A critical question about Large Language Models (LLMs) is whether their apparent deficiency in mathematical reasoning is inherent, or merely a result of insufficient exposure to high-quality mathematical data. To explore this, we developed an automated method for generating high-quality, supervised mathematical datasets. The method carefully mutates existing math problems, ensuring both diversity and validity of the newly generated problems. This is achieved by a neuro-symbolic data generation framework combining the intuitive informalization strengths of LLMs, and the precise symbolic reasoning of math solvers along with projected Markov chain Monte Carlo sampling in the highly-irregular symbolic space. Empirical experiments demonstrate the high quality of data generated by the proposed method, and that the LLMs, specifically LLaMA-2 and Mistral, when realigned with the generated data, surpass their state-of-the-art counterparts.

Training a single model on multiple input domains and/or output tasks allows for compressing information from multiple sources into a unified backbone hence improves model efficiency. It also enables potential positive knowledge transfer across tasks/domains, leading to improved accuracy and data-efficient training. However, optimizing such networks is a challenge, in particular due to discrepancies between the different tasks or domains: Despite several hypotheses and solutions proposed over the years, recent work has shown that uniform scalarization training, i.e., simply minimizing the average of the task losses, yields on-par performance with more costly SotA optimization methods. This raises the issue of how well we understand the training dynamics of multi-task and multi-domain networks. In this work, we first devise a large-scale unified analysis of multi-domain and multi-task learning to better understand the dynamics of scalarization across varied task/domain combinations and model sizes. Following these insights, we then propose to leverage population-based training to efficiently search for the optimal scalarization weights when dealing with a large number of tasks or domains.

We present a series of new PAC-Bayes learning guarantees for randomized algorithms with sample-dependent priors.

We illustrate the online optimization process of RCL in Figure 1. Finally, we discuss the performance of RCL. We consider the management of N batteries. This problem falls into SOCO based on the reduction framework described in [49]. We consider each problem instance as one day (T = 24 hours, plus an initial action).

We study a challenging form of Smoothed Online Convex Optimization, a.k.a.

Most large multimodal models (LMMs) are implemented by feeding visual tokens as a sequence into the first layer of a large language model (LLM). The resulting architecture is simple but significantly increases computation and memory costs, as it has to handle a large number of additional tokens in its input layer. This paper presents a new architecture DeepStack for LMMs. Considering N layers in the language and vision transformer of LMMs, we stack the visual tokens into N groups and feed each group to its aligned transformer layer from bottom to top, as illustrated in Figure 1. Surprisingly, this simple method greatly enhances the power of LMMs to model interactions among visual tokens across layers but with minimal additional cost. We apply DeepStack to both language and vision transformer in LMMs, and validate the effectiveness of DeepStack LMMs with extensive empirical results. Using the same context length, our DeepStack 7B and 13B parameters surpass their counterparts by 2.7 and 2.9 on average across 9 benchmarks, respectively.