Sreedath Panat

Prathamesh Dinesh Joshi, Sahil Pocker, Raj Abhijit Dandekar et al.

As LLMs become increasingly proficient at producing human-like responses, there has been a rise of academic and industrial pursuits dedicated to flagging a given piece of text as "human" or "AI". Most of these pursuits involve modern NLP detectors like T5-Sentinel and RoBERTa-Sentinel, without paying too much attention to issues of interpretability and explainability of these models. In our study, we provide a comprehensive analysis that shows that traditional ML models (Naive-Bayes,MLP, Random Forests, XGBoost) perform as well as modern NLP detectors, in human vs AI text detection. We achieve this by implementing a robust testing procedure on diverse datasets, including curated corpora and real-world samples. Subsequently, by employing the explainable AI technique LIME, we uncover parts of the input that contribute most to the prediction of each model, providing insights into the detection process. Our study contributes to the growing need for developing production-level LLM detection tools, which can leverage a wide range of traditional as well as modern NLP detectors we propose. Finally, the LIME techniques we demonstrate also have the potential to equip these detection tools with interpretability analysis features, making them more reliable and trustworthy in various domains like education, healthcare, and media.

Raj Gaurav Maurya, Vaibhav Shukla, Raj Abhijit Dandekar et al.

Misinformation on social media thrives on surprise, emotion, and identity-driven reasoning, often amplified through human cognitive biases. To investigate these mechanisms, we model large language model (LLM) personas as synthetic agents that mimic user-level biases, ideological alignments, and trust heuristics. Within this setup, we introduce an auditor--node framework to simulate and analyze how misinformation evolves as it circulates through networks of such agents. News articles are propagated across networks of persona-conditioned LLM nodes, each rewriting received content. A question--answering-based auditor then measures factual fidelity at every step, offering interpretable, claim-level tracking of misinformation drift. We formalize a misinformation index and a misinformation propagation rate to quantify factual degradation across homogeneous and heterogeneous branches of up to 30 sequential rewrites. Experiments with 21 personas across 10 domains reveal that identity- and ideology-based personas act as misinformation accelerators, especially in politics, marketing, and technology. By contrast, expert-driven personas preserve factual stability. Controlled-random branch simulations further show that once early distortions emerge, heterogeneous persona interactions rapidly escalate misinformation to propaganda-level distortion. Our taxonomy of misinformation severity -- spanning factual errors, lies, and propaganda -- connects observed drift to established theories in misinformation studies. These findings demonstrate the dual role of LLMs as both proxies for human-like biases and as auditors capable of tracing information fidelity. The proposed framework provides an interpretable, empirically grounded approach for studying, simulating, and mitigating misinformation diffusion in digital ecosystems.

Ammar Shaikh, Raj Abhijit Dandekar, Sreedath Panat et al.

Rapid advancements in Large Language models (LLMs) has significantly enhanced their reasoning capabilities. Despite improved performance on benchmarks, LLMs exhibit notable gaps in their cognitive processes. Additionally, as reflections of human-generated data, these models have the potential to inherit cognitive biases, raising concerns about their reasoning and decision making capabilities. In this paper we present a framework to interpret, understand and provide insights into a host of cognitive biases in LLMs. Conducting our research on frontier language models we're able to elucidate reasoning limitations and biases, and provide reasoning behind these biases by constructing influence graphs that identify phrases and words most responsible for biases manifested in LLMs. We further investigate biases such as round number bias and cognitive bias barrier revealed when noting framing effect in language models.

Sushant Mehta, Raj Dandekar, Rajat Dandekar et al.

We present the first comprehensive study of latent multi-head attention (MLA) for small language models, revealing interesting efficiency-quality trade-offs. Training 30M-parameter GPT models on 100,000 synthetic stories, we benchmark three architectural variants: standard multi-head attention (MHA), MLA, and MLA with rotary positional embeddings (MLA+RoPE). Our key finding is that MLA+RoPE with half-rank latent dimensions (r = d/2) achieves a 45% KV-cache memory reduction while incurring only a 0.3% increase in validation loss (essentially matching MHA quality)- a Pareto improvement for memory constrained deployment. We further show that RoPE is crucial for MLA in small models: without it, MLA underperforms vanilla attention by 3-5%, but with RoPE, it surpasses vanilla by 2%. Inference benchmarks on NVIDIA A100 GPUs reveal that MLA with r=d/2 achieves a 1.4 times speedup over full-rank MLA while maintaining the memory savings. GPT-4 evaluations corroborate perplexity results, with ours achieving the highest quality scores (7.4/10) across grammar, creativity, and consistency metrics. Code and models will be released upon acceptance.

