arXiv subjects

Mehul Motani

Publications and source records attributed to Mehul Motani.

At least 19 recordsLinked to original sources

arXiv2026

Analysis of Memory-Runtime Trade-offs in Caching Strategies for Genetic Programming Symbolic Regression

Genetic Programming Symbolic Regression (GPSR) generates mathematical expressions to model input-output relationships using an evolutionary process. A significant challenge in GPSR lies in the repeated evaluation of entire expressions or their sub-expression, which inflates computational runtime. To address this inefficiency, caching mechanisms have been employed to reduce redundant computations. However, prior studies predominantly employ a single caching strategy, offering limited insights into their comparative performance or memory-runtime trade-offs. In this paper, we present a comprehensive analysis of caching mechanisms for GPSR on synthetic and real-world datasets. We also include an empirical study of key-value usage frequencies under an infinitely large cache, offering insights into optimal cache sizing. Furthermore, we provide actionable guidelines for configuring caching strategies based on computational and memory constraints. Our findings indicate that complex caching mechanisms necessitate a minimum cache size to achieve computational time reductions. Conversely, lightweight caching strategies, such as Least Recently Used (LRU) and, notably, First-In-First-Out (FIFO), can significantly decrease computation time for fitness evaluations, which are a substantial component of the overall runtime.

cs.NE↗

arXiv2026

On the effectiveness of reward functions in reinforcement learning for confidence calibration of large language models

In this paper, we consider the setting where large language models (LLMs) are trained using reinforcement learning (RL) to simultaneously improve reasoning accuracy and verbalize its confidence. Our reward scheme uses two functions for rewarding confidence verbalized by the LLM: one when the LLM is correct and a different one when the LLM is incorrect. With a poorly designed reward scheme, the LLM may be incentivized to answer incorrectly so that it can be confident that its answer is indeed incorrect, a phenomenon that we call confidence reward hacking. We propose the concept of non-hackable confidence reward schemes and define a spectrum of such reward schemes for RL confidence calibration training in LLMs. We demonstrate that selective confidence reward hacking can occur in practical datasets with reward schemes that are not designed to be non-hackable. We also demonstrate that the reward scheme with the best calibration to accuracy tradeoff depends on the dataset and the application, and propose using the reward scheme as a hyperparameter to optimize the tradeoffs in accordance to what is important for the application. The code of our experiments is available in https://anonymous.4open.science/r/rl-confidence-calibration-9ED4/README.md.

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arXiv2026

Age of Information under Source-Aware Truncated ARQ in Multi-Source Wireless Status Updating

This paper studies information timeliness in multi-source wireless Internet of Things (IoT) status updating systems under a truncated Automatic Repeat reQuest (ARQ) protocol. We propose a source-aware truncated ARQ (SATARQ) scheme that allows differentiated maximum transmission times (MTTs) tailored to different sources. This work focuses on a wireless system with preemptive update management. To study the statistical characteristics of the age of information (AoI) process for each source, a multi-dimensional age process (MDAP) is developed and modeled as a Markov chain, tracking both the AoI and the age of the concerned source's update currently in transmission. Via Markov analysis of the MDAP, we obtain analytical expressions for the distributions and averages of the AoI and peak AoI, as well as the average power consumption of IoT device. The timeliness-energy tradeoff is analyzed by examining the impact of the MTT, update generation probability (UGP), and wireless transmission power (TP). Moreover, this work explores the energy efficiency of the wireless status updating process and its relationship with the information timeliness and energy cost. Numerical results validate the theoretical analysis. Finally, it is demonstrated that the proposed SATARQ, combined with the optimization of MTTs, UGPs, and TPs, significantly improves the overall timeliness-energy tradeoff and energy efficiency across all sources.

