When Is a Draft Accepted? A Theory of Acceptance in Speculative Decoding

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.

Air in Your Neighborhood: Fine-Grained AQI Forecasting Using Mobile Sensor Data

Air pollution has become a significant health risk in developing countries. While governments routinely publish air-quality index (AQI) data to track pollution, these values fail to capture the local reality, as sensors are often very sparse. In this paper, we address this gap by predicting AQI in 1 km^2 neighborhoods, using the example of AirDelhi dataset. Using Spatio-temporal GNNs we surpass existing works by 71.654 MSE a 79% reduction, even on unseen coordinates. New insights about AQI such as the existence of strong repetitive short-term patterns and changing spatial relations are also discovered. The code is available on GitHub.

How Much You Ate? Food Portion Estimation on Spoons

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.