Sortition is a form of democracy built on random selection of representatives. Two of the key arguments in favor of sortition are that it provides representation (a random panel reflects the composition of the population) and fairness (everyone has a chance to participate). Uniformly random selection is perfectly fair, but is it representative? Towards answering this question, we introduce the notion of a representation metric on the space of individuals, and assume that the cost of an individual for a panel is determined by the q-th closest representative; the representation of a (random) panel is measured by the ratio between the (expected) sum of costs of the optimal panel for the individuals and that of the given panel. For k/2

Results from experiments on three large real-world benchmark datasets demonstrate that OptFeature performs well in terms of accuracy and efficiency. Additional studies support the feasibility of our method.

Stimulus-drivenbrain-computer interfaces (BCIs), such astheP300 speller,rely onusing asequence ofsensory stimuli toelicit specific neural responses ascontrol signals, while a user attends to relevant target stimuli that occur within the sequence. In current BCIs, the stimulus presentation schedule is typically generated in a pseudo-random fashion. Given the non-stationarity of brain electrical signals, a better strategy could be to adapt the stimulus presentation schedule in real-time by selecting the optimal stimuli that will maximize the signal-to-noise ratios of the elicited neural responses and provide the most information about the user's intent based on the uncertainties of the data being measured. However, the high-dimensional stimulus space limits the development of algorithms with tractable solutions for optimized stimulus selection to allow for real-time decision-making within the stringent time requirements of BCI processing.

However, autoregressive sampling generates tokens one at a time making it slow, and even prohibitive in certain tasks.

Computerized adaptive testing (CA T), as a tool that can efficiently measure student's ability, has been widely used in various standardized tests (e.g., GMA T and

Despite recent advances in LLMs, the task of code generation is still challenging. To cope, code selection algorithms select the best program from multiple programs generated by an LLM. However, existing algorithms can fail to identify the correct program, either because they fail to distinguish nonequivalent programs or because they rely on an LLM and assume it always correctly determines the output for every input. We present ExPairT-LLM, an exact learning algorithm for code selection that selects a program by posing two new types of queries to an LLM oracle: pairwise membership and pairwise equivalence. These queries are simpler for LLMs and enable ExPairT-LLM to identify the correct program through a tournament, which is robust to some LLM mistakes. We evaluate ExPairT-LLM on four popular code datasets. Its pass@1 (success rate) outperforms the state-of-the-art code selection algorithm on average by +13.0% and up to +27.1%. It also improves the pass@1 of LLMs performing complex reasoning by +24.0%.

Large Language Models (LLMs) have shown remarkable abilities in a wide variety of reasoning and factual knowledge tasks (Achiam et al., 2023; Bubeck et al., 2023; Katz et al., 2024), but their large size makes inference expensive. With the advent of agentic systems that interact with the external world, LLMs are poised to become even more ubiquitous in science, technology, and society, but the tremendous inference cost presents a challenge for realizing the full potential of these agents. One way to quell the computational expense associated with LLM inference is to use small language models (SLMs). With orders of magnitude fewer parameters, SLMs are faster, cheaper, and easier to finetune for specialised skills like tool use, making them natural specialists using proprietary data or within agentic systems (Belcak et al., 2025). Training language models typically involves three stages: pre-training on large general-purpose corpora, supervised finetuning (SFT), and reinforcement learning from human feedback (RLHF) or from verifiable rewards (RLVR) (Ouyang et al., 2022).

We present an improved incremental selection algorithm of the selection algorithm presented in [1] and prove all the selected conjectures.