Sahil Sidheekh

Sahil Sidheekh, Chris B. Dock, Tushar Jain et al.

Normalizing flows provide an elegant approach to generative modeling that allows for efficient sampling and exact density evaluation of unknown data distributions. However, current techniques have significant limitations in their expressivity when the data distribution is supported on a low-dimensional manifold or has a non-trivial topology. We introduce a novel statistical framework for learning a mixture of local normalizing flows as "chart maps" over the data manifold. Our framework augments the expressivity of recent approaches while preserving the signature property of normalizing flows, that they admit exact density evaluation. We learn a suitable atlas of charts for the data manifold via a vector quantized auto-encoder (VQ-AE) and the distributions over them using a conditional flow. We validate experimentally that our probabilistic framework enables existing approaches to better model data distributions over complex manifolds.

Sahil Sidheekh, Sriraam Natarajan

Probabilistic circuits (PCs) enable exact and tractable inference but employ data independent mixture weights that limit their ability to capture local geometry of the data manifold. We propose Voronoi tessellations (VT) as a natural way to incorporate geometric structure directly into the sum nodes of a PC. However, naïvely introducing such structure breaks tractability. We formalize this incompatibility and develop two complementary solutions: (1) an approximate inference framework that provides guaranteed lower and upper bounds for inference, and (2) a structural condition for VT under which exact tractable inference is recovered. Finally, we introduce a differentiable relaxation for VT that enables gradient-based learning and empirically validate the resulting approach on standard density estimation tasks.

Pranuthi Tenali, Sahil Sidheekh, Saurabh Mathur et al.

Multimodal fusion requires integrating information from multiple sources that may conflict depending on context. Existing fusion approaches typically rely on static assumptions about source reliability, limiting their ability to resolve conflicts when a modality becomes unreliable due to situational factors such as sensor degradation or class-specific corruption. We introduce C$^2$MF, a context-specfic credibility-aware multimodal fusion framework that models per-instance source reliability using a Conditional Probabilistic Circuit (CPC). We formalize instance-level reliability through Context-Specific Information Credibility (CSIC), a KL-divergence-based measure computed exactly from the CPC. CSIC generalizes conventional static credibility estimates as a special case, enabling principled and adaptive reliability assessment. To evaluate robustness under cross-modal conflicts, we propose the Conflict benchmark, in which class-specific corruptions deliberately induce discrepancies between different modalities. Experimental results show that C$^2$MF improves predictive accuracy by up to 29% over static-reliability baselines in high-noise settings, while preserving the interpretability advantages of probabilistic circuit-based fusion.

Sahil Sidheekh, Sriraam Natarajan

We present a comprehensive survey of the advancements and techniques in the field of tractable probabilistic generative modeling, primarily focusing on Probabilistic Circuits (PCs). We provide a unified perspective on the inherent trade-offs between expressivity and tractability, highlighting the design principles and algorithmic extensions that have enabled building expressive and efficient PCs, and provide a taxonomy of the field. We also discuss recent efforts to build deep and hybrid PCs by fusing notions from deep neural models, and outline the challenges and open questions that can guide future research in this evolving field.

Sahil Sidheekh, Pranuthi Tenali, Saurabh Mathur et al.

We consider the problem of late multi-modal fusion for discriminative learning. Motivated by noisy, multi-source domains that require understanding the reliability of each data source, we explore the notion of credibility in the context of multi-modal fusion. We propose a combination function that uses probabilistic circuits (PCs) to combine predictive distributions over individual modalities. We also define a probabilistic measure to evaluate the credibility of each modality via inference queries over the PC. Our experimental evaluation demonstrates that our fusion method can reliably infer credibility while maintaining competitive performance with the state-of-the-art.

Athresh Karanam, Saurabh Mathur, Sahil Sidheekh et al.

