Nithin Nagaraj

Deeksha Sethi, Nithin Nagaraj, Harikrishnan N B

Learning from limited and imbalanced data is a challenging problem in the Artificial Intelligence community. Real-time scenarios demand decision-making from rare events wherein the data are typically imbalanced. These situations commonly arise in medical applications, cybersecurity, catastrophic predictions etc. This motivates the development of learning algorithms capable of learning from imbalanced data. Human brain effortlessly learns from imbalanced data. Inspired by the chaotic neuronal firing in the human brain, a novel learning algorithm namely Neurochaos Learning (NL) was recently proposed. NL is categorized in three blocks: Feature Transformation, Neurochaos Feature Extraction (CFX), and Classification. In this work, the efficacy of neurochaos feature transformation and extraction for classification in imbalanced learning is studied. We propose a unique combination of neurochaos based feature transformation and extraction with traditional ML algorithms. The explored datasets in this study revolve around medical diagnosis, banknote fraud detection, environmental applications and spoken-digit classification. In this study, experiments are performed in both high and low training sample regime. In the former, five out of nine datasets have shown a performance boost in terms of macro F1-score after using CFX features. The highest performance boost obtained is 25.97% for Statlog (Heart) dataset using CFX+Decision Tree. In the low training sample regime (from just one to nine training samples per class), the highest performance boost of 144.38% is obtained for Haberman's Survival dataset using CFX+Random Forest. NL offers enormous flexibility of combining CFX with any ML classifier to boost its performance, especially for learning tasks with limited and imbalanced data.

Pooja Honna, Ayush Patravali, Nithin Nagaraj et al.

Neurochaos Learning (NL) has shown promise in recent times over traditional deep learning due to its two key features: ability to learn from small sized training samples, and low compute requirements. In prior work, NL has been implemented and extensively tested on separable and time series data, and demonstrated its superior performance on both classification and regression tasks. In this paper, we investigate the next step in NL, viz., applying NL to linked data, in particular, data that is represented in the form of knowledge graphs. We integrate linked data into NL by implementing node aggregation on knowledge graphs, and then feeding the aggregated node features to the simplest NL architecture: ChaosNet. We demonstrate the results of our implementation on homophilic graph datasets as well as heterophilic graph datasets of verying heterophily. We show better efficacy of our approach on homophilic graphs than on heterophilic graphs. While doing so, we also present our analysis of the results, as well as suggestions for future work.

Rajan Sahu, Shivam Chadha, Nithin Nagaraj et al.

Reducing the size of a neural network (pruning) by removing weights without impacting its performance is an important problem for resource-constrained devices. In the past, pruning was typically accomplished by ranking or penalizing weights based on criteria like magnitude and removing low-ranked weights before retraining the remaining ones. Pruning strategies may also involve removing neurons from the network in order to achieve the desired reduction in network size. We formulate pruning as an optimization problem with the objective of minimizing misclassifications by selecting specific weights. To accomplish this, we have introduced the concept of chaos in learning (Lyapunov exponents) via weight updates and exploiting causality to identify the causal weights responsible for misclassification. Such a pruned network maintains the original performance and retains feature explainability.

Harikrishnan N B, Arham Jain, Nithin Nagaraj

Decision Tree is a well understood Machine Learning model that is based on minimizing impurities in the internal nodes. The most common impurity measures are Shannon entropy and Gini impurity. These impurity measures are insensitive to the order of training data and hence the final tree obtained is invariant to any permutation of the data. This is a limitation in terms of modeling when there are temporal order dependencies between data instances. In this research, we propose the adoption of Effort-To-Compress (ETC) - a complexity measure, for the first time, as an alternative impurity measure. Unlike Shannon entropy and Gini impurity, structural impurity based on ETC is able to capture order dependencies in the data, thus obtaining potentially different decision trees for different permutations of the same data instances, a concept we term as Permutation Decision Trees (PDT). We then introduce the notion of Permutation Bagging achieved using permutation decision trees without the need for random feature selection and sub-sampling. We conduct a performance comparison between Permutation Decision Trees and classical decision trees across various real-world datasets, including Appendicitis, Breast Cancer Wisconsin, Diabetes Pima Indian, Ionosphere, Iris, Sonar, and Wine. Our findings reveal that PDT demonstrates comparable performance to classical decision trees across most datasets. Remarkably, in certain instances, PDT even slightly surpasses the performance of classical decision trees. In comparing Permutation Bagging with Random Forest, we attain comparable performance to Random Forest models consisting of 50 to 1000 trees, using merely 21 trees. This highlights the efficiency and effectiveness of Permutation Bagging in achieving comparable performance outcomes with significantly fewer trees.