Ranabir Devgupta, Raj Abhijit Dandekar, Rajat Dandekar et al.

In this study, we apply two pillars of Scientific Machine Learning: Neural Ordinary Differential Equations (Neural ODEs) and Universal Differential Equations (UDEs) to the Lotka Volterra Predator Prey Model, a fundamental ecological model describing the dynamic interactions between predator and prey populations. The Lotka-Volterra model is critical for understanding ecological dynamics, population control, and species interactions, as it is represented by a system of differential equations. In this work, we aim to uncover the underlying differential equations without prior knowledge of the system, relying solely on training data and neural networks. Using robust modeling in the Julia programming language, we demonstrate that both Neural ODEs and UDEs can be effectively utilized for prediction and forecasting of the Lotka-Volterra system. More importantly, we introduce the forecasting breakdown point: the time at which forecasting fails for both Neural ODEs and UDEs. We observe how UDEs outperform Neural ODEs by effectively recovering the underlying dynamics and achieving accurate forecasting with significantly less training data. Additionally, we introduce Gaussian noise of varying magnitudes (from mild to high) to simulate real-world data perturbations and show that UDEs exhibit superior robustness, effectively recovering the underlying dynamics even in the presence of noisy data, while Neural ODEs struggle with high levels of noise. Through extensive hyperparameter optimization, we offer insights into neural network architectures, activation functions, and optimizers that yield the best results. This study opens the door to applying Scientific Machine Learning frameworks for forecasting tasks across a wide range of ecological and scientific domains.

Raymundo Vazquez Martinez, Raj Abhijit Dandekar, Rajat Dandekar et al.

In this study, we apply two pillars of Scientific Machine Learning: Neural Ordinary Differential Equations (Neural ODEs) and Universal Differential Equations (UDEs) to the Chandrasekhar White Dwarf Equation (CWDE). The CWDE is fundamental for understanding the life cycle of a star, and describes the relationship between the density of the white dwarf and its distance from the center. Despite the rise in Scientific Machine Learning frameworks, very less attention has been paid to the systematic applications of the above SciML pillars on astronomy based ODEs. Through robust modeling in the Julia programming language, we show that both Neural ODEs and UDEs can be used effectively for both prediction as well as forecasting of the CWDE. More importantly, we introduce the forecasting breakdown point - the time at which forecasting fails for both Neural ODEs and UDEs. Through a robust hyperparameter optimization testing, we provide insights on the neural network architecture, activation functions and optimizers which provide the best results. This study provides opens a door to investigate the applicability of Scientific Machine Learning frameworks in forecasting tasks for a wide range of scientific domains.

Sushant Mehta, Raj Dandekar, Rajat Dandekar et al.

We present MoE-MLA-RoPE, a novel architecture combination that combines Mixture of Experts (MoE) with Multi-head Latent Attention (MLA) and Rotary Position Embeddings (RoPE) for efficient language modeling. Our approach addresses the fundamental trade-off between model capacity and computational efficiency through three key innovations: (1) fine-grained expert routing with 64 micro-experts and top-$k$ selection, enabling flexible specialization through 3.6 * 10^7 possible expert combinations; (2) shared expert isolation that dedicates 2 always active experts for common patterns while routing to 6 of 62 specialized experts; and (3) gradient-conflict-free load balancing that maintains expert utilization without interfering with primary loss optimization. Extensive experiments on models ranging from 17M to 202M parameters demonstrate that MoE-MLA-RoPE with compression ratio r=d/2 achieves 68% KV cache memory reduction and 3.2x inference speedup while maintaining competitive perplexity (0.8% degradation). Compared to the parameters with 53.9M parameters, MoE-MLA-RoPE improves the validation loss by 6.9% over the vanilla transformers while using 42% fewer active parameters per forward pass. FLOP-matched experiments reveal even larger gains: 11.1% improvement with 3.2x inference acceleration. Automated evaluation using GPT-4 as a judge confirms quality improvements in generation, with higher scores on coherence (8.1/10), creativity (7.9/10) and grammatical correctness (8.2/10). Our results establish that architectural novelty, not parameter scaling, defines the efficiency frontier for resource-constrained language model deployment.

