Estimating the density of a distribution from its samples is a fundamental problem in statistics. Hypothesis selection addresses the setting where, in addition to a sample set, we are given $n$ candidate distributions -- referred to as hypotheses -- and the goal is to determine which one best describes the underlying data distribution. This problem is known to be solvable very efficiently, requiring roughly $O(\log n)$ samples and running in $\tilde{O}(n)$ time. The quality of the output is measured via the total variation distance to the unknown distribution, and the approximation factor of the algorithm determines how large this distance is compared to the optimal distance achieved by the best candidate hypothesis. It is known that $α= 3$ is the optimal approximation factor for this problem. We study hypothesis selection under the constraint of differential privacy. We propose a differentially private algorithm in the central model that runs in nearly-linear time with respect to the number of hypotheses, achieves the optimal approximation factor, and incurs only a modest increase in sample complexity, which remains polylogarithmic in $n$. This resolves an open question posed by [Bun, Kamath, Steinke, Wu, NeurIPS 2019]. Prior to our work, existing upper bounds required quadratic time.

In orthogonal frequency division multiplexing (OFDM), accurate channel estimation is crucial. Classical signal processing based approaches, such as minimum mean-squared error (MMSE) estimation, often require second-order statistics that are difficult to obtain in practice. Recent deep neural networks based methods have been introduced to address this; yet they often suffer from high complexity. This paper proposes an Attention-aided MMSE (A-MMSE), a novel model-based DNN framework that learns the optimal MMSE filter via the Attention Transformer. Once trained, the A-MMSE estimates the channel through a single linear operation for channel estimation, eliminating nonlinear activations during inference and thus reducing computational complexity. To enhance the learning efficiency of the A-MMSE, we develop a two-stage Attention encoder, designed to effectively capture the channel correlation structure. Additionally, a rank-adaptive extension of the proposed A-MMSE allows flexible trade-offs between complexity and channel estimation accuracy. Extensive simulations with 3GPP TDL channel models demonstrate that the proposed A-MMSE consistently outperforms other baseline methods in terms of normalized MSE across a wide range of SNR conditions. In particular, the A-MMSE and its rank-adaptive extension establish a new frontier in the performance complexity trade-off, redefining the standard for practical channel estimation methods.

We provide an introduction to the topic of path signatures as means of feature extraction for machine learning from data streams. The article stresses the mathematical theory underlying the signature methodology, highlighting the conceptual character without plunging into the technical details of rigorous proofs. These notes are based on an introductory presentation given to students of the Research Experience for Undergraduates in Industrial Mathematics and Statistics at Worcester Polytechnic Institute in June 2024.

Large language models (LLMs) have been prominent in various tasks, including text generation and summarisation. The applicability of LLMs to the generation of product reviews is gaining momentum, paving the way for the generation of movie reviews. In this study, we propose a framework that generates movie reviews using three LLMs (GPT-4o, DeepSeek-V3, and Gemini-2.0), and evaluate their performance by comparing the generated outputs with IMDb user reviews. We use movie subtitles and screenplays as input to the LLMs and investigate how they affect the quality of reviews generated. We review the LLM-based movie reviews in terms of vocabulary, sentiment polarity, similarity, and thematic consistency in comparison to IMDB user reviews. The results demonstrate that LLMs are capable of generating syntactically fluent and structurally complete movie reviews. Nevertheless, there is still a noticeable gap in emotional richness and stylistic coherence between LLM-generated and IMDb reviews, suggesting that further refinement is needed to improve the overall quality of movie review generation. We provided a survey-based analysis where participants were told to distinguish between LLM and IMDb user reviews. The results show that LLM-generated reviews are difficult to distinguish from IMDB user reviews. We found that DeepSeek-V3 produced the most balanced reviews, closely matching IMDb reviews. GPT-4o overemphasised positive emotions, while Gemini-2.0 captured negative emotions better but showed excessive emotional intensity.

The rise of large language models (LLMs) has created a new job role: the Prompt Engineer. Despite growing interest in this position, we still do not fully understand what skills this new job role requires or how common these jobs are. We analyzed 20,662 job postings on LinkedIn, including 72 prompt engineer positions, to learn more about this emerging role. We found that prompt engineering is still rare (less than 0.5% of sampled job postings) but has a unique skill profile. Prompt engineers need AI knowledge (22.8%), prompt design skills (18.7%), good communication (21.9%), and creative problem-solving (15.8%) skills. These requirements significantly differ from those of established roles, such as data scientists and machine learning engineers, showing that prompt engineering is becoming its own profession. Our findings help job seekers, employers, and educational institutions in better understanding the emerging field of prompt engineering.

