Popular metrics for clustering comparison, like the Adjusted Rand Index and the Adjusted Mutual Information, are type II biased. The Standardized Mutual Information removes this bias but suffers from counterintuitive non-monotonicity and poor computational efficiency. We introduce the p-value adjusted Rand Index (PMI2), the first cluster comparison method that is type II unbiased and provably monotonous. The PMI2 has fast approximations that outperform the Standardized Mutual information. We demonstrate its unbiased clustering selection, approximation quality, and runtime efficiency on synthetic benchmarks. In experiments on image and social network datasets, we show how the PMI2 can help practitioners choose better clustering and community detection algorithms.

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

Weuse"panel" torefer tothegroup of people who deliberate, and "assembly" to refer to the actual deliberation step.

The advantages of adaptive experiments have led to their rapid adoption in economics, other fields, as well as among practitioners. However, adaptive experiments pose challenges for causal inference. This note suggests a BOLS (batched ordinary least squares) test statistic for inference of treatment effects in adaptive experiments. The statistic provides a precision-equalizing aggregation of per-period treatment-control differences under heteroskedasticity. The combined test statistic is a normalized average of heteroskedastic per-period z-statistics and can be used to construct asymptotically valid confidence intervals. We provide simulation results comparing rejection rates in the typical case with few treatment periods and few (or many) observations per batch.

Long-term memory is essential for natural, realistic dialogue. However, current large language model (LLM) memory systems rely on either brute-force context expansion or static retrieval pipelines that fail on edge-constrained devices. We introduce Mnemosyne, an unsupervised, human-inspired long-term memory architecture designed for edge-based LLMs. Our approach uses graph-structured storage, modular substance and redundancy filters, memory committing and pruning mechanisms, and probabilistic recall with temporal decay and refresh processes modeled after human memory. Mnemosyne also introduces a concentrated "core summary" efficiently derived from a fixed-length subset of the memory graph to capture the user's personality and other domain-specific long-term details such as, using healthcare application as an example, post-recovery ambitions and attitude towards care. Unlike existing retrieval-augmented methods, Mnemosyne is designed for use in longitudinal healthcare assistants, where repetitive and semantically similar but temporally distinct conversations are limited by naive retrieval. In experiments with longitudinal healthcare dialogues, Mnemosyne demonstrates the highest win rate of 65.8% in blind human evaluations of realism and long-term memory capability compared to a baseline RAG win rate of 31.1%. Mnemosyne also achieves current highest LoCoMo benchmark scores in temporal reasoning and single-hop retrieval compared to other same-backboned techniques. Further, the average overall score of 54.6% was second highest across all methods, beating commonly used Mem0 and OpenAI baselines among others. This demonstrates that improved factual recall, enhanced temporal reasoning, and much more natural user-facing responses can be feasible with an edge-compatible and easily transferable unsupervised memory architecture.

While some adaptive experimental strategies exist for the identification of the single best subgroup, they commonly do not enable the identification of the best set of subgroups.

Test-time scaling improves the reasoning capabilities of large language models (LLMs) by allocating extra compute to generate longer Chains-of-Thoughts (CoTs). This enables models to tackle more complex problem by breaking them down into additional steps, backtracking, and correcting mistakes. Despite its strong performance--demonstrated by OpenAI's o1 and DeepSeek R1, the conditions in the training data under which long CoTs emerge, and when such long CoTs improve the performance, remain unclear. In this paper, we study the performance of test-time scaling for transformers trained on an in-context weight prediction task for linear regression. Our analysis provides a theoretical explanation for several intriguing observations: First, at any fixed test error, increasing test-time compute allows us to reduce the number of in-context examples (context length) in training prompts. Second, if the skills required to solve a downstream task are not sufficiently present in the training data, increasing test-time compute can harm performance. Finally, we characterize task hardness via the smallest eigenvalue of its feature covariance matrix and show that training on a diverse, relevant, and hard set of tasks results in best performance for test-time scaling. We confirm our findings with experiments on large, nonlinear transformer architectures.