Designing Compact Neural Architectures via Neuron Gating and Mixed Activation

Neural Architecture Search (NAS) is naturally formulated as a bilevel optimization problem, where the upper-level optimizes the architecture using validation performance and the lower-level trains network parameters using training loss. However, NAS is computationally expensive due to discrete architectural decisions, exponentially growing search spaces, and the high cost of training candidate architectures. This work develops a general bilevel optimization framework for NAS across diverse architectures, including MLPs, CNNs, RNNs, and Transformers, to identify compact architectures with strong predictive performance. We propose three scalable formulations that replace discrete neuron- and activation-level decisions with continuous relaxations, enabling differentiable optimization over otherwise combinatorial architecture spaces. These formulations give rise to three NAS methods: NAS based on Neuron Gating (NAS-NG), NAS based on Mixed Activation (NAS-MA), and NAS based on Neuron Gating and Mixed Activation (NAS-NGMA). Experiments on MLPs and CNNs using MNIST and CIFAR-10 show that the proposed methods consistently identify compact architectures with competitive or improved predictive performance. On MNIST, NAS-NGMA achieves 98.68% test accuracy with 7.69M MLP parameters, while NAS-NG achieves 99.63% accuracy with only 0.26M CNN parameters. On CIFAR-10, the proposed methods consistently outperform vanilla DARTS. Further experiments demonstrate that NAS-NG can optimize substantially over-parameterized and literature-optimal architectures, improving accuracy while reducing parameters. These results establish relaxed bilevel optimization as a scalable alternative to discrete NAS and provide a general framework for efficient neuron- and activation-level architecture optimization.

LP-NAS: Linear Programming-based Neural Architecture Search

Neural Architecture Search (NAS) aims to automate neural network architecture design, reducing reliance on human expertise. Among the various NAS methods, differentiable NAS has gained prominence due to its efficiency and accuracy compared to conventional NAS approaches. Since differentiable NAS relaxes the architecture search space into a continuous domain, it is possible to apply principles from continuous optimization to NAS. In this paper, we propose Linear Programming-based NAS (LP-NAS), a mathematical programming-based framework for differentiable NAS that is applicable to a wide range of continuous search spaces. LP-NAS formulates a linear program (LP) using the validation-loss gradient and the training-loss Hessian to compute an architecture update direction that improves generalization while preserving the optimality of the model parameters. By following this LP-derived descent direction, LP-NAS efficiently navigates the architecture search space, leading to faster and more effective architecture optimization. We introduce two computationally efficient variants of LP-NAS, namely S-LP-NAS and R-LP-NAS. Applying LP-NAS to the Differentiable Architecture Search (DARTS) search space results in two algorithmic variants, S-LP-DARTS and R-LP-DARTS. Both variants achieve faster convergence and significantly higher validation performance during the early search iterations than the standard DARTS algorithm. Extensive experiments on CIFAR-10 and CIFAR-100 show that LP-DARTS outperforms standard DARTS in both the architecture search and evaluation phases. Additionally, we compare our approach with several DARTS variants (P-DARTS, PC-DARTS, and STO-DARTS) on the CIFAR-10 dataset and demonstrate its effectiveness. Furthermore, we validate the transferability of the discovered architectures through experiments on the ImageNet dataset.

Bilevel Optimization for Neural Architecture Search

Bilevel optimization has become an influential and widely adopted framework for addressing hierarchical optimization problems in machine learning, providing an effective approach to modeling the interaction between two levels of optimization, with applications such as hyperparameter tuning, meta-learning, adversarial training, and data poisoning. Neural Architecture Search (NAS), a subfield of hyperparameter optimization, is a prime example of a bilevel optimization problem, with architecture parameters optimized at the outer-level and network weights optimized at the inner level. This paper presents a structured overview of NAS through the lens of bilevel optimization. We categorize existing NAS approaches into two main classes: sampling-based methods, which search optimal architectures using different architecture samplers, and bilevel theory-based methods, which solve the architecture search problem using bilevel optimization principles. We further highlight our current research direction, wherein the bilevel NAS formulation is addressed through an auxiliary mathematical programming framework. This framework enables the systematic integration of second-order information from the model's training loss function and ensures the optimality of the model parameters while modifying architecture parameters. By simultaneously updating the architecture and model parameters along their respective optimal descent directions derived from the auxiliary mathematical program, these methods achieve more principled and theoretically consistent results. The same auxiliary program can also be used for simultaneous hyperparameter and model fine-tuning. A comparative analysis shows that bilevel theory-based approaches generally outperform sampling-based methods, both in accuracy and efficiency.