Tanmay Ghosh, Shaurabh Anand, Rakesh Gomaji Nannewar et al.

Deep learning models for precipitation forecasting often function as black boxes, limiting their adoption in real-world weather prediction. To enhance transparency while maintaining accuracy, we developed an interpretable deep learning framework for short-term precipitation prediction in four major Indian cities: Bengaluru, Mumbai, Delhi, and Kolkata, spanning diverse climate zones. We implemented a hybrid Time-Distributed CNN-ConvLSTM (Convolutional Neural Network-Long Short-Term Memory) architecture, trained on multi-decadal ERA5 reanalysis data. The architecture was optimized for each city with a different number of convolutional filters: Bengaluru (32), Mumbai and Delhi (64), and Kolkata (128). The models achieved root mean square error (RMSE) values of 0.21 mm/day (Bengaluru), 0.52 mm/day (Mumbai), 0.48 mm/day (Delhi), and 1.80 mm/day (Kolkata). Through interpretability analysis using permutation importance, Gradient-weighted Class Activation Mapping (Grad-CAM), temporal occlusion, and counterfactual perturbation, we identified distinct patterns in the model's behavior. The model relied on city-specific variables, with prediction horizons ranging from one day for Bengaluru to five days for Kolkata. This study demonstrates how explainable AI (xAI) can provide accurate forecasts and transparent insights into precipitation patterns in diverse urban environments.

Harikrishnan N B, Anuja Vats, Nithin Nagaraj et al.

Modern machine learning approaches often prioritize performance at the cost of increased complexity, computational demands, and reduced interpretability. This paper introduces a novel framework that challenges this trend by reinterpreting learning from an information-theoretic perspective, viewing it as a search for encoding schemes that capture intrinsic data structures through compact representations. Rather than following the conventional approach of fitting data to complex models, we propose a fundamentally different method that maps data to intervals of initial conditions in a dynamical system. Our GLS (Generalized Lüroth Series) coding compression classifier employs skew tent maps - a class of chaotic maps - both for encoding data into initial conditions and for subsequent recovery. The effectiveness of this simple framework is noteworthy, with performance closely approaching that of well-established machine learning methods. On the breast cancer dataset, our approach achieves 92.98\% accuracy, comparable to Naive Bayes at 94.74\%. While these results do not exceed state-of-the-art performance, the significance of our contribution lies not in outperforming existing methods but in demonstrating that a fundamentally simpler, more interpretable approach can achieve competitive results.

Remya Ajai A S, Nithin Nagaraj

Inspired by the human brain's structure and function, Artificial Neural Networks (ANN) were developed for data classification. However, existing Neural Networks, including Deep Neural Networks, do not mimic the brain's rich structure. They lack key features such as randomness and neuron heterogeneity, which are inherently chaotic in their firing behavior. Neurochaos Learning (NL), a chaos-based neural network, recently employed one-dimensional chaotic maps like Generalized Lüroth Series (GLS) and Logistic map as neurons. For the first time, we propose a random heterogeneous extension of NL, where various chaotic neurons are randomly placed in the input layer, mimicking the randomness and heterogeneous nature of human brain networks. We evaluated the performance of the newly proposed Random Heterogeneous Neurochaos Learning (RHNL) architectures combined with traditional Machine Learning (ML) methods. On public datasets, RHNL outperformed both homogeneous NL and fixed heterogeneous NL architectures in nearly all classification tasks. RHNL achieved high F1 scores on the Wine dataset (1.0), Bank Note Authentication dataset (0.99), Breast Cancer Wisconsin dataset (0.99), and Free Spoken Digit Dataset (FSDD) (0.98). These RHNL results are among the best in the literature for these datasets. We investigated RHNL performance on image datasets, where it outperformed stand-alone ML classifiers. In low training sample regimes, RHNL was the best among stand-alone ML. Our architecture bridges the gap between existing ANN architectures and the human brain's chaotic, random, and heterogeneous properties. We foresee the development of several novel learning algorithms centered around Random Heterogeneous Neurochaos Learning in the coming days.

Harikrishnan N B, Shubham Bhilare, Aditi Kathpalia et al.

