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In recent years, general-purpose large language models (LLMs) such as GPT, Gemini, Claude, and DeepSeek have advanced at an unprecedented pace. Despite these achievements, their application to finance remains challenging, due to fragmented…

Generating intermediate steps, or Chain of Thought (CoT), is an effective way to significantly improve language models' (LM) multi-step reasoning capability. However, the CoT lengths can grow rapidly with the problem complexity, easily…

With the rapid progress of Multimodal Large Language Models (MLLMs), unified MLLMs that jointly perform image understanding and generation have advanced significantly. However, despite the inherent reasoning capabilities of unified MLLMs…

Supervised Fine-Tuning (SFT) on long Chain-of-Thought (CoT) trajectories has become a pivotal phase in building large reasoning models. However, how CoT trajectories from different sources influence the generalization performance of models…

Reasoning in Large Language Models (LLMs) often suffers from inefficient long chain-of-thought traces with redundant self-exploration and validation, which inflate computational costs and even degrade performance. Inspired by human…

Large Reasoning Models (LRMs) have achieved remarkable success, yet they often suffer from producing unnecessary and verbose reasoning chains. We identify a core aspect of this issue as "invalid thinking" -- models tend to repeatedly…

Lifting attempts to speed up probabilistic inference by exploiting symmetries in the model. Exact lifted inference methods, like their propositional counterparts, work by recursively decomposing the model and the problem. In the…

The number of trees T in the random forest (RF) algorithm for supervised learning has to be set by the user. It is controversial whether T should simply be set to the largest computationally manageable value or whether a smaller T may in…

DeepSeek R1 has significantly advanced complex reasoning for large language models (LLMs). While recent methods have attempted to replicate R1's reasoning capabilities in multimodal settings, they face limitations, including inconsistencies…

Multimodal large language models (MLLMs) promise enhanced reasoning by integrating diverse inputs such as text, vision, and audio. Yet cross-modal reasoning remains underexplored, with conflicting reports on whether added modalities help or…

With the rapid advancement of Artificial Intelligence (AI), Large Language Models (LLMs) have significantly impacted a wide array of domains, including healthcare, engineering, science, education, and mathematical reasoning. Among these,…

While recent success of large reasoning models (LRMs) significantly advanced LLMs' reasoning capability by optimizing the final answer accuracy using reinforcement learning, they may also drastically increase the output length due to…

Recent advancements in reinforcement learning (RL) for large language models (LLMs), exemplified by DeepSeek R1, have shown that even a simple question-answering task can substantially improve an LLM's reasoning capabilities. In this work,…

Ensemble learning methods are designed to benefit from multiple learning algorithms for better predictive performance. The tradeoff of this improved performance is slower speed and larger size of ensemble learning systems compared to single…

Reasoning LLMs such as OpenAI o1, o3 and DeepSeek R1 have made significant progress in mathematics and coding, yet find challenging advanced tasks such as International Mathematical Olympiad (IMO) combinatorics problems, Abstraction and…

We introduce Seed1.5-Thinking, capable of reasoning through thinking before responding, resulting in improved performance on a wide range of benchmarks. Seed1.5-Thinking achieves 86.7 on AIME 2024, 55.0 on Codeforces and 77.3 on GPQA,…

Large language models have shown strong reasoning capabilities through chain-structured methods such as Chain-of-Thought. Recent studies optimize thought structures by generating parallel or tree-like structures, switching between long and…

Large Reasoning Models (LRMs) achieve strong performance by generating long chains of thought (CoT), but often overthink, continuing to reason after a solution has already stabilized and thereby wasting tokens and increasing latency.…

Reinforcement learning with verifiable rewards (RLVR) has been shown to enhance the reasoning capabilities of large language models (LLMs), enabling the development of large reasoning models (LRMs). However, LRMs such as DeepSeek-R1 and…

Test-time scaling has emerged as an effective way to improve language models on challenging reasoning tasks. However, most existing methods treat each problem in isolation and do not systematically reuse knowledge from prior reasoning…