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arXiv2025

Tab-PET: Graph-Based Positional Encodings for Tabular Transformers

Supervised learning with tabular data presents unique challenges, including low data sizes, the absence of structural cues, and heterogeneous features spanning both categorical and continuous domains. Unlike vision and language tasks, where models can exploit inductive biases in the data, tabular data lacks inherent positional structure, hindering the effectiveness of self-attention mechanisms. While recent transformer-based models like TabTransformer, SAINT, and FT-Transformer (which we refer to as 3T) have shown promise on tabular data, they typically operate without leveraging structural cues such as positional encodings (PEs), as no prior structural information is usually available. In this work, we find both theoretically and empirically that structural cues, specifically PEs can be a useful tool to improve generalization performance for tabular transformers. We find that PEs impart the ability to reduce the effective rank (a form of intrinsic dimensionality) of the features, effectively simplifying the task by reducing the dimensionality of the problem, yielding improved generalization. To that end, we propose Tab-PET (PEs for Tabular Transformers), a graph-based framework for estimating and inculcating PEs into embeddings. Inspired by approaches that derive PEs from graph topology, we explore two paradigms for graph estimation: association-based and causality-based. We empirically demonstrate that graph-derived PEs significantly improve performance across 50 classification and regression datasets for 3T. Notably, association-based graphs consistently yield more stable and pronounced gains compared to causality-driven ones. Our work highlights an unexpected role of PEs in tabular transformers, revealing how they can be harnessed to improve generalization.

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arXiv2025

Absorbing Markov Chain-Based Analysis of Age of Information in Discrete-Time Dual-Queue Systems

Status update systems require the timely collection of sensing information for which deploying multiple sensors/servers to obtain diversity gains is considered as a promising solution. In this work, we construct an absorbing Markov chain (AMC) to exactly model Age of Information (AoI) in a discretetime dual-queue (DTDQ) status update system with generate at will (GAW) status updates, discrete phase-type (DPH-type) distributed service times and transmission freezing. Specifically, transmission is frozen for a certain number of slots following the initiation of a transmission, after which one of the two servers is allowed to simultaneously sample the monitored physical process and transmit a status update packet, according to the availabilities and priorities of the two servers. Based on the discrete-time AMC, we provide the exact distributions of both AoI and peak AoI (PAoI), enabling the derivation of arbitrary order moments. In addition, we analytically study the role of freezing using several typical service time distributions, including geometric, uniform, and triangular distributions. The introduction of freezing for DTDQ systems is demonstrated to be significantly beneficial in reducing the mean AoI for various service time distributions. Additionally, we study the impact of the statistical parameters of the service times and heterogeneity between the two servers on the freezing gain, i.e., reduction in mean AoI attained with optimum freezing policies.

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arXiv2025

Teaching the Teacher: The Role of Teacher-Student Smoothness Alignment in Genetic Programming-based Symbolic Distillation

Obtaining human-readable symbolic formulas via genetic programming-based symbolic distillation of a deep neural network trained on the target dataset presents a promising yet underexplored path towards explainable artificial intelligence (XAI); however, the standard pipeline frequently yields symbolic models with poor predictive accuracy. We identify a fundamental misalignment in functional complexity as the primary barrier to achieving better accuracy: standard Artificial Neural Networks (ANNs) often learn accurate but highly irregular functions, while Symbolic Regression typically prioritizes parsimony, often resulting in a much simpler class of models that are unable to sufficiently distill or learn from the ANN teacher. To bridge this gap, we propose a framework that actively regularizes the teacher's functional smoothness using Jacobian and Lipschitz penalties, aiming to distill better student models than the standard pipeline. We characterize the trade-off between predictive accuracy and functional complexity through a robust study involving 20 datasets and 50 independent trials. Our results demonstrate that students distilled from smoothness-regularized teachers achieve statistically significant improvements in R^2 scores, compared to the standard pipeline. We also perform ablation studies on the student model algorithm. Our findings suggest that smoothness alignment between teacher and student models is a critical factor for symbolic distillation.

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arXiv2024

The Dispersion of Broadcast Channels With Degraded Message Sets Using Gaussian Codebooks

We study the two-user broadcast channel with degraded message sets and derive second-order achievability rate regions. Specifically, the channel noises are not necessarily Gaussian and we use spherical codebooks for both users. The weak user with worse channel quality applies nearest neighbor decoding by treating the signal of the other user as interference. For the strong user with better channel quality, we consider two decoding schemes: successive interference cancellation (SIC) decoding and joint nearest neighbor (JNN) decoding. We adopt two performance criteria: separate error probabilities (SEP) and joint error probability (JEP). Counterintuitively, the second-order achievable rate regions under both SIC and JNN decoding are identical although JNN decoding usually yields better performance in other multiterminal problems with Gaussian noise. Furthermore, we generalize our results to the case with quasi-static fading and show that the asymptotic notion of outage capacity region is an accurate performance measure even at finite blocklengths.

