Aaryam Sharma

Aaryam Sharma

Speculative decoding accelerates language model inference by using a fast drafter to propose candidate tokens that are then verified by a larger target model. Existing theory largely studies the stochastic, distribution-preserving setting, where the goal is to exactly sample from the target distribution. In contrast, many practical systems use greedy decoding, relaxed acceptance rules, or tree-based candidate sets, where success is governed by local ranking and threshold events rather than exact distributional equality. We develop a theory for these regimes. We identify that many common acceptance criteria have rejection regions that can be characterized as lower level sets of the target distribution. For these, we characterize the exact KL divergence required for rejection yielding exact certificates and sharp margin-based bounds for strict greedy decoding, additive and multiplicative relaxed acceptance, top-(m) relaxed criteria, and entropy-thresholded acceptance. We then extend the framework to greedy tree decoding, deriving exact and margin-only certificates for when the target greedy token remains covered by the drafter's top-(m) candidates. Finally, we evaluate the resulting certificates on Qwen3 models, showing that relaxed and tree-based criteria substantially enlarge the region of certified acceptance, especially on decoding steps with low target model distribution margin. These results complement existing distribution-preserving analyses of speculative decoding by characterizing the deterministic local acceptance events common in practical inference systems.

Aaryam Sharma, Chris Czarnecki, Yuhao Chen et al.

Monitoring dietary intake is a crucial aspect of promoting healthy living. In recent years, advances in computer vision technology have facilitated dietary intake monitoring through the use of images and depth cameras. However, the current state-of-the-art image-based food portion estimation algorithms assume that users take images of their meals one or two times, which can be inconvenient and fail to capture food items that are not visible from a top-down perspective, such as ingredients submerged in a stew. To address these limitations, we introduce an innovative solution that utilizes stationary user-facing cameras to track food items on utensils, not requiring any change of camera perspective after installation. The shallow depth of utensils provides a more favorable angle for capturing food items, and tracking them on the utensil's surface offers a significantly more accurate estimation of dietary intake without the need for post-meal image capture. The system is reliable for estimation of nutritional content of liquid-solid heterogeneous mixtures such as soups and stews. Through a series of experiments, we demonstrate the exceptional potential of our method as a non-invasive, user-friendly, and highly accurate dietary intake monitoring tool.

Aaryam Sharma

Topological data analysis (TDA) is a relatively new field that is gaining rapid adoption due to its robustness and ability to effectively describe complex datasets by quantifying geometric information. In imaging contexts, TDA typically models data as filtered cubical complexes from which we can extract discriminative features using persistence homology. Meanwhile, convolutional neural networks (CNNs) have been shown to be biased towards texture based local features. To address this limitation, we propose a TDA feature engineering pipeline and a simple method to integrate topological features with deep learning models on remote sensing classification. Our method improves the performance of a ResNet18 model on the EuroSAT dataset by 1.44% achieving 99.33% accuracy, which surpasses all previously reported single-model accuracies, including those with larger architectures, such as ResNet50 (2x larger) and XL Vision Transformers (197x larger). We additionally show that our method's accuracy is 1.82% higher than our ResNet18 baseline on the RESISC45 dataset. To our knowledge, this is the first application of TDA features in satellite scene classification with deep learning. This demonstrates that TDA features can be integrated with deep learning models, even on datasets without explicit topological structures, thereby increasing the applicability of TDA. A clean implementation of our method will be made publicly available upon publication.