LiFT: Local Search via Linear Programming for Overfitting-Controlled Transformers

This paper proposes a Linear Programming (LP)-based local search framework for fine-tuning pretrained transformer models with explicit control against overfitting. The approach formulates transformer fine-tuning as a bilevel optimization-based regularization problem, in which model parameters and regularization hyperparameters are jointly updated. Information collected during initial warm-up iterations, including validation gradients and training Hessian information, is used to construct a local descent direction by solving an LP that minimizes a scaled directional derivative while preserving training optimality. This validation-aware descent direction enables focused local updates of both parameters and regularization hyperparameters, reducing overfitting without requiring repeated full retraining cycles. The resulting method, termed Linear Programming-based Fine-Tuning (LiFT) for transformers, differs from conventional fine-tuning by systematically identifying task-specific updates rather than relying on heuristic or grid-based hyperparameter selection. Experiments on GPT-2 Small fine-tuned on WikiText-2 demonstrate that LiFT enables effective adaptation through selective tuning of transformer blocks and regularization parameters, yielding consistent improvements in test perplexity across multiple layer configurations and regularization settings, with particularly pronounced gains in overfitting-prone scenarios. Beyond empirical performance, LiFT establishes a principled connection between transformer fine-tuning, bilevel optimization, local search, and regularization theory.

Operator Calculus for Population-Based Optimization: A Mean-Field Convergence Theory

Population-based and distributional optimization methods, from evolution strategies and consensus-based optimization to covariance-matrix adaptation and stochastic gradient methods viewed as distributional dynamics, are widely used for nonconvex or black-box problems, yet their convergence analyses remain fragmented across algorithm-specific techniques. We introduce an operator calculus in which a broad class of such methods, after choosing an appropriate state space and, where necessary, augmenting the state by memory or strategy variables, is described as a composition of three elementary operators (mutation, selection, and recombination) acting on probability measures. Under explicit stability and regularity conditions, the composite operator admits a pre-generator whose continuous-time limit is a transport-reaction-jump (TRJ) PDE that preserves the operator splitting. On this foundation we establish a modular Lyapunov principle. If a state-space Lyapunov function both dissipates under the full generator and controls the relevant search-space gauges, then the state-space Lyapunov functional and the induced search errors decay exponentially. The additive generator structure allows dissipation estimates to be assembled operator by operator, providing a toolkit for certifying convergence of composite mean-field algorithms.

Predictive Hotspot Mapping for Data-driven Crime Prediction

Predictive hotspot mapping is an important problem in crime prediction and control. An accurate hotspot mapping helps in appropriately targeting the available resources to manage crime in cities. With an aim to make data-driven decisions and automate policing and patrolling operations, police departments across the world are moving towards predictive approaches relying on historical data. In this paper, we create a non-parametric model using a spatio-temporal kernel density formulation for the purpose of crime prediction based on historical data. The proposed approach is also able to incorporate expert inputs coming from humans through alternate sources. The approach has been extensively evaluated in a real-world setting by collaborating with the Delhi police department to make crime predictions that would help in effective assignment of patrol vehicles to control street crime. The results obtained in the paper are promising and can be easily applied in other settings. We release the algorithm and the dataset (masked) used in our study to support future research that will be useful in achieving further improvements.

