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.

Spiking neural networks (SNNs), recognized as an energy-efficient alternative to traditional artificial neural networks (ANNs), have advanced rapidly through the scaling of models and datasets. However, such scaling incurs considerable training overhead, posing challenges for researchers with limited computational resources and hindering the sustained development of SNNs. Data pruning is a promising strategy for accelerating training by retaining the most informative examples and discarding redundant ones, but it remains largely unexplored in SNNs. Directly applying ANN-based data pruning methods to SNNs fails to capture the intrinsic importance of examples and suffers from high gradient variance. To address these challenges, we propose a novel spike-aware data pruning (SADP) method. SADP reduces gradient variance by determining each example's selection probability to be proportional to its gradient norm, while avoiding the high cost of direct gradient computation through an efficient upper bound, termed spike-aware importance score. This score accounts for the influence of all-or-nothing spikes on the gradient norm and can be computed with negligible overhead. Extensive experiments across diverse datasets and architectures demonstrate that SADP consistently outperforms data pruning baselines and achieves training speedups close to the theoretical maxima at different pruning ratios. Notably, SADP reduces training time by 35% on ImageNet while maintaining accuracy comparable to that of full-data training. This work, therefore, establishes a data-centric paradigm for efficient SNN training and paves the way for scaling SNNs to larger models and datasets. The source code will be released publicly after the review process.

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.

However, for many real-world problems it is not enough to just minimize regret on a particular problem instance. For example, suppose we have run an online education experiment using a bandit algorithm where we test different types of teaching strategies.