Discovering causal direction from temporal observational data is particularly challenging for symbolic sequences, where functional models and noise assumptions are often unavailable. We propose a novel \emph{Dictionary Based Pattern Entropy ($DPE$)} framework that infers both the direction of causation and the specific subpatterns driving changes in the effect variable. The framework integrates \emph{Algorithmic Information Theory} (AIT) and \emph{Shannon Information Theory}. Causation is interpreted as the emergence of compact, rule based patterns in the candidate cause that systematically constrain the effect. $DPE$ constructs direction-specific dictionaries and quantifies their influence using entropy-based measures, enabling a principled link between deterministic pattern structure and stochastic variability. Causal direction is inferred via a minimum-uncertainty criterion, selecting the direction exhibiting stronger and more consistent pattern-driven organization. As summarized in Table 7, $DPE$ consistently achieves reliable performance across diverse synthetic systems, including delayed bit-flip perturbations, AR(1) coupling, 1D skew-tent maps, and sparse processes, outperforming or matching competing AIT-based methods ($ETC_E$, $ETC_P$, $LZ_P$). In biological and ecological datasets, performance is competitive, while alternative methods show advantages in specific genomic settings. Overall, the results demonstrate that minimizing pattern level uncertainty yields a robust, interpretable, and broadly applicable framework for causal discovery.

Akhila Henry, Nithin Nagaraj

Neurochaos Learning (NL) is a brain-inspired classification framework that employs chaotic dynamics to extract features from input data and yields state of the art performance on classification tasks. However, NL requires the tuning of multiple hyperparameters and computing of four chaotic features per input sample. In this paper, we propose AutochaosNet - a novel, hyperparameter-free variant of the NL algorithm that eliminates the need for both training and parameter optimization. AutochaosNet leverages a universal chaotic sequence derived from the Champernowne constant and uses the input stimulus to define firing time bounds for feature extraction. Two simplified variants - TM AutochaosNet and TM-FR AutochaosNet - are evaluated against the existing NL architecture - ChaosNet. Our results demonstrate that AutochaosNet achieves competitive or superior classification performance while significantly reducing training time due to reduced computational effort. In addition to eliminating training and hyperparameter tuning, AutochaosNet exhibits excellent generalisation capabilities, making it a scalable and efficient choice for real-world classification tasks. Future work will focus on identifying universal orbits under various chaotic maps and incorporating them into the NL framework to further enhance performance.

Akhila Henry, Nithin Nagaraj

This study presents novel Augmented Regression Models using Neurochaos Learning (NL), where Tracemean features derived from the Neurochaos Learning framework are integrated with traditional regression algorithms : Linear Regression, Ridge Regression, Lasso Regression, and Support Vector Regression (SVR). Our approach was evaluated using ten diverse real-life datasets and a synthetically generated dataset of the form $y = mx + c + ε$. Results show that incorporating the Tracemean feature (mean of the chaotic neural traces of the neurons in the NL architecture) significantly enhances regression performance, particularly in Augmented Lasso Regression and Augmented SVR, where six out of ten real-life datasets exhibited improved predictive accuracy. Among the models, Augmented Chaotic Ridge Regression achieved the highest average performance boost (11.35 %). Additionally, experiments on the simulated dataset demonstrated that the Mean Squared Error (MSE) of the augmented models consistently decreased and converged towards the Minimum Mean Squared Error (MMSE) as the sample size increased. This work demonstrates the potential of chaos-inspired features in regression tasks, offering a pathway to more accurate and computationally efficient prediction models.

Vishrut Ramraj, Nithin Nagaraj, Harikrishnan N B

In this paper, we explore the application of Permutation Decision Trees (PDT) and strategic trailing for predicting stock market movements and executing profitable trades in the Indian stock market. We focus on high-frequency data using 5-minute candlesticks for the top 50 stocks listed in the NIFTY 50 index and Forex pairs such as XAUUSD and EURUSD. We implement a trading strategy that aims to buy stocks at lower prices and sell them at higher prices, capitalizing on short-term market fluctuations. Due to regulatory constraints in India, short selling is not considered in our strategy. The model incorporates various technical indicators and employs hyperparameters such as the trailing stop-loss value and support thresholds to manage risk effectively. We trained and tested data on a 3 month dataset provided by Yahoo Finance. Our bot based on Permutation Decision Tree achieved a profit of 1.1802\% over the testing period, where as a bot based on LSTM gave a return of 0.557\% over the testing period and a bot based on RNN gave a return of 0.5896\% over the testing period. All of the bots outperform the buy-and-hold strategy, which resulted in a loss of 2.29\%.

