Test-time scaling (TTS) improves language model reasoning by allocating additional test-time compute, but prior work mainly studies closed-ended tasks such as math and coding. We study TTS for automated equation discovery, an open-ended setting where models search over candidate equations and rely on observed datapoints for feedback. We formulate LLM-driven equation discovery as an iterative search process that unifies Best-of-N, sequential refinement, tree search, and evolution-style methods under a common compute-allocation view. To isolate allocation effects from prompt engineering and other heuristics, we compare minimal parallel controllers under fixed budgets. On LLM-SRBench equation-discovery tasks, we find that search width is the dominant allocation parameter: the best width in our sweep generally increases with the compute budget, while the population–branching split and controller choice matter less. Appropriate width selection also improves wall-clock efficiency by increasing parallelism. These results suggest that, given an informative verifier, controlling exploration and exploitation is central to scaling LLM-based equation discovery.

Detecting out-of-distribution (OOD) instances is crucial for NLP models in practical applications. Although numerous OOD detection methods exist, most of them are empirical. Backed by theoretical analysis, this paper advocates for the measurement of the “OOD-ness” of a test case x through the likelihood ratio between out-distribution P_out and in-distribution P_in. We argue that the state-of-the-art (SOTA) feature-based OOD detection methods, such as Maha and KNN, are suboptimal since they only estimate in-distribution density p_in(x). To address this issue, we propose FLATS, a principled solution for OOD detection based on likelihood ratio. Moreover, we demonstrate that FLATS can serve as a general framework capable of enhancing other OOD detection methods by incorporating out-distribution density p_out(x) estimation. Experiments show that FLATS establishes a new SOTA on popular benchmarks.

Recent work on applying large language models (LMs) achieves impressive performance in many NLP applications. Adapting or posttraining an LM using an unlabeled domain corpus can produce even better performance for end-tasks in the domain. This paper proposes the problem of continually extending an LM by incrementally post-train the LM with a sequence of unlabeled domain corpora to expand its knowledge without forgetting its previous skills. The goal is to improve the few-shot end-task learning in these domains. The resulting system is called CPT (Continual PostTraining), which to our knowledge, is the first continual post-training system. Experimental results verify its effectiveness.

Domain-adaptive pre-training (or DA-training for short), also known as post-training, aimsto train a pre-trained general-purpose language model (LM) using an unlabeled corpus of aparticular domain to adapt the LM so that end-tasks in the domain can give improved performances. However, existing DA-training methods are in some sense blind as they do not explicitly identify what knowledge in the LM should be preserved and what should be changed by the domain corpus. This paper shows that the existing methods are suboptimal and proposes a novel method to perform a more informed adaptation of the knowledge in the LM by (1) soft-masking the attention heads based on their importance to best preserve the general knowledge in the LM and (2) contrasting the representations of the general and the full (both general and domain knowledge) to learn an integrated representation with both general and domain-specific knowledge. Experimental results will demonstrate the effectiveness of the proposed approach.