Creativity or Brute Force? Using Brainteasers as a Window into the Problem-Solving Abilities of Large Language Models

Accuracy remains a standard metric for evaluating AI systems, but it offers limited insight into how models arrive at their solutions. In this work, we introduce a benchmark based on brainteasers written in long narrative form to probe more deeply into the types of reasoning strategies that models use. Brainteasers are well-suited for this goal because they can be solved with multiple approaches, such as a few-step solution that uses a creative insight or a longer solution that uses more brute force. We investigate large language models (LLMs) across multiple layers of reasoning, focusing not only on correctness but also on the quality and creativity of their solutions. We investigate many aspects of the reasoning process: (1) semantic parsing of the brainteasers into precise mathematical competition style formats; (2) generating solutions from these mathematical forms; (3) self-correcting solutions based on gold solutions; (4) producing step-by-step sketches of solutions; and (5) making use of hints. We find that LLMs are in many cases able to find creative, insightful solutions to brainteasers, suggesting that they capture some of the capacities needed to solve novel problems in creative ways. Nonetheless, there also remain situations where they rely on brute force despite the availability of more efficient, creative solutions, highlighting a potential direction for improvement in the reasoning abilities of LLMs.

Stochastic Constrained Decentralized Optimization for Machine Learning with Fewer Data Oracles: a Gradient Sliding Approach

In modern decentralized applications, ensuring communication efficiency and privacy for the users are the key challenges. In order to train machine-learning models, the algorithm has to communicate to the data center and sample data for its gradient computation, thus exposing the data and increasing the communication cost. This gives rise to the need for a decentralized optimization algorithm that is communication-efficient and minimizes the number of gradient computations. To this end, we propose the primal-dual sliding with conditional gradient sliding framework, which is communication-efficient and achieves an $\varepsilon$-approximate solution with the optimal gradient complexity of $O(1/\sqrt{\varepsilon}+\sigma^2/{\varepsilon^2})$ and $O(\log(1/\varepsilon)+\sigma^2/\varepsilon)$ for the convex and strongly convex setting respectively and an LO (Linear Optimization) complexity of $O(1/\varepsilon^2)$ for both settings given a stochastic gradient oracle with variance $\sigma^2$. Compared with the prior work \cite{wai-fw-2017}, our framework relaxes the assumption of the optimal solution being a strict interior point of the feasible set and enjoys wider applicability for large-scale training using a stochastic gradient oracle. We also demonstrate the efficiency of our algorithms with various numerical experiments.