M. Li

Xuyuan Wang, Donglin Han, Michael Y. Li

We consider the problem of parameter inference for ordinary differential equation (ODE) models with structural non-identifiability. Such models arise in a wide range of scientific fields, including control theory, systems biology, and public health. Structural non-identifiability occurs when distinct parameter values provide identical model outputs, resulting in lower-dimensional manifolds of observationally equivalent solutions in the parameter space. This poses challenges for Bayesian inference and Markov chain Monte Carlo (MCMC) methods, often leading to poor mixing and slow convergence. We develop two MCMC methods that use information from structural identifiability analysis. The first, Identifiability-Aware Geometric MCMC, constructs proposals that move within and between non-identifiable manifolds. The second, Identifiability-Aware Pseudo-Marginal MCMC, performs inference on the space of identifiable parameter combinations and reconstructs full parameter values. We show that both methods target the correct posterior distribution and are ergodic under standard conditions. Numerical examples demonstrate improved sampling efficiency and convergence compared with standard MCMC methods.

Ben Prystawski, Kushin Mukherjee, Daniel Wurgaft et al.

AI-based scientific automation is increasingly possible by using agents to generate hypotheses, design experiments, and analyze data. Data collection is a major bottleneck in this pipeline, however. Psychology, and computational cognitive science in particular, is well-positioned to benefit from AI experimentation because theories are often represented as code and crowdsourcing platforms enable programmatic human data collection at scale. Here, we apply automated discovery techniques to the project of generating theories in computational cognitive science, with an agent-based system collecting human data independently through crowdsourced survey experiments. As a testbed, we use a classic case study from cognitive psychology: judging which sequences of coin flips seem subjectively more random. Our system, auto-psych, uses nested agent-based discovery loops to generate explanatory theories of human behavior. The inner loop conjectures, fits, and critiques probabilistic cognitive models; the outer loop designs experiments to test these models, launches them online, and analyzes the data. This system can quickly and reliably recover ground-truth theories from synthetic data via systematic experimentation, but the nested structure is critical to model performance. Further, in three independent sequences of human experiments, the system finds theories that fit the data better than theories generated from the scientific literature. This work thus demonstrates the feasibility of automated data collection and theory discovery in computational cognitive science.

Jubayer Ibn Hamid, Ifdita Hasan Orney, Michael Y. Li et al.

Language model reasoning can be substantially improved at test time via scaffolds that scale inference compute across different primitives -- sequential reasoning within a trace, independently sampled parallel traces, and aggregation of multiple reasoning traces into a final response. During post-training, however, language models are optimized only for sequential reasoning within a single trace. We introduce Sequential-Parallel-Aggregative Reinforcement Learning (SPIRAL), a framework in which a language model is trained to use all three primitives, as part of a unified inference compute pipeline. Concretely, the language model first samples a set of independent traces in parallel, each produced through sequential chain-of-thought reasoning, and then generates a final aggregation trace conditioned on those traces; all components are optimized end-to-end against the reward of the final aggregated response. To train this system, SPIRAL uses set reinforcement learning to teach models to produce a set of traces that are collectively useful for an aggregator and standard reinforcement learning to teach models to aggregate the set into improved final responses. Our experiments on reasoning tasks show that SPIRAL effectively scales with inference compute, outperforming GRPO by up to 11$\times$ scaling efficiency and 15% higher performance when all three compute primitives are scaled.

Kexin Huang, Ying Jin, Ryan Li et al.

Hypotheses are central to information acquisition, decision-making, and discovery. However, many real-world hypotheses are abstract, high-level statements that are difficult to validate directly. This challenge is further intensified by the rise of hypothesis generation from Large Language Models (LLMs), which are prone to hallucination and produce hypotheses in volumes that make manual validation impractical. Here we propose Popper, an agentic framework for rigorous automated validation of free-form hypotheses. Guided by Karl Popper's principle of falsification, Popper validates a hypothesis using LLM agents that design and execute falsification experiments targeting its measurable implications. A novel sequential testing framework ensures strict Type-I error control while actively gathering evidence from diverse observations, whether drawn from existing data or newly conducted procedures. We demonstrate Popper on six domains including biology, economics, and sociology. Popper delivers robust error control, high power, and scalability. Furthermore, compared to human scientists, Popper achieved comparable performance in validating complex biological hypotheses while reducing time by 10 folds, providing a scalable, rigorous solution for hypothesis validation.