Probabilistic Circuits (PCs) have emerged as an efficient framework for representing and learning complex probability distributions. Nevertheless, the existing body of research on PCs predominantly concentrates on data-driven parameter learning, often neglecting the potential of knowledge-intensive learning, a particular issue in data-scarce/knowledge-rich domains such as healthcare. To bridge this gap, we propose a novel unified framework that can systematically integrate diverse domain knowledge into the parameter learning process of PCs. Experiments on several benchmarks as well as real world datasets show that our proposed framework can both effectively and efficiently leverage domain knowledge to achieve superior performance compared to purely data-driven learning approaches.

Fateme Golivand Darvishvand, Hikaru Shindo, Sahil Sidheekh et al.

Reinforcement learning (RL) has experienced a second wind in the past decade. While incredibly successful in images and videos, these systems still operate within the realm of propositional tasks ignoring the inherent structure that exists in the problem. Consequently, relational extensions (RRL) have been developed for such structured problems that allow for effective generalization to arbitrary number of objects. However, they inherently make strong assumptions about the problem structure. We introduce a novel framework that combines RRL with object-centric representation to handle both structured and unstructured data. We enhance learning by allowing the system to actively query the human expert for guidance by explicitly modeling the uncertainty over the policy. Our empirical evaluation demonstrates the effectiveness and efficiency of our proposed approach.

Hrithik Suresh, Sahil Sidheekh, Vishnu Shreeram M. P et al.

Probabilistic Circuits (PCs) are a class of generative models that allow exact and tractable inference for a wide range of queries. While recent developments have enabled the learning of deep and expressive PCs, this increased capacity can often lead to overfitting, especially when data is limited. We analyze PC overfitting from a log-likelihood-landscape perspective and show that it is often caused by convergence to sharp optima that generalize poorly. Inspired by sharpness aware minimization in neural networks, we propose a Hessian-based regularizer for training PCs. As a key contribution, we show that the trace of the Hessian of the log-likelihood-a sharpness proxy that is typically intractable in deep neural networks-can be computed efficiently for PCs. Minimizing this Hessian trace induces a gradient-norm-based regularizer that yields simple closed-form parameter updates for EM, and integrates seamlessly with gradient based learning methods. Experiments on synthetic and real-world datasets demonstrate that our method consistently guides PCs toward flatter minima, improves generalization performance.

Steven Braun, Sahil Sidheekh, Antonio Vergari et al.

Probabilistic circuits (PCs) are powerful probabilistic models that enable exact and tractable inference, making them highly suitable for probabilistic reasoning and inference tasks. While dominant in neural networks, representation learning with PCs remains underexplored, with prior approaches relying on external neural embeddings or activation-based encodings. To address this gap, we introduce autoencoding probabilistic circuits (APCs), a novel framework leveraging the tractability of PCs to model probabilistic embeddings explicitly. APCs extend PCs by jointly modeling data and embeddings, obtaining embedding representations through tractable probabilistic inference. The PC encoder allows the framework to natively handle arbitrary missing data and is seamlessly integrated with a neural decoder in a hybrid, end-to-end trainable architecture enabled by differentiable sampling. Our empirical evaluation demonstrates that APCs outperform existing PC-based autoencoding methods in reconstruction quality, generate embeddings competitive with, and exhibit superior robustness in handling missing data compared to neural autoencoders. These results highlight APCs as a powerful and flexible representation learning method that exploits the probabilistic inference capabilities of PCs, showing promising directions for robust inference, out-of-distribution detection, and knowledge distillation.

Aroof Aimen, Sahil Sidheekh, Narayanan C. Krishnan

Meta-learning (ML) has emerged as a promising direction in learning models under constrained resource settings like few-shot learning. The popular approaches for ML either learn a generalizable initial model or a generic parametric optimizer through episodic training. The former approaches leverage the knowledge from a batch of tasks to learn an optimal prior. In this work, we study the importance of a batch for ML. Specifically, we first incorporate a batch episodic training regimen to improve the learning of the generic parametric optimizer. We also hypothesize that the common assumption in batch episodic training that each task in a batch has an equal contribution to learning an optimal meta-model need not be true. We propose to weight the tasks in a batch according to their "importance" in improving the meta-model's learning. To this end, we introduce a training curriculum motivated by selective focus in humans, called task attended meta-training, to weight the tasks in a batch. Task attention is a standalone module that can be integrated with any batch episodic training regimen. The comparisons of the models with their non-task-attended counterparts on complex datasets like miniImageNet and tieredImageNet validate its effectiveness.

