We thank all reviewers for the constructive comments! We will carefully resolve all writing, format, and notation issues. These results will be included in the camera-ready version. Our main goal is to design an efficient, concise, and practical IL framework. It is nearly impossible to make instance-level decisions by using a complex meta-sampler (e.g., set a large output layer R: For clarity, Eq. 3 shows the unnormalized sampling weights (noted in the paper).

Here we present a new class of optimality for coding systems. Members of that class are displaced linearly from optimal coding and thus exhibit Zipf's law, namely a power-law distribution of frequency ranks. Within that class, Zipf's law, the size-rank law and the size-probability law form a group-like structure. We identify human languages that are members of the class. All languages showing sufficient agreement with Zipf's law are potential members of the class. In contrast, there are communication systems in other species that cannot be members of that class for exhibiting an exponential distribution instead but dolphins and humpback whales might. We provide a new insight into plots of frequency versus rank in double logarithmic scale. For any system, a straight line in that scale indicates that the lengths of optimal codes under non-singular coding and under uniquely decodable encoding are displaced by a linear function whose slope is the exponent of Zipf's law. For systems under compression and constrained to be uniquely decodable, such a straight line may indicate that the system is coding close to optimality. We provide support for the hypothesis that Zipf's law originates from compression and define testable conditions for the emergence of Zipf's law in compressing systems.

Coreference resolution in biomedical texts presents unique challenges due to complex domain-specific terminology, high ambiguity in mention forms, and long-distance dependencies between coreferring expressions. In this work, we present a comprehensive evaluation of generative large language models (LLMs) for coreference resolution in the biomedical domain. Using the CRAFT corpus as our benchmark, we assess the LLMs' performance with four prompting experiments that vary in their use of local, contextual enrichment, and domain-specific cues such as abbreviations and entity dictionaries. We benchmark these approaches against a discriminative span-based encoder, SpanBERT, to compare the efficacy of generative versus discriminative methods. Our results demonstrate that while LLMs exhibit strong surface-level coreference capabilities, especially when supplemented with domain-grounding prompts, their performance remains sensitive to long-range context and mentions ambiguity. Notably, the LLaMA 8B and 17B models show superior precision and F1 scores under entity-augmented prompting, highlighting the potential of lightweight prompt engineering for enhancing LLM utility in biomedical NLP tasks.

Matrix-based preconditioned optimizers, such as Muon, have recently been shown to be more efficient than scalar-based optimizers for training large-scale neural networks, including large language models (LLMs). On the other hand, recent benchmarks on optimizers for LLM pre-training have demonstrated that variance-reduction techniques such as MARS can achieve substantial speedups over standard optimizers that do not employ variance reduction. In this paper, to achieve the best of both worlds, we introduce MARS-M, a new optimizer that integrates the variance reduction technique in MARS with Muon. Under standard regularity conditions, we prove that Muon-M converges to a first-order stationary point at a rate of $\tilde{\mathcal{O}}(T^{-1/3})$, which improves upon $\tilde{\mathcal{O}}(T^{-1/4})$ rate attained by Muon. Our empirical results on language modeling and computer vision tasks demonstrate that MARS-M consistently yields lower losses and improved performance across various downstream benchmarks. The implementation of MARS-M is available at https://github.com/AGI-Arena/MARS/tree/main/MARS_M.

Purpose: Large language models (LLMs) have proven performance for certain diagnostic tasks, however limited studies have evaluated their consistency in recommending appropriate medication regimens for a given diagnosis. Medication management is a complex task that requires synthesis of drug formulation and complete order instructions for safe use. Here, the performance of GPT 4o, an LLM available with ChatGPT, was tested for three medication management tasks. Methods: GPT-4o performance was tested using three medication tasks: identifying available formulations for a given generic drug name, identifying drug-drug interactions (DDI) for a given medication regimen, and preparing a medication order for a given generic drug name. For each experiment, the models raw text response was captured exactly as returned and evaluated using clinician evaluation in addition to standard LLM metrics, including Term Frequency-Inverse Document Frequency (TF IDF) vectors, normalized Levenshtein similarity, and Recall-Oriented Understudy for Gisting Evaluation (ROUGE 1/ROUGE L F1) between each response and its reference string. Results: For the first task of drug-formulation matching, GPT-4o had 49% accuracy for generic medications being matched to all available formulations, with an average of 1.23 omissions per medication and 1.14 hallucinations per medication. For the second task of drug-drug interaction identification, the accuracy was 54.7% for identifying the DDI pair. For the third task, GPT-4o generated order sentences containing no medication or abbreviation errors in 65.8% of cases. Conclusions: Model performance for basic medication tasks was consistently poor. This evaluation highlights the need for domain-specific training through clinician-annotated datasets and a comprehensive evaluation framework for benchmarking performance.

This derivation first appeared in the first author's blog post [53]. Its derivation, based on Lu et al. For the HMC baseline, we use the default implementation of NUTS in Pyro. For the MAP, VB, and CSGHMC baselines, we use the same settings as Daxberger et al. The diagonal Hessian is used for CIFAR-100 and all-layer F-MNIST, while the full Hessian is used for other cases.

Expanding the abbreviated column names of tables, such as "esal" to "employee salary", is critical for many downstream NLP tasks for tabular data, such as NL2SQL, table QA, and keyword search. This problem arises in enterprises, domain sciences, government agencies, and more. In this paper, we make three contributions that significantly advance the state of the art. First, we show that the synthetic public data used by prior work has major limitations, and we introduce four new datasets in enterprise/science domains, with real-world abbreviations. Second, we show that accuracy measures used by prior work seriously undercount correct expansions, and we propose new synonym-aware measures that capture accuracy much more accurately. Finally, we develop Columbo, a powerful LLM-based solution that exploits context, rules, chain-of-thought reasoning, and token-level analysis. Extensive experiments show that Columbo significantly outperforms NameGuess, the current most advanced solution, by 4-29%, over five datasets. Columbo has been used in production on EDI, a major data lake for environmental sciences.