Mukund Agarwalla, Himanshu Kumar, Raj Dandekar et al.

Vision-Language Models (VLMs), such as GPT-4V and Llama 3.2 vision, have garnered significant research attention for their ability to leverage Large Language Models (LLMs) in multimodal tasks. However, their potential is constrained by inherent challenges, including proprietary restrictions, substantial computational demands, and limited accessibility. Smaller models, such as GIT and BLIP, exhibit marked limitations, often failing to generate coherent and consistent text beyond a few tokens, even with extensive training. This underscores a pivotal inquiry: how small can a VLM be and still produce fluent and consistent text? Drawing inspiration from the exceptional learning process of 3-4 year old children, who rely heavily on visual cues for understanding and communication, we introduce two novel datasets: ShortDesc (featuring concise image descriptions) and LongDesc (containing more detailed image descriptions). These datasets consist of image-text pairs where the text is restricted to the simple vocabulary and syntax typically used by young children, generated with a scaled-down model, GPT-4o. Using these datasets, we demonstrate that it is possible to train VLMs that are significantly smaller, up to 10 times smaller than state of the art(SOTA) small VLMs while maintaining architectural simplicity. To evaluate the outputs, we leverage GPT-4o to grade the text, as if stories written by students, on creativity, meaningfulness, and consistency, assigning scores out of 10. This method addresses limitations of standard benchmarks by accommodating unstructured outputs and providing a multidimensional evaluation of the model capabilities. Our findings contribute to the development of lightweight, accessible multimodal models for resource constrained environments.

Kavya Subramanian, Prathamesh Dinesh Joshi, Raj Abhijit Dandekar et al.

Forecasting tumor growth is critical for optimizing treatment. Classical growth models such as the Gompertz and Bertalanffy equations capture general tumor dynamics but may fail to adapt to patient-specific variability, particularly with limited data available. In this study, we leverage Neural Ordinary Differential Equations (Neural ODEs) and Universal Differential Equations (UDEs), two pillars of Scientific Machine Learning (SciML), to construct adaptive tumor growth models capable of learning from experimental data. Using the Gompertz model as a baseline, we replace rigid terms with adaptive neural networks to capture hidden dynamics through robust modeling in the Julia programming language. We use our models to perform forecasting under data constraints and symbolic recovery to transform the learned dynamics into explicit mathematical expressions. Our approach has the potential to improve predictive accuracy, guiding dynamic and effective treatment strategies for improved clinical outcomes.

Miheer Salunke, Prathamesh Dinesh Joshi, Raj Abhijit Dandekar et al.

Auditory sensory overload affects 50-70% of individuals with Autism Spectrum Disorder (ASD), yet existing approaches, such as mechanistic models (Hodgkin Huxley type, Wilson Cowan, excitation inhibition balance), clinical tools (EEG/MEG, Sensory Profile scales), and ML methods (Neural ODEs, predictive coding), either assume fixed parameters or lack interpretability, missing autism heterogeneity. We present a Scientific Machine Learning approach using Universal Differential Equations (UDEs) to model sensory adaptation dynamics in autism. Our framework combines ordinary differential equations grounded in biophysics with neural networks to capture both mechanistic understanding and individual variability. We demonstrate that UDEs achieve a 90.8% improvement over pure Neural ODEs while using 73.5% fewer parameters. The model successfully recovers physiological parameters within the 2% error and provides a quantitative risk assessment for sensory overload, predicting 17.2% risk for pulse stimuli with specific temporal patterns. This framework establishes foundations for personalized, evidence-based interventions in autism, with direct applications to wearable technology and clinical practice.

Sushant Mehta, Raj Dandekar, Rajat Dandekar et al.

