qc-kmeans: A Quantum Compressive K-Means Algorithm for NISQ Devices

Clustering on NISQ hardware is constrained by data loading and limited qubits. We present \textbf{qc-kmeans}, a hybrid compressive $k$-means that summarizes a dataset with a constant-size Fourier-feature sketch and selects centroids by solving small per-group QUBOs with shallow QAOA circuits. The QFF sketch estimator is unbiased with mean-squared error $O(\varepsilon^2)$ for $B,S=\Theta(\varepsilon^{-2})$, and the peak-qubit requirement $q_{\text{peak}}=\max\{D,\lceil \log_2 B\rceil + 1\}$ does not scale with the number of samples. A refinement step with elitist retention ensures non-increasing surrogate cost. In Qiskit Aer simulations (depth $p{=}1$), the method ran with $\le 9$ qubits on low-dimensional synthetic benchmarks and achieved competitive sum-of-squared errors relative to quantum baselines; runtimes are not directly comparable. On nine real datasets (up to $4.3\times 10^5$ points), the pipeline maintained constant peak-qubit usage in simulation. Under IBM noise models, accuracy was similar to the idealized setting. Overall, qc-kmeans offers a NISQ-oriented formulation with shallow, bounded-width circuits and competitive clustering quality in simulation.

A Scalable Global Optimization Algorithm For Constrained Clustering

Constrained clustering leverages limited domain knowledge to improve clustering performance and interpretability, but incorporating pairwise must-link and cannot-link constraints is an NP-hard challenge, making global optimization intractable. Existing mixed-integer optimization methods are confined to small-scale datasets, limiting their utility. We propose Sample-Driven Constrained Group-Based Branch-and-Bound (SDC-GBB), a decomposable branch-and-bound (BB) framework that collapses must-linked samples into centroid-based pseudo-samples and prunes cannot-link through geometric rules, while preserving convergence and guaranteeing global optimality. By integrating grouped-sample Lagrangian decomposition and geometric elimination rules for efficient lower and upper bounds, the algorithm attains highly scalable pairwise k-Means constrained clustering via parallelism. Experimental results show that our approach handles datasets with 200,000 samples with cannot-link constraints and 1,500,000 samples with must-link constraints, which is 200 - 1500 times larger than the current state-of-the-art under comparable constraint settings, while reaching an optimality gap of less than 3%. In providing deterministic global guarantees, our method also avoids the search failures that off-the-shelf heuristics often encounter on large datasets.

Giving AI Personalities Leads to More Human-Like Reasoning

In computational cognitive modeling, capturing the full spectrum of human judgment and decision-making processes, beyond just optimal behaviors, is a significant challenge. This study explores whether Large Language Models (LLMs) can emulate the breadth of human reasoning by predicting both intuitive, fast System 1 and deliberate, slow System 2 processes. We investigate the potential of AI to mimic diverse reasoning behaviors across a human population, addressing what we call the "full reasoning spectrum problem". We designed reasoning tasks using a novel generalization of the Natural Language Inference (NLI) format to evaluate LLMs' ability to replicate human reasoning. The questions were crafted to elicit both System 1 and System 2 responses. Human responses were collected through crowd-sourcing and the entire distribution was modeled, rather than just the majority of the answers. We used personality-based prompting inspired by the Big Five personality model to elicit AI responses reflecting specific personality traits, capturing the diversity of human reasoning, and exploring how personality traits influence LLM outputs. Combined with genetic algorithms to optimize the weighting of these prompts, this method was tested alongside traditional machine learning models. The results show that LLMs can mimic human response distributions, with open-source models like Llama and Mistral outperforming proprietary GPT models. Personality-based prompting, especially when optimized with genetic algorithms, significantly enhanced LLMs' ability to predict human response distributions, suggesting that capturing suboptimal, naturalistic reasoning may require modeling techniques incorporating diverse reasoning styles and psychological profiles. The study concludes that personality-based prompting combined with genetic algorithms is promising for enhancing AI's 'human-ness' in reasoning.