Retrieval-Augmented Generation (RAG) has emerged as a powerful paradigm to enhance large language models (LLMs) by conditioning generation on external evidence retrieved at inference time. While RAG addresses critical limitations of parametric knowledge storage-such as factual inconsistency and domain inflexibility-it introduces new challenges in retrieval quality, grounding fidelity, pipeline efficiency, and robustness against noisy or adversarial inputs. This survey provides a comprehensive synthesis of recent advances in RAG systems, offering a taxonomy that categorizes architectures into retriever-centric, generator-centric, hybrid, and robustness-oriented designs. We systematically analyze enhancements across retrieval optimization, context filtering, decoding control, and efficiency improvements, supported by comparative performance analyses on short-form and multi-hop question answering tasks. Furthermore, we review state-of-the-art evaluation frameworks and benchmarks, highlighting trends in retrieval-aware evaluation, robustness testing, and federated retrieval settings. Our analysis reveals recurring trade-offs between retrieval precision and generation flexibility, efficiency and faithfulness, and modularity and coordination. We conclude by identifying open challenges and future research directions, including adaptive retrieval architectures, real-time retrieval integration, structured reasoning over multi-hop evidence, and privacy-preserving retrieval mechanisms. This survey aims to consolidate current knowledge in RAG research and serve as a foundation for the next generation of retrieval-augmented language modeling systems.

Humanity is progressing towards automated product development, a trend that promises faster creation of better products and thus the acceleration of technological progress. However, increasing reliance on non-human agents for this process introduces many risks. This perspective aims to initiate a discussion on these risks and appropriate mitigation strategies. To this end, we outline a set of principles for safer AI-driven product development which emphasize human oversight, accountability, and explainable design, among others. The risk assessment covers both technical risks which affect product quality and safety, and sociotechnical risks which affect society. While AI-driven product development is still in its early stages, this discussion will help balance its opportunities and risks without delaying essential progress in understanding, norm-setting, and regulation.

This survey explores the integration of machine learning (ML) into EDA workflows for analog and RF circuits, addressing challenges unique to analog design, which include complex constraints, nonlinear design spaces, and high computational costs. State-of-the-art learning and optimization techniques are reviewed for circuit tasks such as constraint formulation, topology generation, device modeling, sizing, placement, and routing. The survey highlights the capability of ML to enhance automation, improve design quality, and reduce time-to-market while meeting the target specifications of an analog or RF circuit. Emerging trends and cross-cutting challenges, including robustness to variations and considerations of interconnect parasitics, are also discussed.

This article presents a structured framework for Human-AI collaboration in Security Operations Centers (SOCs), integrating AI autonomy, trust calibration, and Human-in-the-loop decision making. Existing frameworks in SOCs often focus narrowly on automation, lacking systematic structures to manage human oversight, trust calibration, and scalable autonomy with AI. Many assume static or binary autonomy settings, failing to account for the varied complexity, criticality, and risk across SOC tasks considering Humans and AI collaboration. To address these limitations, we propose a novel autonomy tiered framework grounded in five levels of AI autonomy from manual to fully autonomous, mapped to Human-in-the-Loop (HITL) roles and task-specific trust thresholds. This enables adaptive and explainable AI integration across core SOC functions, including monitoring, protection, threat detection, alert triage, and incident response. The proposed framework differentiates itself from previous research by creating formal connections between autonomy, trust, and HITL across various SOC levels, which allows for adaptive task distribution according to operational complexity and associated risks. The framework is exemplified through a simulated cyber range that features the cybersecurity AI-Avatar, a fine-tuned LLM-based SOC assistant. The AI-Avatar case study illustrates human-AI collaboration for SOC tasks, reducing alert fatigue, enhancing response coordination, and strategically calibrating trust. This research systematically presents both the theoretical and practical aspects and feasibility of designing next-generation cognitive SOCs that leverage AI not to replace but to enhance human decision-making.

AI copilots represent a new generation of AI-powered systems designed to assist users, particularly knowledge workers and developers, in complex, context-rich tasks. As these systems become more embedded in daily workflows, personalization has emerged as a critical factor for improving usability, effectiveness, and user satisfaction. Central to this personalization is preference optimization: the system's ability to detect, interpret, and align with individual user preferences. While prior work in intelligent assistants and optimization algorithms is extensive, their intersection within AI copilots remains underexplored. This survey addresses that gap by examining how user preferences are operationalized in AI copilots. We investigate how preference signals are sourced, modeled across different interaction stages, and refined through feedback loops. Building on a comprehensive literature review, we define the concept of an AI copilot and introduce a taxonomy of preference optimization techniques across pre-, mid-, and post-interaction phases. Each technique is evaluated in terms of advantages, limitations, and design implications. By consolidating fragmented efforts across AI personalization, human-AI interaction, and language model adaptation, this work offers both a unified conceptual foundation and a practical design perspective for building user-aligned, persona-aware AI copilots that support end-to-end adaptability and deployment.