Large Language Models (LLMs) are transforming Intelligent Tutoring Systems (ITS) via more natural explanations, multi-turn dialogue, and more adaptive support for students. Yet their effectiveness depends on rigorous benchmarking to ensure reliability, fairness, and pedagogical soundness. Such benchmarking relies on detailed student data, especially data that accurately reflects the actual distribution of wrong answers and misconceptions. A robust dataset of domain-specific wrong answers and misconceptions is critical for the ITS research community. Such a dataset enables training and testing of LLM-based ITS designed to correct misconceived student responses and guide students appropriately. Unfortunately, in advanced areas such as Theoretical Computer Science (TCS), such data are scarce, costly to collect, and limited by privacy concerns. To address this problem, we propose a synthetic data generation technique grounded in real-world data. First, we curate a set of human-generated (question, answer, misconception) tuples to seed an LLM with the goal of generating a corpus of incorrect answers that resemble the kinds of mistakes students make while solving undergraduate-level math and algorithmic problems. Then, we prompt LLMs to generate a dataset with a similar distribution of mistakes. Once validated for one topic, the technique can be transferred to others. Our goal is to lay the groundwork for scalable benchmarks that enable rigorous evaluation and broader adoption of LLM-based tutoring systems in the most conceptually demanding areas of computer science education, namely, Theoretical Computer Science.

Stochastic gradient descent without replacement sampling is widely used in practice for model training. However, the vast majority of SGD analyses assumes data is sampled with replacement, and when the function minimized is strongly convex, an $\mathcal{O}\left(\frac{1}{T}\right)$ rate can be established when SGD is run for $T$ iterations. A recent line of breakthrough works on SGD without replacement (SGDo) established an $\mathcal{O}\left(\frac{n}{T^2}\right)$ convergence rate when the function minimized is strongly convex and is a sum of $n$ smooth functions, and an $\mathcal{O}\left(\frac{1}{T^2}+\frac{n^3}{T^3}\right)$ rate for sums of quadratics. On the other hand, the tightest known lower bound postulates an $\Omega\left(\frac{1}{T^2}+\frac{n^2}{T^3}\right)$ rate, leaving open the possibility of better SGDo convergence rates in the general case. In this paper, we close this gap and show that SGD without replacement achieves a rate of $\mathcal{O}\left(\frac{1}{T^2}+\frac{n^2}{T^3}\right)$ when the sum of the functions is a quadratic, and offer a new lower bound of $\Omega\left(\frac{n}{T^2}\right)$ for strongly convex functions that are sums of smooth functions.

Single-photon avalanche diodes (SPADs) are starting to play a pivotal role in the development of photon-efficient, long-range LiDAR systems. However, due to non-linearities in their image formation model, a high photon flux (e.g., due to strong sunlight) leads to distortion of the incident temporal waveform, and potentially, large depth errors. Operating SPADs in low flux regimes can mitigate these distortions, but, often requires attenuating the signal and thus, results in low signal-to-noise ratio. In this paper, we address the following basic question: what is the optimal photon flux that a SPAD-based LiDAR should be operated in? We derive a closed form expression for the optimal flux, which is quasi-depth-invariant, and depends on the ambient light strength. The optimal flux is lower than what a SPAD typically measures in real world scenarios, but surprisingly, considerably higher than what is conventionally suggested for avoiding distortions. We propose a simple, adaptive approach for achieving the optimal flux by attenuating incident flux based on an estimate of ambient light strength. Using extensive simulations and a hardware prototype, we show that the optimal flux criterion holds for several depth estimators, under a wide range of illumination conditions.

Single-photon avalanche diodes (SPADs) are becoming popular in time-of-flight depth-ranging due to their unique ability to capture individual photons with picosecond timing resolution. However, ambient light (e.g., sunlight) incident on a SPAD-based 3D camera leads to severe non-linear distortions (pileup) in the measured waveform, resulting in large depth errors. We propose asynchronous single-photon 3D imaging, a family of acquisition schemes to mitigate pileup during data acquisition itself. Asynchronous acquisition temporally misaligns SPAD measurement windows and the laser cycles through deterministically predefined or randomized offsets. Our key insight is that pileup distortions can be “averaged out” by choosing a sequence of offsets that span the entire depth range. We develop a generalized image formation model and perform theoretical analysis to explore the space of asynchronous acquisition schemes and design high-performance schemes. Our simulations and experiments demonstrate an improvement in depth accuracy of up to an order of magnitude as compared to the state-of-the-art, across a wide range of imaging scenarios, including those with high ambient flux.

ABSTRACT With the rapid evolution of the Internet, security has become a major area of concern and, consequently, an interesting research area. Different applications transmit sensitive information over the Internet, which creates increased chances for attackers to look into every piece of data, unless it is secured using secure socket layer (SSL) certificate. However, the present SSL certificates too face challenges because of various attacks, and these certificates need to be verified before transmitting information. In this paper, we show how the concepts of learning automata (LA) can be used to verify SSL certificates. The proposed LA‐based system can detect safe or unsafe SSL certificates. The LA reward/penalty scheme is used to build the trust value for SSL certificates. Copyright © 2013 John Wiley & Sons, Ltd.