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arXiv2024

TaskGen: A Task-Based, Memory-Infused Agentic Framework using StrictJSON

TaskGen is an open-sourced agentic framework which uses an Agent to solve an arbitrary task by breaking them down into subtasks. Each subtask is mapped to an Equipped Function or another Agent to execute. In order to reduce verbosity (and hence token usage), TaskGen uses StrictJSON that ensures JSON output from the Large Language Model (LLM), along with additional features such as type checking and iterative error correction. Key to the philosophy of TaskGen is the management of information/memory on a need-to-know basis. We empirically evaluate TaskGen on various environments such as 40x40 dynamic maze navigation with changing obstacle locations (100% solve rate), TextWorld escape room solving with dense rewards and detailed goals (96% solve rate), web browsing (69% of actions successful), solving the MATH dataset (71% solve rate over 100 Level-5 problems), Retrieval Augmented Generation on NaturalQuestions dataset (F1 score of 47.03%)

cs.AI↗

arXiv2023

Large Language Model (LLM) as a System of Multiple Expert Agents: An Approach to solve the Abstraction and Reasoning Corpus (ARC) Challenge

We attempt to solve the Abstraction and Reasoning Corpus (ARC) Challenge using Large Language Models (LLMs) as a system of multiple expert agents. Using the flexibility of LLMs to be prompted to do various novel tasks using zero-shot, few-shot, context-grounded prompting, we explore the feasibility of using LLMs to solve the ARC Challenge. We firstly convert the input image into multiple suitable text-based abstraction spaces. We then utilise the associative power of LLMs to derive the input-output relationship and map this to actions in the form of a working program, similar to Voyager / Ghost in the MineCraft. In addition, we use iterative environmental feedback in order to guide LLMs to solve the task. Our proposed approach achieves 50 solves out of 111 training set problems (45%) with just three abstraction spaces - grid, object and pixel - and we believe that with more abstraction spaces and learnable actions, we will be able to solve more.

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arXiv2023

Local Intrinsic Dimensional Entropy

Most entropy measures depend on the spread of the probability distribution over the sample space $\mathcal{X}$, and the maximum entropy achievable scales proportionately with the sample space cardinality $|\mathcal{X}|$. For a finite $|\mathcal{X}|$, this yields robust entropy measures which satisfy many important properties, such as invariance to bijections, while the same is not true for continuous spaces (where $|\mathcal{X}|=\infty$). Furthermore, since $\mathbb{R}$ and $\mathbb{R}^d$ ($d\in \mathbb{Z}^+$) have the same cardinality (from Cantor's correspondence argument), cardinality-dependent entropy measures cannot encode the data dimensionality. In this work, we question the role of cardinality and distribution spread in defining entropy measures for continuous spaces, which can undergo multiple rounds of transformations and distortions, e.g., in neural networks. We find that the average value of the local intrinsic dimension of a distribution, denoted as ID-Entropy, can serve as a robust entropy measure for continuous spaces, while capturing the data dimensionality. We find that ID-Entropy satisfies many desirable properties and can be extended to conditional entropy, joint entropy and mutual-information variants. ID-Entropy also yields new information bottleneck principles and also links to causality. In the context of deep learning, for feedforward architectures, we show, theoretically and empirically, that the ID-Entropy of a hidden layer directly controls the generalization gap for both classifiers and auto-encoders, when the target function is Lipschitz continuous. Our work primarily shows that, for continuous spaces, taking a structural rather than a statistical approach yields entropy measures which preserve intrinsic data dimensionality, while being relevant for studying various architectures.

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arXiv2023

Learning, Fast and Slow: A Goal-Directed Memory-Based Approach for Dynamic Environments

Model-based next state prediction and state value prediction are slow to converge. To address these challenges, we do the following: i) Instead of a neural network, we do model-based planning using a parallel memory retrieval system (which we term the slow mechanism); ii) Instead of learning state values, we guide the agent's actions using goal-directed exploration, by using a neural network to choose the next action given the current state and the goal state (which we term the fast mechanism). The goal-directed exploration is trained online using hippocampal replay of visited states and future imagined states every single time step, leading to fast and efficient training. Empirical studies show that our proposed method has a 92% solve rate across 100 episodes in a dynamically changing grid world, significantly outperforming state-of-the-art actor critic mechanisms such as PPO (54%), TRPO (50%) and A2C (24%). Ablation studies demonstrate that both mechanisms are crucial. We posit that the future of Reinforcement Learning (RL) will be to model goals and sub-goals for various tasks, and plan it out in a goal-directed memory-based approach.

