Skywork: A More Open Bilingual Foundation Model

In this technical report, we present Skywork-13B, a family of large language models (LLMs) trained on a corpus of over 3.2 trillion tokens drawn from both English and Chinese texts. This bilingual foundation model is the most extensively trained and openly published LLMs of comparable size to date. We introduce a two-stage training methodology using a segmented corpus, targeting general purpose training and then domain-specific enhancement training, respectively. We show that our model not only excels on popular benchmarks, but also achieves \emph{state of the art} performance in Chinese language modeling on diverse domains. Furthermore, we propose a novel leakage detection method, demonstrating that test data contamination is a pressing issue warranting further investigation by the LLM community. To spur future research, we release Skywork-13B along with checkpoints obtained during intermediate stages of the training process. We are also releasing part of our SkyPile corpus, a collection of over 150 billion tokens of web text, which is the largest high quality open Chinese pre-training corpus to date. We hope Skywork-13B and our open corpus will serve as a valuable open-source resource to democratize access to high-quality LLMs.

SkyMath: Technical Report

Large language models (LLMs) have shown great potential to solve varieties of natural language processing (NLP) tasks, including mathematical reasoning. In this work, we present SkyMath, a large language model for mathematics with 13 billion parameters. By applying self-compare fine-tuning, we have enhanced mathematical reasoning abilities of Skywork-13B-Base remarkably. On GSM8K, SkyMath outperforms all known open-source models of similar size and has established a new SOTA performance.

CMATH: Can Your Language Model Pass Chinese Elementary School Math Test?

We present the Chinese Elementary School Math Word Problems (CMATH) dataset, comprising 1.7k elementary school-level math word problems with detailed annotations, source from actual Chinese workbooks and exams. This dataset aims to provide a benchmark tool for assessing the following question: to what grade level of elementary school math do the abilities of popular large language models (LLMs) correspond? We evaluate a variety of popular LLMs, including both commercial and open-source options, and discover that only GPT-4 achieves success (accuracy $\geq$ 60\%) across all six elementary school grades, while other models falter at different grade levels. Furthermore, we assess the robustness of several top-performing LLMs by augmenting the original problems in the CMATH dataset with distracting information. Our findings reveal that GPT-4 is able to maintains robustness, while other model fail. We anticipate that our study will expose limitations in LLMs' arithmetic and reasoning capabilities, and promote their ongoing development and advancement.

A Flexible Multi-Task Model for BERT Serving

In this demonstration, we present an efficient BERT-based multi-task (MT) framework that is particularly suitable for iterative and incremental development of the tasks. The proposed framework is based on the idea of partial fine-tuning, i.e. only fine-tune some top layers of BERT while keep the other layers frozen. For each task, we train independently a single-task (ST) model using partial fine-tuning. Then we compress the task-specific layers in each ST model using knowledge distillation. Those compressed ST models are finally merged into one MT model so that the frozen layers of the former are shared across the tasks. We exemplify our approach on eight GLUE tasks, demonstrating that it is able to achieve both strong performance and efficiency. We have implemented our method in the utterance understanding system of XiaoAI, a commercial AI assistant developed by Xiaomi. We estimate that our model reduces the overall serving cost by 86%.

Masked Conditional Random Fields for Sequence Labeling

Conditional Random Field (CRF) based neural models are among the most performant methods for solving sequence labeling problems. Despite its great success, CRF has the shortcoming of occasionally generating illegal sequences of tags, e.g. sequences containing an "I-" tag immediately after an "O" tag, which is forbidden by the underlying BIO tagging scheme. In this work, we propose Masked Conditional Random Field (MCRF), an easy to implement variant of CRF that impose restrictions on candidate paths during both training and decoding phases. We show that the proposed method thoroughly resolves this issue and brings consistent improvement over existing CRF-based models with near zero additional cost.

A convergence and asymptotic analysis of the generalized symmetric FastICA algorithm

This contribution deals with the generalized symmetric FastICA algorithm in the domain of Independent Component Analysis (ICA). The generalized symmetric version of FastICA has been shown to have the potential to achieve the Cram\'er-Rao Bound (CRB) by allowing the usage of different nonlinearity functions in its parallel implementations of one-unit FastICA. In spite of this appealing property, a rigorous study of the asymptotic error of the generalized symmetric FastICA algorithm is still missing in the community. In fact, all the existing results exhibit certain limitations, such as ignoring the impact of data standardization on the asymptotic statistics or being based on a heuristic approach. In this work, we aim at filling this blank. The first result of this contribution is the characterization of the limits of the generalized symmetric FastICA. It is shown that the algorithm optimizes a function that is a sum of the contrast functions used by traditional one-unit FastICA with a correction of the sign. Based on this characterization, we derive a closed-form analytic expression of the asymptotic covariance matrix of the generalized symmetric FastICA estimator using the method of estimating equation and M-estimator.

Convex recovery of tensors using nuclear norm penalization

The subdifferential of convex functions of the singular spectrum of real matrices has been widely studied in matrix analysis, optimization and automatic control theory. Convex analysis and optimization over spaces of tensors is now gaining much interest due to its potential applications to signal processing, statistics and engineering. The goal of this paper is to present an applications to the problem of low rank tensor recovery based on linear random measurement by extending the results of Tropp to the tensors setting.

An Overview of the Asymptotic Performance of the Family of the FastICA Algorithms

This contribution summarizes the results on the asymptotic performance of several variants of the FastICA algorithm. A number of new closed-form expressions are presented.

A study of the fixed points and spurious solutions of the FastICA algorithm

The FastICA algorithm is one of the most popular iterative algorithms in the domain of linear independent component analysis. Despite its success, it is observed that FastICA occasionally yields outcomes that do not correspond to any true solutions (known as demixing vectors) of the ICA problem. These outcomes are commonly referred to as spurious solutions. Although FastICA is among the most extensively studied ICA algorithms, the occurrence of spurious solutions are not yet completely understood by the community. In this contribution, we aim at addressing this issue. In the first part of this work, we are interested in the relationship between demixing vectors, local optimizers of the contrast function and (attractive or unattractive) fixed points of FastICA algorithm. Characterizations of these sets are given, and an inclusion relationship is discovered. In the second part, we investigate the possible scenarios where spurious solutions occur. We show that when certain bimodal Gaussian mixtures distributions are involved, there may exist spurious solutions that are attractive fixed points of FastICA. In this case, popular nonlinearities such as "gauss" or "tanh" tend to yield spurious solutions, whereas only "kurtosis" may give reliable results. Some advices are given for the practical choice of nonlinearity function.