Nanjangud C. Narendra, Nithin Nagaraj

Deep learning implemented via neural networks, has revolutionized machine learning by providing methods for complex tasks such as object detection/classification and prediction. However, architectures based on deep neural networks have started to yield diminishing returns, primarily due to their statistical nature and inability to capture causal structure in the training data. Another issue with deep learning is its high energy consumption, which is not that desirable from a sustainability perspective. Therefore, alternative approaches are being considered to address these issues, both of which are inspired by the functioning of the human brain. One approach is causal learning, which takes into account causality among the items in the dataset on which the neural network is trained. It is expected that this will help minimize the spurious correlations that are prevalent in the learned representations of deep neural networks. The other approach is Neurochaos Learning, a recent development, which draws its inspiration from the nonlinear chaotic firing intrinsic to neurons in biological neural networks (brain/central nervous system). Both approaches have shown improved results over just deep learning alone. To that end, in this position paper, we investigate how causal and neurochaos learning approaches can be integrated together to produce better results, especially in domains that contain linked data. We propose an approach for this integration to enhance classification, prediction and reinforcement learning. We also propose a set of research questions that need to be investigated in order to make this integration a reality.

Dhruthi, Nithin Nagaraj, Harikrishnan N B

Inferring causal relationships in the decision-making processes of machine learning algorithms is a crucial step toward achieving explainable Artificial Intelligence (AI). In this research, we introduce a novel causality measure and a distance metric derived from Lempel-Ziv (LZ) complexity. We explore how the proposed causality measure can be used in decision trees by enabling splits based on features that most strongly \textit{cause} the outcome. We further evaluate the effectiveness of the causality-based decision tree and the distance-based decision tree in comparison to a traditional decision tree using Gini impurity. While the proposed methods demonstrate comparable classification performance overall, the causality-based decision tree significantly outperforms both the distance-based decision tree and the Gini-based decision tree on datasets generated from causal models. This result indicates that the proposed approach can capture insights beyond those of classical decision trees, especially in causally structured data. Based on the features used in the LZ causal measure based decision tree, we introduce a causal strength for each features in the dataset so as to infer the predominant causal variables for the occurrence of the outcome.

Tanmay Ghosh, Nithin Nagaraj

The decision making involved behind the mode choice is critical for transportation planning. While statistical learning techniques like discrete choice models have been used traditionally, machine learning (ML) models have gained traction recently among the transportation planners due to their higher predictive performance. However, the black box nature of ML models pose significant interpretability challenges, limiting their practical application in decision and policy making. This study utilised a dataset of $1350$ households belonging to low and low-middle income bracket in the city of Bengaluru to investigate mode choice decision making behaviour using Multinomial logit model and ML classifiers like decision trees, random forests, extreme gradient boosting and support vector machines. In terms of accuracy, random forest model performed the best ($0.788$ on training data and $0.605$ on testing data) compared to all the other models. This research has adopted modern interpretability techniques like feature importance and individual conditional expectation plots to explain the decision making behaviour using ML models. A higher travel costs significantly reduce the predicted probability of bus usage compared to other modes (a $0.66\%$ and $0.34\%$ reduction using Random Forests and XGBoost model for $10\%$ increase in travel cost). However, reducing travel time by $10\%$ increases the preference for the metro ($0.16\%$ in Random Forests and 0.42% in XGBoost). This research augments the ongoing research on mode choice analysis using machine learning techniques, which would help in improving the understanding of the performance of these models with real-world data in terms of both accuracy and interpretability.

Harikrishnan N B, Aditi Kathpalia, Nithin Nagaraj

Discovering cause-effect from observational data is an important but challenging problem in science and engineering. In this work, a recently proposed brain inspired learning algorithm namely-\emph{Neurochaos Learning} (NL) is used for the classification of cause-effect from simulated data. The data instances used are generated from coupled AR processes, coupled 1D chaotic skew tent maps, coupled 1D chaotic logistic maps and a real-world prey-predator system. The proposed method consistently outperforms a five layer Deep Neural Network architecture for coupling coefficient values ranging from $0.1$ to $0.7$. Further, we investigate the preservation of causality in the feature extracted space of NL using Granger Causality (GC) for coupled AR processes and and Compression-Complexity Causality (CCC) for coupled chaotic systems and real-world prey-predator dataset. This ability of NL to preserve causality under a chaotic transformation and successfully classify cause and effect time series (including a transfer learning scenario) is highly desirable in causal machine learning applications.