cs.AI↗

arXiv2023

On Finite Blocklength Lossy Source Coding

In this monograph, we review recent advances in second-order asymptotics for lossy source coding, which provides approximations to the finite blocklength performance of optimal codes. The monograph is divided into three parts. In part I, we motivate the monograph, present basic definitions, introduce mathematical tools and illustrate the motivation of non-asymptotic and second-order asymptotics via the example of lossless source coding. In part II, we first present existing results for the rate-distortion problem with proof sketches. Subsequently, we present five generations of the rate-distortion problem to tackle various aspects of practical quantization tasks: noisy source, noisy channel, mismatched code, Gauss-Markov source and fixed-to-variable length compression. By presenting theoretical bounds for these settings, we illustrate the effect of noisy observation of the source, the influence of noisy transmission of the compressed information, the effect of using a fixed coding scheme for an arbitrary source and the roles of source memory and variable rate. In part III, we present four multiterminal generalizations of the rate-distortion problem to consider multiple encoders, decoders or source sequences: the Kaspi problem, the successive refinement problem, the Fu-Yeung problem and the Gray-Wyner problem. By presenting theoretical bounds for these multiterminal problems, we illustrate the role of side information, the optimality of stop and transmit, the effect of simultaneous lossless and lossy compression, and the tradeoff between encoders' rates in compressing correlated sources. Finally, we conclude the monograph, mention related results and discuss future directions.

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arXiv2022

Optimizing Learning Rate Schedules for Iterative Pruning of Deep Neural Networks

The importance of learning rate (LR) schedules on network pruning has been observed in a few recent works. As an example, Frankle and Carbin (2019) highlighted that winning tickets (i.e., accuracy preserving subnetworks) can not be found without applying a LR warmup schedule and Renda, Frankle and Carbin (2020) demonstrated that rewinding the LR to its initial state at the end of each pruning cycle improves performance. In this paper, we go one step further by first providing a theoretical justification for the surprising effect of LR schedules. Next, we propose a LR schedule for network pruning called SILO, which stands for S-shaped Improved Learning rate Optimization. The advantages of SILO over existing state-of-the-art (SOTA) LR schedules are two-fold: (i) SILO has a strong theoretical motivation and dynamically adjusts the LR during pruning to improve generalization. Specifically, SILO increases the LR upper bound (max_lr) in an S-shape. This leads to an improvement of 2% - 4% in extensive experiments with various types of networks (e.g., Vision Transformers, ResNet) on popular datasets such as ImageNet, CIFAR-10/100. (ii) In addition to the strong theoretical motivation, SILO is empirically optimal in the sense of matching an Oracle, which exhaustively searches for the optimal value of max_lr via grid search. We find that SILO is able to precisely adjust the value of max_lr to be within the Oracle optimized interval, resulting in performance competitive with the Oracle with significantly lower complexity.

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arXiv2022

Improving Mutual Information based Feature Selection by Boosting Unique Relevance

Mutual Information (MI) based feature selection makes use of MI to evaluate each feature and eventually shortlists a relevant feature subset, in order to address issues associated with high-dimensional datasets. Despite the effectiveness of MI in feature selection, we notice that many state-of-the-art algorithms disregard the so-called unique relevance (UR) of features, and arrive at a suboptimal selected feature subset which contains a non-negligible number of redundant features. We point out that the heart of the problem is that all these MIBFS algorithms follow the criterion of Maximize Relevance with Minimum Redundancy (MRwMR), which does not explicitly target UR. This motivates us to augment the existing criterion with the objective of boosting unique relevance (BUR), leading to a new criterion called MRwMR-BUR. Depending on the task being addressed, MRwMR-BUR has two variants, termed MRwMR-BUR-KSG and MRwMR-BUR-CLF, which estimate UR differently. MRwMR-BUR-KSG estimates UR via a nearest-neighbor based approach called the KSG estimator and is designed for three major tasks: (i) Classification Performance. (ii) Feature Interpretability. (iii) Classifier Generalization. MRwMR-BUR-CLF estimates UR via a classifier based approach. It adapts UR to different classifiers, further improving the competitiveness of MRwMR-BUR for classification performance oriented tasks. The performance of both MRwMR-BUR-KSG and MRwMR-BUR-CLF is validated via experiments using six public datasets and three popular classifiers. Specifically, as compared to MRwMR, the proposed MRwMR-BUR-KSG improves the test accuracy by 2% - 3% with 25% - 30% fewer features being selected, without increasing the algorithm complexity. MRwMR-BUR-CLF further improves the classification performance by 3.8%- 5.5% (relative to MRwMR), and it also outperforms three popular classifier dependent feature selection methods.

