Suboptimality bounds for trace-bounded SDPs enable a faster and scalable low-rank SDP solver SDPLR+

Semidefinite programs (SDPs) and their solvers are powerful tools with many applications in machine learning and data science. Designing scalable SDP solvers is challenging because by standard the positive semidefinite decision variable is an $n \times n$ dense matrix, even though the input is often an $n \times n$ sparse matrix. However, the information in the solution may not correspond to a full-rank dense matrix as shown by Bavinok and Pataki. Two decades ago, Burer and Monterio developed an SDP solver $\texttt{SDPLR}$ that optimizes over a low-rank factorization instead of the full matrix. This greatly decreases the storage cost and works well for many problems. The original solver $\texttt{SDPLR}$ tracks only the primal infeasibility of the solution, limiting the technique's flexibility to produce moderate accuracy solutions. We use a suboptimality bound for trace-bounded SDP problems that enables us to track the progress better and perform early termination. We then develop $\texttt{SDPLR+}$, which starts the optimization with an extremely low-rank factorization and dynamically updates the rank based on the primal infeasibility and suboptimality. This further speeds up the computation and saves the storage cost. Numerical experiments on Max Cut, Minimum Bisection, Cut Norm, and Lov\'{a}sz Theta problems with many recent memory-efficient scalable SDP solvers demonstrate its scalability up to problems with million-by-million decision variables and it is often the fastest solver to a moderate accuracy of $10^{-2}$.

Is Next Token Prediction Sufficient for GPT? Exploration on Code Logic Comprehension

Large language models (LLMs) has experienced exponential growth, they demonstrate remarkable performance across various tasks. Notwithstanding, contemporary research primarily centers on enhancing the size and quality of pretraining data, still utilizing the next token prediction task on autoregressive transformer model structure. The efficacy of this task in truly facilitating the model's comprehension of code logic remains questionable, we speculate that it still interprets code as mere text, while human emphasizes the underlying logical knowledge. In order to prove it, we introduce a new task, "Logically Equivalent Code Selection," which necessitates the selection of logically equivalent code from a candidate set, given a query code. Our experimental findings indicate that current LLMs underperform in this task, since they understand code by unordered bag of keywords. To ameliorate their performance, we propose an advanced pretraining task, "Next Token Prediction+". This task aims to modify the sentence embedding distribution of the LLM without sacrificing its generative capabilities. Our experimental results reveal that following this pretraining, both Code Llama and StarCoder, the prevalent code domain pretraining models, display significant improvements on our logically equivalent code selection task and the code completion task.

Rethinking the Instruction Quality: LIFT is What You Need

Instruction tuning, a specialized technique to enhance large language model (LLM) performance via instruction datasets, relies heavily on the quality of employed data. Existing quality improvement methods alter instruction data through dataset expansion or curation. However, the expansion method risks data redundancy, potentially compromising LLM performance, while the curation approach confines the LLM's potential to the original dataset. Our aim is to surpass the original data quality without encountering these shortcomings. To achieve this, we propose LIFT (LLM Instruction Fusion Transfer), a novel and versatile paradigm designed to elevate the instruction quality to new heights. LIFT strategically broadens data distribution to encompass more high-quality subspaces and eliminates redundancy, concentrating on high-quality segments across overall data subspaces. Experimental results demonstrate that, even with a limited quantity of high-quality instruction data selected by our paradigm, LLMs not only consistently uphold robust performance across various tasks but also surpass some state-of-the-art results, highlighting the significant improvement in instruction quality achieved by our paradigm.

SUT: Active Defects Probing for Transcompiler Models

Automatic Program translation has enormous application value and hence has been attracting significant interest from AI researchers. However, we observe that current program translation models still make elementary syntax errors, particularly, when the target language does not have syntax elements in the source language. Metrics like BLUE, CodeBLUE and computation accuracy may not expose these issues. In this paper we introduce a new metrics for programming language translation and these metrics address these basic syntax errors. We develop a novel active defects probing suite called Syntactic Unit Tests (SUT) which includes a highly interpretable evaluation harness for accuracy and test scoring. Experiments have shown that even powerful models like ChatGPT still make mistakes on these basic unit tests. Specifically, compared to previous program translation task evaluation dataset, its pass rate on our unit tests has decreased by 26.15%. Further our evaluation harness reveal syntactic element errors in which these models exhibit deficiencies.