We present a comprehensive theoretical and empirical study of the Muon optimizer for training transformers only with a small to medium decoder (30M - 200M parameters), with an emphasis on its mathematical foundations, convergence properties and synergistic interactions with modern architectural optimizations. Building on recent work showing Muon's scalability, we provide rigorous theoretical analysis including: (i)showing the convergence rate under standard assumptions, (ii) spectral regularization properties that prevent gradient explosion, (iii) connection to natural gradient descent on the Stiefel manifold, and (iv) equivalence to steepest gradient descent under the spectral norm. Crucially, we demonstrate that Muon expands the Pareto frontier in the compute-time trade-off by maintaining superior data efficiency at large batch sizes, a key finding of~\cite{essentialai2025muon} that we validate across our model scales. Empirically, Muon reaches the target loss with 48-52\% of the training calculated by AdamW while maintaining or improving the final perplexity, consistent with larger-scale results. When combined with Multi-Head Latent Attention (MLA) and Mixture-of-Experts (MoE), we observe multiplicative efficiency gains: MLA+MoE+Muon achieves 68\% memory reduction and 3.2$\times$ inference speedup, while improving perplexity by 8-12\%. We provide detailed procedures on 15 architectural and optimizer components, stability analyzes across 100+ training runs, and practical implementation guidelines including Newton-Schulz coefficients $(3.4445, -4.7750, 2.0315)$ optimized by~\cite{su2024muonblog}. Our theoretical analysis and comprehensive experiments establish Muon as a principled, robust alternative to AdamW that particularly excels when combined with modern efficiency techniques and large-batch training regimes.

Satyanarayana Raju G. V., Prathamesh Dinesh Joshi, Raj Abhijit Dandekar et al.

Soil Organic Carbon (SOC) is a foundation of soil health and global climate resilience, yet its prediction remains difficult because of intricate physical, chemical, and biological processes. In this study, we explore a Scientific Machine Learning (SciML) framework built on Universal Differential Equations (UDEs) to forecast SOC dynamics across soil depth and time. UDEs blend mechanistic physics, such as advection diffusion transport, with neural networks that learn nonlinear microbial production and respiration. Using synthetic datasets, we systematically evaluated six experimental cases, progressing from clean, noise free benchmarks to stress tests with high (35%) multiplicative, spatially correlated noise. Our results highlight both the potential and limitations of the approach. In noise free and moderate noise settings, the UDE accurately reconstructed SOC dynamics. In clean terminal profile at 50 years (Case 4) achieved near perfect fidelity, with MSE = 1.6e-5, and R2 = 0.9999. Case 5, with 7% noise, remained robust (MSE = 3.4e-6, R2 = 0.99998), capturing depth wise SOC trends while tolerating realistic measurement uncertainty. In contrast, Case 3 (35% noise at t = 0) showed clear evidence of overfitting: the model reproduced noisy inputs with high accuracy but lost generalization against the clean truth (R2 = 0.94). Case 6 (35% noise at t = 50) collapsed toward overly smooth mean profiles, failing to capture depth wise variability and yielding negative R2, underscoring the limits of standard training under severe uncertainty. These findings suggest that UDEs are well suited for scalable, noise tolerant SOC forecasting, though advancing toward field deployment will require noise aware loss functions, probabilistic modelling, and tighter integration of microbial dynamics.

Nachiket N. Naik, Prathamesh Dinesh Joshi, Raj Abhijit Dandekar et al.

We study learning of continuous-time inventory dynamics under stochastic demand and quantify when structure helps or hurts forecasting of the bullwhip effect. BULL-ODE compares a fully learned Neural ODE (NODE) that models the entire right-hand side against a physics-informed Universal Differential Equation (UDE) that preserves conservation and order-up-to structure while learning a small residual policy term. Classical supply chain models explain the bullwhip through control/forecasting choices and information sharing, while recent physics-informed and neural differential equation methods blend domain constraints with learned components. It is unclear whether structural bias helps or hinders forecasting under different demand regimes. We address this by using a single-echelon testbed with three demand regimes - AR(1) (autocorrelated), i.i.d. Gaussian, and heavy-tailed lognormal. Training is done on varying fractions of each trajectory, followed by evaluation of multi-step forecasts for inventory I, order rate O, and demand D. Across the structured regimes, UDE consistently generalizes better: with 90% of the training horizon, inventory RMSE drops from 4.92 (NODE) to 0.26 (UDE) under AR(1) and from 5.96 to 0.95 under Gaussian demand. Under heavy-tailed lognormal shocks, the flexibility of NODE is better. These trends persist as train18 ing data shrinks, with NODE exhibiting phase drift in extrapolation while UDE remains stable but underreacts to rare spikes. Our results provide concrete guidance: enforce structure when noise is light-tailed or temporally correlated; relax structure when extreme events dominate. Beyond inventory control, the results offer guidance for hybrid modeling in scientific and engineering systems: enforce known structure when conservation laws and modest noise dominate, and relax structure to capture extremes in settings where rare events drive dynamics.