Aditi Kathpalia, Keerti P. Charantimath, Nithin Nagaraj

The science of causality explains/determines 'cause-effect' relationship between the entities of a system by providing mathematical tools for the purpose. In spite of all the success and widespread applications of machine-learning (ML) algorithms, these algorithms are based on statistical learning alone. Currently, they are nowhere close to 'human-like' intelligence as they fail to answer and learn based on the important "Why?" questions. Hence, researchers are attempting to integrate ML with the science of causality. Among the many causal learning issues encountered by ML, one is that these algorithms are dumb to the temporal order or structure in data. In this work we develop a machine learning pipeline based on a recently proposed 'neurochaos' feature learning technique (ChaosFEX feature extractor), that helps us to learn generalized causal-structure in given time-series data.

Abhsihek Nandekar, Preeth Khona, Rajani M. B. et al.

The musicological analysis of Carnatic music is challenging, owing to its rich structure and complexity. Automated \textit{rāga} classification, pitch detection, tonal analysis, modelling and information retrieval of this form of southern Indian classical music have, however, made significant progress in recent times. A causal analysis to investigate the musicological structure of Carnatic compositions and the identification of the relationships embedded in them have never been previously attempted. In this study, we propose a novel framework for causal discovery, using a compression-complexity measure. Owing to the limited number of compositions available, however, we generated surrogates to further facilitate the analysis of the prevailing causal relationships. Our analysis indicates that the context-free grammar, inferred from more complex compositions, such as the \textit{Mē\d{l}akarta} \textit{rāga}, are a \textit{structural cause} for the \textit{Janya} \textit{rāga}. We also analyse certain special cases of the \textit{Janya rāga} in order to understand their origins and structure better.

Anwesh Bhattacharya, Snehanshu Saha, Nithin Nagaraj

It has been well documented that the use of exponentially-averaged momentum (EM) in particle swarm optimization (PSO) is advantageous over the vanilla PSO algorithm. In the single-objective setting, it leads to faster convergence and avoidance of local minima. Naturally, one would expect that the same advantages of EM carry over to the multi-objective setting. Hence, we extend the state of the art Multi-objective optimization (MOO) solver, SMPSO, by incorporating EM in it. As a consequence, we develop the mathematical formalism of constriction fairness which is at the core of extended SMPSO algorithm. The proposed solver matches the performance of SMPSO across the ZDT, DTLZ and WFG problem suites and even outperforms it in certain instances.

Harikrishnan NB, Nithin Nagaraj

Chaos and Noise are ubiquitous in the Brain. Inspired by the chaotic firing of neurons and the constructive role of noise in neuronal models, we for the first time connect chaos, noise and learning. In this paper, we demonstrate Stochastic Resonance (SR) phenomenon in Neurochaos Learning (NL). SR manifests at the level of a single neuron of NL and enables efficient subthreshold signal detection. Furthermore, SR is shown to occur in single and multiple neuronal NL architecture for classification tasks - both on simulated and real-world spoken digit datasets. Intermediate levels of noise in neurochaos learning enables peak performance in classification tasks thus highlighting the role of SR in AI applications, especially in brain inspired learning architectures.

Pranay SY, Nithin Nagaraj

Causal inference is one of the most fundamental problems across all domains of science. We address the problem of inferring a causal direction from two observed discrete symbolic sequences $X$ and $Y$. We present a framework which relies on lossless compressors for inferring context-free grammars (CFGs) from sequence pairs and quantifies the extent to which the grammar inferred from one sequence compresses the other sequence. We infer $X$ causes $Y$ if the grammar inferred from $X$ better compresses $Y$ than in the other direction. To put this notion to practice, we propose three models that use the Compression-Complexity Measures (CCMs) - Lempel-Ziv (LZ) complexity and Effort-To-Compress (ETC) to infer CFGs and discover causal directions without demanding temporal structures. We evaluate these models on synthetic and real-world benchmarks and empirically observe performances competitive with current state-of-the-art methods. Lastly, we present two unique applications of the proposed models for causal inference directly from pairs of genome sequences belonging to the SARS-CoV-2 virus. Using a large number of sequences, we show that our models capture directed causal information exchange between sequence pairs, presenting novel opportunities for addressing key issues such as contact-tracing, motif discovery, evolution of virulence and pathogenicity in future applications.