Program Translation via Code Distillation

Software version migration and program translation are an important and costly part of the lifecycle of large codebases. Traditional machine translation relies on parallel corpora for supervised translation, which is not feasible for program translation due to a dearth of aligned data. Recent unsupervised neural machine translation techniques have overcome data limitations by included techniques such as back translation and low level compiler intermediate representations (IR). These methods face significant challenges due to the noise in code snippet alignment and the diversity of IRs respectively. In this paper we propose a novel model called Code Distillation (CoDist) whereby we capture the semantic and structural equivalence of code in a language agnostic intermediate representation. Distilled code serves as a translation pivot for any programming language, leading by construction to parallel corpora which scale to all available source code by simply applying the distillation compiler. We demonstrate that our approach achieves state-of-the-art performance on CodeXGLUE and TransCoder GeeksForGeeks translation benchmarks, with an average absolute increase of 12.7% on the TransCoder GeeksforGeeks translation benchmark compare to TransCoder-ST.

A Multi-robot Coverage Path Planning Algorithm Based on Improved DARP Algorithm

The research on multi-robot coverage path planning (CPP) has been attracting more and more attention. In order to achieve efficient coverage, this paper proposes an improved DARP coverage algorithm. The improved DARP algorithm based on A* algorithm is used to assign tasks to robots and then combined with STC algorithm based on Up-First algorithm to achieve full coverage of the task area. Compared with the initial DARP algorithm, this algorithm has higher efficiency and higher coverage rate.

A flexible PageRank-based graph embedding framework closely related to spectral eigenvector embeddings

We study a simple embedding technique based on a matrix of personalized PageRank vectors seeded on a random set of nodes. We show that the embedding produced by the element-wise logarithm of this matrix (1) are related to the spectral embedding for a class of graphs where spectral embeddings are significant, and hence useful representation of the data, (2) can be done for the entire network or a smaller part of it, which enables precise local representation, and (3) uses a relatively small number of PageRank vectors compared to the size of the networks. Most importantly, the general nature of this embedding strategy opens up many emerging applications, where eigenvector and spectral techniques may not be well established, to the PageRank-based relatives. For instance, similar techniques can be used on PageRank vectors from hypergraphs to get "spectral-like" embeddings.

Continual Learning for Text Classification with Information Disentanglement Based Regularization

Continual learning has become increasingly important as it enables NLP models to constantly learn and gain knowledge over time. Previous continual learning methods are mainly designed to preserve knowledge from previous tasks, without much emphasis on how to well generalize models to new tasks. In this work, we propose an information disentanglement based regularization method for continual learning on text classification. Our proposed method first disentangles text hidden spaces into representations that are generic to all tasks and representations specific to each individual task, and further regularizes these representations differently to better constrain the knowledge required to generalize. We also introduce two simple auxiliary tasks: next sentence prediction and task-id prediction, for learning better generic and specific representation spaces. Experiments conducted on large-scale benchmarks demonstrate the effectiveness of our method in continual text classification tasks with various sequences and lengths over state-of-the-art baselines. We have publicly released our code at https://github.com/GT-SALT/IDBR.

Stochastic-Sign SGD for Federated Learning with Theoretical Guarantees

Federated learning (FL) has emerged as a prominent distributed learning paradigm. FL entails some pressing needs for developing novel parameter estimation approaches with theoretical guarantees of convergence, which are also communication efficient, differentially private and Byzantine resilient in the heterogeneous data distribution settings. Quantization-based SGD solvers have been widely adopted in FL and the recently proposed SIGNSGD with majority vote shows a promising direction. However, no existing methods enjoy all the aforementioned properties. In this paper, we propose an intuitively-simple yet theoretically-sound method based on SIGNSGD to bridge the gap. We present Stochastic-Sign SGD which utilizes novel stochastic-sign based gradient compressors enabling the aforementioned properties in a unified framework. We also present an error-feedback variant of the proposed Stochastic-Sign SGD which further improves the learning performance in FL. We test the proposed method with extensive experiments using deep neural networks on the MNIST dataset. The experimental results corroborate the effectiveness of the proposed method.