Control algorithms in production environments typically require domain experts to tune their parameters and logic for specific scenarios. However, existing research predominantly focuses on algorithmic performance under ideal or default configurations, overlooking the critical aspect of Tuning Potential. To bridge this gap, we introduce Crucible, an agent that employs an LLM-driven, multi-level expert simulation to turn algorithms and defines a formalized metric to quantitatively evaluate their Tuning Potential. We demonstrate Crucible's effectiveness across a wide spectrum of case studies, from classic control tasks to complex computer systems, and validate its findings in a real-world deployment. Our experimental results reveal that Crucible systematically quantifies the tunable space across different algorithms. Furthermore, Crucibleprovides a new dimension for algorithm analysis and design, which ultimately leads to performance improvements.

We present a novel approach to formalise and solve search-based problems using large language models, which significantly improves upon previous state-of-theart results. We demonstrate the efficacy of this approach on benchmarks like the logic puzzles tasks in ZebraLogicBench. Instead of letting the LLM attempt to directly solve the puzzles, our method prompts the model to formalise the problem in a logic-focused, human-readable, domain-specific language (DSL) called Logic.py. This formalised representation is then solved using a constraint solver, leveraging the strengths of both the language model and the solver. Our approach achieves a remarkable 65% absolute improvement over the baseline performance of Llama 3.1 70B on ZebraLogicBench, increasing its accuracy to over 90%. This significant advancement demonstrates the potential of combining language models with domain-specific languages and auxiliary tools on traditionally challenging tasks for LLMs.

Multimodal symbolic logical reasoning, which aims to deduce new facts from multimodal input via formal logic, is critical in high-stakes applications such as autonomous driving and medical diagnosis, as its rigorous, deterministic reasoning helps prevent serious consequences. To evaluate such capabilities of current state-of-the-art vision language models (VLMs), we introduce MuSLR, the first multimodal symbolic logical reasoning grounded in formal logical rules. We curate a benchmark dataset for MuSLR comprising 1,093 instances across 7 domains, including 35 atomic symbolic logic and 976 logical combinations, with reasoning depths ranging from 2 to 9. We evaluate 7 state-of-the-art VLMs on our benchmark and find that they all struggle with multimodal symbolic reasoning, with the best model, GPT-4.1, achieving only 46.8%. Thus, we propose LogiCAM, a modular framework that applies formal logical rules to multimodal inputs, boosting GPT-4.1's

It has been observed that transformers with greater depth (that is, more layers) have more capabilities, but can we establish formally which capabilities are gained? We answer this question with a theoretical proof followed by an empirical study. First, we consider transformers that round to fixed precision except inside attention. We show that this subclass of transformers is expressively equivalent to the programming language C-RASP and this equivalence preserves depth. Second, we prove that deeper C-RASP programs are more expressive than shallower C-RASP programs, implying that deeper transformers are more expressive than shallower transformers (within the subclass mentioned above). The same is also proven for transformers with positional encodings (like RoPE and ALiBi). These results are established by studying a temporal logic with counting operators equivalent to C-RASP. Finally, we provide empirical evidence that our theory predicts the depth required for transformers without positional encodings to length-generalize on a family of sequential dependency tasks.

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This is not generally allowable. F can do this because random-search logs contain interchangeable trials.

We demonstrate our framework's utility by proving and methods that are guaranteed to be defended against deception, given bounded sistent conclusions about performance. Our framework enables us to prove EHPO put forth a logical framework to capture its semantics and how it can lead to inconrigorous. We call this process epistemic hyperparameter optimization (EHPO), and deception, the process of drawing conclusions from HPO should be made more provide a theoretical complement to this prior work, arguing that, to avoid such the opposite. In short, the way we choose hyperparameters can deceive us. We yield the conclusion that J outperforms K, whereas searching another can entail research.

Large language models (LLMs) have shown increasing capability in problem-solving and decision-making, largely based on the step-by-step chain-of-thought reasoning processes. However, evaluating these reasoning abilities has become increasingly challenging. Existing outcome-based benchmarks are beginning to saturate, becoming less effective in tracking meaningful progress. To address this, we present a process-based benchmark MR-Ben that demands a meta-reasoning skill, where LMs are asked to locate and analyse potential errors in automatically generated reasoning steps. Our meta-reasoning paradigm is especially suited for system-2 slow thinking, mirroring the human cognitive process of carefully examining assumptions, conditions, calculations, and logic to identify mistakes. MR-Ben comprises 5,975 questions curated by human experts across a wide range of subjects, including physics, chemistry, logic, coding, and more. Through our designed metrics for assessing meta-reasoning on this benchmark, we identify interesting limitations and weaknesses of current LLMs (open-source and closed-source models). For example, with models like the o1 series from OpenAI demonstrating strong performance by effectively scrutinizing the solution space, many other state-of-the-art models fall significantly behind on MR-Ben, exposing potential shortcomings in their training strategies and inference methodologies.

Reasoning over TKGs has two challenges: 1.

Large language models (LLMs) can be seen as atomic units of computation mapping sequences to a distribution over sequences.