics and physics. A comparative performance analysis confirms the effi-
cacy of the proposed models in synthesizing creativity compared SOTA methods. While this
research lays a strong foundation for computational creativity in scientific problem generation,
it also emphasizes the need for future advancements that integrate contextual reasoning and
perceptual knowledge to unlock AI’s full potential for cross-domain learning, enabling the
application of acquired knowledge across diverse domains.
Declaration on Generative AI
The author(s) have not employed any Generative AI tools.
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