Harikrishnan NB, Pranay SY, Nithin Nagaraj

There has been empirical evidence of presence of non-linearity and chaos at the level of single neurons in biological neural networks. The properties of chaotic neurons inspires us to employ them in artificial learning systems. Here, we propose a Neurochaos Learning (NL) architecture, where the neurons used to extract features from data are 1D chaotic maps. ChaosFEX+SVM, an instance of this NL architecture, is proposed as a hybrid combination of chaos and classical machine learning algorithm. We formally prove that a single layer of NL with a finite number of 1D chaotic neurons satisfies the Universal Approximation Theorem with an exact value for the number of chaotic neurons needed to approximate a discrete real valued function with finite support. This is made possible due to the topological transitivity property of chaos and the existence of uncountably infinite number of dense orbits for the chosen 1D chaotic map. The chaotic neurons in NL get activated under the presence of an input stimulus (data) and output a chaotic firing trajectory. From such chaotic firing trajectories of individual neurons of NL, we extract Firing Time, Firing Rate, Energy and Entropy that constitute ChaosFEX features. These ChaosFEX features are then fed to a Support Vector Machine with linear kernel for classification. The effectiveness of chaotic feature engineering performed by NL (ChaosFEX+SVM) is demonstrated for synthetic and real world datasets in the low and high training sample regimes. Specifically, we consider the problem of classification of genome sequences of SARS-CoV-2 from other coronaviruses (SARS-CoV-1, MERS-CoV and others). With just one training sample per class for 1000 random trials of training, we report an average macro F1-score > 0.99 for the classification of SARS-CoV-2 from SARS-CoV-1 genome sequences. Robustness of ChaosFEX features to additive noise is also demonstrated.

Harikrishnan Nellippallil Balakrishnan, Aditi Kathpalia, Snehanshu Saha et al.

Inspired by chaotic firing of neurons in the brain, we propose ChaosNet -- a novel chaos based artificial neural network architecture for classification tasks. ChaosNet is built using layers of neurons, each of which is a 1D chaotic map known as the Generalized Luroth Series (GLS) which has been shown in earlier works to possess very useful properties for compression, cryptography and for computing XOR and other logical operations. In this work, we design a novel learning algorithm on ChaosNet that exploits the topological transitivity property of the chaotic GLS neurons. The proposed learning algorithm gives consistently good performance accuracy in a number of classification tasks on well known publicly available datasets with very limited training samples. Even with as low as 7 (or fewer) training samples/class (which accounts for less than 0.05% of the total available data), ChaosNet yields performance accuracies in the range 73.89 % - 98.33 %. We demonstrate the robustness of ChaosNet to additive parameter noise and also provide an example implementation of a 2-layer ChaosNet for enhancing classification accuracy. We envisage the development of several other novel learning algorithms on ChaosNet in the near future.

Snehanshu Saha, Nithin Nagaraj, Archana Mathur et al.

We present analytical exploration of novel activation functions as consequence of integration of several ideas leading to implementation and subsequent use in habitability classification of exoplanets. Neural networks, although a powerful engine in supervised methods, often require expensive tuning efforts for optimized performance. Habitability classes are hard to discriminate, especially when attributes used as hard markers of separation are removed from the data set. The solution is approached from the point of investigating analytical properties of the proposed activation functions. The theory of ordinary differential equations and fixed point are exploited to justify the "lack of tuning efforts" to achieve optimal performance compared to traditional activation functions. Additionally, the relationship between the proposed activation functions and the more popular ones is established through extensive analytical and empirical evidence. Finally, the activation functions have been implemented in plain vanilla feed-forward neural network to classify exoplanets.

Harikrishnan N B, Nithin Nagaraj

The practical success of widely used machine learning (ML) and deep learning (DL) algorithms in Artificial Intelligence (AI) community owes to availability of large datasets for training and huge computational resources. Despite the enormous practical success of AI, these algorithms are only loosely inspired from the biological brain and do not mimic any of the fundamental properties of neurons in the brain, one such property being the chaotic firing of biological neurons. This motivates us to develop a novel neuronal architecture where the individual neurons are intrinsically chaotic in nature. By making use of the topological transitivity property of chaos, our neuronal network is able to perform classification tasks with very less number of training samples. For the MNIST dataset, with as low as $0.1 \%$ of the total training data, our method outperforms ML and matches DL in classification accuracy for up to $7$ training samples/class. For the Iris dataset, our accuracy is comparable with ML algorithms, and even with just two training samples/class, we report an accuracy as high as $95.8 \%$. This work highlights the effectiveness of chaos and its properties for learning and paves the way for chaos-inspired neuronal architectures by closely mimicking the chaotic nature of neurons in the brain.