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arXiv2022

Towards Better Long-range Time Series Forecasting using Generative Forecasting

Long-range time series forecasting is usually based on one of two existing forecasting strategies: Direct Forecasting and Iterative Forecasting, where the former provides low bias, high variance forecasts and the latter leads to low variance, high bias forecasts. In this paper, we propose a new forecasting strategy called Generative Forecasting (GenF), which generates synthetic data for the next few time steps and then makes long-range forecasts based on generated and observed data. We theoretically prove that GenF is able to better balance the forecasting variance and bias, leading to a much smaller forecasting error. We implement GenF via three components: (i) a novel conditional Wasserstein Generative Adversarial Network (GAN) based generator for synthetic time series data generation, called CWGAN-TS. (ii) a transformer based predictor, which makes long-range predictions using both generated and observed data. (iii) an information theoretic clustering algorithm to improve the training of both the CWGAN-TS and the transformer based predictor. The experimental results on five public datasets demonstrate that GenF significantly outperforms a diverse range of state-of-the-art benchmarks and classical approaches. Specifically, we find a 5% - 11% improvement in predictive performance (mean absolute error) while having a 15% - 50% reduction in parameters compared to the benchmarks. Lastly, we conduct an ablation study to further explore and demonstrate the effectiveness of the components comprising GenF.

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arXiv2022

AP: Selective Activation for De-sparsifying Pruned Neural Networks

The rectified linear unit (ReLU) is a highly successful activation function in neural networks as it allows networks to easily obtain sparse representations, which reduces overfitting in overparameterized networks. However, in network pruning, we find that the sparsity introduced by ReLU, which we quantify by a term called dynamic dead neuron rate (DNR), is not beneficial for the pruned network. Interestingly, the more the network is pruned, the smaller the dynamic DNR becomes during optimization. This motivates us to propose a method to explicitly reduce the dynamic DNR for the pruned network, i.e., de-sparsify the network. We refer to our method as Activating-while-Pruning (AP). We note that AP does not function as a stand-alone method, as it does not evaluate the importance of weights. Instead, it works in tandem with existing pruning methods and aims to improve their performance by selective activation of nodes to reduce the dynamic DNR. We conduct extensive experiments using popular networks (e.g., ResNet, VGG) via two classical and three state-of-the-art pruning methods. The experimental results on public datasets (e.g., CIFAR-10/100) suggest that AP works well with existing pruning methods and improves the performance by 3% - 4%. For larger scale datasets (e.g., ImageNet) and state-of-the-art networks (e.g., vision transformer), we observe an improvement of 2% - 3% with AP as opposed to without. Lastly, we conduct an ablation study to examine the effectiveness of the components comprising AP.

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arXiv2022

Achieving Low Complexity Neural Decoders via Iterative Pruning

The advancement of deep learning has led to the development of neural decoders for low latency communications. However, neural decoders can be very complex which can lead to increased computation and latency. We consider iterative pruning approaches (such as the lottery ticket hypothesis algorithm) to prune weights in neural decoders. Decoders with fewer number of weights can have lower latency and lower complexity while retaining the accuracy of the original model. This will make neural decoders more suitable for mobile and other edge devices with limited computational power. We also propose semi-soft decision decoding for neural decoders which can be used to improve the bit error rate performance of the pruned network.

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arXiv2022

Towards Better Long-range Time Series Forecasting using Generative Adversarial Networks

Long-range time series forecasting is usually based on one of two existing forecasting strategies: Direct Forecasting and Iterative Forecasting, where the former provides low bias, high variance forecasts and the later leads to low variance, high bias forecasts. In this paper, we propose a new forecasting strategy called Generative Forecasting (GenF), which generates synthetic data for the next few time steps and then makes long-range forecasts based on generated and observed data. We theoretically prove that GenF is able to better balance the forecasting variance and bias, leading to a much smaller forecasting error. We implement GenF via three components: (i) a novel conditional Wasserstein Generative Adversarial Network (GAN) based generator for synthetic time series data generation, called CWGAN-TS. (ii) a transformer based predictor, which makes long-range predictions using both generated and observed data. (iii) an information theoretic clustering algorithm to improve the training of both the CWGAN-TS and the transformer based predictor. The experimental results on five public datasets demonstrate that GenF significantly outperforms a diverse range of state-of-the-art benchmarks and classical approaches. Specifically, we find a 5% - 11% improvement in predictive performance (mean absolute error) while having a 15% - 50% reduction in parameters compared to the benchmarks. Lastly, we conduct an ablation study to demonstrate the effectiveness of the components comprising GenF.

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