Sahil Sidheekh, Aroof Aimen, Narayanan C. Krishnan

Despite the accomplishments of Generative Adversarial Networks (GANs) in modeling data distributions, training them remains a challenging task. A contributing factor to this difficulty is the non-intuitive nature of the GAN loss curves, which necessitates a subjective evaluation of the generated output to infer training progress. Recently, motivated by game theory, duality gap has been proposed as a domain agnostic measure to monitor GAN training. However, it is restricted to the setting when the GAN converges to a Nash equilibrium. But GANs need not always converge to a Nash equilibrium to model the data distribution. In this work, we extend the notion of duality gap to proximal duality gap that is applicable to the general context of training GANs where Nash equilibria may not exist. We show theoretically that the proximal duality gap is capable of monitoring the convergence of GANs to a wider spectrum of equilibria that subsumes Nash equilibria. We also theoretically establish the relationship between the proximal duality gap and the divergence between the real and generated data distributions for different GAN formulations. Our results provide new insights into the nature of GAN convergence. Finally, we validate experimentally the usefulness of proximal duality gap for monitoring and influencing GAN training.

Aroof Aimen, Sahil Sidheekh, Vineet Madan et al.

Meta-learning (ML) has emerged as a promising learning method under resource constraints such as few-shot learning. ML approaches typically propose a methodology to learn generalizable models. In this work-in-progress paper, we put the recent ML approaches to a stress test to discover their limitations. Precisely, we measure the performance of ML approaches for few-shot learning against increasing task complexity. Our results show a quick degradation in the performance of initialization strategies for ML (MAML, TAML, and MetaSGD), while surprisingly, approaches that use an optimization strategy (MetaLSTM) perform significantly better. We further demonstrate the effectiveness of an optimization strategy for ML (MetaLSTM++) trained in a MAML manner over a pure optimization strategy. Our experiments also show that the optimization strategies for ML achieve higher transferability from simple to complex tasks.

Sahil Sidheekh

The availability of large amounts of data and compelling computation power have made deep learning models much popular for text classification and sentiment analysis. Deep neural networks have achieved competitive performance on the above tasks when trained on naive text representations such as word count, term frequency, and binary matrix embeddings. However, many of the above representations result in the input space having a dimension of the order of the vocabulary size, which is enormous. This leads to a blow-up in the number of parameters to be learned, and the computational cost becomes infeasible when scaling to domains that require retaining a colossal vocabulary. This work proposes using singular value decomposition to transform the high dimensional input space to a lower-dimensional latent space. We show that neural networks trained on this lower-dimensional space are not only able to retain performance while savoring significant reduction in the computational complexity but, in many situations, also outperforms the classical neural networks trained on the native input space.

Sahil Sidheekh, Aroof Aimen, Vineet Madan et al.

Generative adversarial network (GAN) is among the most popular deep learning models for learning complex data distributions. However, training a GAN is known to be a challenging task. This is often attributed to the lack of correlation between the training progress and the trajectory of the generator and discriminator losses and the need for the GAN's subjective evaluation. A recently proposed measure inspired by game theory - the duality gap, aims to bridge this gap. However, as we demonstrate, the duality gap's capability remains constrained due to limitations posed by its estimation process. This paper presents a theoretical understanding of this limitation and proposes a more dependable estimation process for the duality gap. At the crux of our approach is the idea that local perturbations can help agents in a zero-sum game escape non-Nash saddle points efficiently. Through exhaustive experimentation across GAN models and datasets, we establish the efficacy of our approach in capturing the GAN training progress with minimal increase to the computational complexity. Further, we show that our estimate, with its ability to identify model convergence/divergence, is a potential performance measure that can be used to tune the hyperparameters of a GAN.