Decomposition of Difficulties in Complex Optimization Problems Using a Bilevel Approach

Practical optimization problems may contain different kinds of difficulties that are often not tractable if one relies on a particular optimization method. Different optimization approaches offer different strengths that are good at tackling one or more difficulty in an optimization problem. For instance, evolutionary algorithms have a niche in handling complexities like discontinuity, non-differentiability, discreteness and non-convexity. However, evolutionary algorithms may get computationally expensive for mathematically well behaved problems with large number of variables for which classical mathematical programming approaches are better suited. In this paper, we demonstrate a decomposition strategy that allows us to synergistically apply two complementary approaches at the same time on a complex optimization problem. Evolutionary algorithms are useful in this context as their flexibility makes pairing with other solution approaches easy. The decomposition idea is a special case of bilevel optimization that separates the difficulties into two levels and assigns different approaches at each level that is better equipped at handling them. We demonstrate the benefits of the proposed decomposition idea on a wide range of test problems.

A Linear Programming Enhanced Genetic Algorithm for Hyperparameter Tuning in Machine Learning

In this paper, we formulate the hyperparameter tuning problem in machine learning as a bilevel program. The bilevel program is solved using a micro genetic algorithm that is enhanced with a linear program. While the genetic algorithm searches over discrete hyperparameters, the linear program enhancement allows hyper local search over continuous hyperparameters. The major contribution in this paper is the formulation of a linear program that supports fast search over continuous hyperparameters, and can be integrated with any hyperparameter search technique. It can also be applied directly on any trained machine learning or deep learning model for the purpose of fine-tuning. We test the performance of the proposed approach on two datasets, MNIST and CIFAR-10. Our results clearly demonstrate that using the linear program enhancement offers significant promise when incorporated with any population-based approach for hyperparameter tuning.

SEntFiN 1.0: Entity-Aware Sentiment Analysis for Financial News

Fine-grained financial sentiment analysis on news headlines is a challenging task requiring human-annotated datasets to achieve high performance. Limited studies have tried to address the sentiment extraction task in a setting where multiple entities are present in a news headline. In an effort to further research in this area, we make publicly available SEntFiN 1.0, a human-annotated dataset of 10,753 news headlines with entity-sentiment annotations, of which 2,847 headlines contain multiple entities, often with conflicting sentiments. We augment our dataset with a database of over 1,000 financial entities and their various representations in news media amounting to over 5,000 phrases. We propose a framework that enables the extraction of entity-relevant sentiments using a feature-based approach rather than an expression-based approach. For sentiment extraction, we utilize 12 different learning schemes utilizing lexicon-based and pre-trained sentence representations and five classification approaches. Our experiments indicate that lexicon-based n-gram ensembles are above par with pre-trained word embedding schemes such as GloVe. Overall, RoBERTa and finBERT (domain-specific BERT) achieve the highest average accuracy of 94.29% and F1-score of 93.27%. Further, using over 210,000 entity-sentiment predictions, we validate the economic effect of sentiments on aggregate market movements over a long duration.

A Globally Convergent Gradient-based Bilevel Hyperparameter Optimization Method

Hyperparameter optimization in machine learning is often achieved using naive techniques that only lead to an approximate set of hyperparameters. Although techniques such as Bayesian optimization perform an intelligent search on a given domain of hyperparameters, it does not guarantee an optimal solution. A major drawback of most of these approaches is an exponential increase of their search domain with number of hyperparameters, increasing the computational cost and making the approaches slow. The hyperparameter optimization problem is inherently a bilevel optimization task, and some studies have attempted bilevel solution methodologies for solving this problem. However, these studies assume a unique set of model weights that minimize the training loss, which is generally violated by deep learning architectures. This paper discusses a gradient-based bilevel method addressing these drawbacks for solving the hyperparameter optimization problem. The proposed method can handle continuous hyperparameters for which we have chosen the regularization hyperparameter in our experiments. The method guarantees convergence to the set of optimal hyperparameters that this study has theoretically proven. The idea is based on approximating the lower-level optimal value function using Gaussian process regression. As a result, the bilevel problem is reduced to a single level constrained optimization task that is solved using the augmented Lagrangian method. We have performed an extensive computational study on the MNIST and CIFAR-10 datasets on multi-layer perceptron and LeNet architectures that confirms the efficiency of the proposed method. A comparative study against grid search, random search, Bayesian optimization, and HyberBand method on various hyperparameter problems shows that the proposed algorithm converges with lower computation and leads to models that generalize better on the testing set.