Karthik Pappu, Prathamesh Dinesh Joshi, Raj Abhijit Dandekar et al.

Accurately modeling malware propagation is essential for designing effective cybersecurity defenses, particularly against adaptive threats that evolve in real time. While traditional epidemiological models and recent neural approaches offer useful foundations, they often fail to fully capture the nonlinear feedback mechanisms present in real-world networks. In this work, we apply scientific machine learning to malware modeling by evaluating three approaches: classical Ordinary Differential Equations (ODEs), Universal Differential Equations (UDEs), and Neural ODEs. Using data from the Code Red worm outbreak, we show that the UDE approach substantially reduces prediction error compared to both traditional and neural baselines by 44%, while preserving interpretability. We introduce a symbolic recovery method that transforms the learned neural feedback into explicit mathematical expressions, revealing suppression mechanisms such as network saturation, security response, and malware variant evolution. Our results demonstrate that hybrid physics-informed models can outperform both purely analytical and purely neural approaches, offering improved predictive accuracy and deeper insight into the dynamics of malware spread. These findings support the development of early warning systems, efficient outbreak response strategies, and targeted cyber defense interventions.

Karishma Battina, Prathamesh Dinesh Joshi, Raj Abhijit Dandekar et al.

Traditional numerical methods often struggle with the complexity and scale of modeling pollutant transport across vast and dynamic oceanic domains. This paper introduces a Physics-Informed Neural Network (PINN) framework to simulate the dispersion of pollutants governed by the 2D advection-diffusion equation. The model achieves physically consistent predictions by embedding physical laws and fitting to noisy synthetic data, generated via a finite difference method (FDM), directly into the neural network training process. This approach addresses challenges such as non-linear dynamics and the enforcement of boundary and initial conditions. Synthetic data sets, augmented with varying noise levels, are used to capture real-world variability. The training incorporates a hybrid loss function including PDE residuals, boundary/initial condition conformity, and a weighted data fit term. The approach takes advantage of the Julia language scientific computing ecosystem for high-performance simulations, offering a scalable and flexible alternative to traditional solvers

Sharv Murgai, Hrishikesh Bhagwat, Raj Abhijit Dandekar et al.

Carbon emissions are rising at an alarming rate, posing a significant threat to global efforts to mitigate climate change. Electric vehicles have emerged as a promising solution, but their reliance on lithium-ion batteries introduces the critical challenge of battery degradation. Accurate prediction and forecasting of battery degradation over both short and long time spans are essential for optimizing performance, extending battery life, and ensuring effective long-term energy management. This directly influences the reliability, safety, and sustainability of EVs, supporting their widespread adoption and aligning with key UN SDGs. In this paper, we present a novel approach to the prediction and long-term forecasting of battery degradation using Scientific Machine Learning framework which integrates domain knowledge with neural networks, offering more interpretable and scientifically grounded solutions for both predicting short-term battery health and forecasting degradation over extended periods. This hybrid approach captures both known and unknown degradation dynamics, improving predictive accuracy while reducing data requirements. We incorporate ground-truth data to inform our models, ensuring that both the predictions and forecasts reflect practical conditions. The model achieved MSE of 9.90 with the UDE and 11.55 with the NeuralODE, in experimental data, a loss of 1.6986 with the UDE, and a MSE of 2.49 in the NeuralODE, demonstrating the enhanced precision of our approach. This integration of data-driven insights with SciML's strengths in interpretability and scalability allows for robust battery management. By enhancing battery longevity and minimizing waste, our approach contributes to the sustainability of energy systems and accelerates the global transition toward cleaner, more responsible energy solutions, aligning with the UN's SDG agenda.