Despite the advancements in large language models (LLMs) for mathematical reasoning, solving competition-level math problems remains a significant challenge, especially for open-source LLMs without external tools. We introduce the MMIQC dataset, comprising a mixture of processed web data and synthetic question-response pairs, aimed at enhancing the mathematical reasoning capabilities of base language models. Models fine-tuned on MMIQC consistently surpass their counterparts in performance on the MATH benchmark across various model sizes. Notably, Qwen-72B-MMIQC achieves a 45.0% accuracy, exceeding the previous open-source state-of-the-art by 8.2% and outperforming the initial version GPT-4 released in 2023. Extensive evaluation results on Hungarian high school finals suggest that such improvement can generalize to unseen data. Our ablation study on MMIQC reveals that a large part of the improvement can be attributed to our novel augmentation method, Iterative Question Composing (IQC), which involves iteratively composing new questions from seed problems using an LLM and applying rejection sampling through another LLM.

Generative Flow Networks (GFlowNets) are a novel class of generative models designed to sample from unnormalized distributions and have found applications in various important tasks, attracting great research interest in their training algorithms. In general, GFlowNets are trained by fitting the forward flow to the backward flow on sampled training objects. Prior work focused on the choice of training objects, parameterizations, sampling and resampling strategies, and backward policies, aiming to enhance credit assignment, exploration, or exploitation of the training process. However, the choice of regression loss, which can highly influence the exploration and exploitation behavior of the under-training policy, has been overlooked. Due to the lack of theoretical understanding for choosing an appropriate regression loss, most existing algorithms train the flow network by minimizing the squared error of the forward and backward flows in log-space, i.e., using the quadratic regression loss. In this work, we rigorously prove that distinct regression losses correspond to specific divergence measures, enabling us to design and analyze regression losses according to the desired properties of the corresponding divergence measures. Specifically, we examine two key properties: zero-forcing and zero-avoiding, where the former promotes exploitation and higher rewards, and the latter encourages exploration and enhances diversity. Based on our theoretical framework, we propose three novel regression losses, namely, Shifted-Cosh, Linex(1/2), and Linex(1). We evaluate them across three benchmarks: hyper-grid, bit-sequence generation, and molecule generation. Our proposed losses are compatible with most existing training algorithms, and significantly improve the performances of the algorithms concerning convergence speed, sample diversity, and robustness.

Scaling language models to handle longer input sequences typically necessitates large key-value (KV) caches, resulting in substantial memory overhead during inference. In this paper, we propose Tensor Product Attention (TPA), a novel attention mechanism that uses tensor decompositions to represent queries, keys, and values compactly, substantially shrinking the KV cache size at inference time. By factorizing these representations into contextual low-rank components and seamlessly integrating with Rotary Position Embedding (RoPE), TPA achieves improved model quality alongside memory efficiency. Based on TPA, we introduce the Tensor ProducT ATTenTion Transformer (T6), a new model architecture for sequence modeling. Through extensive empirical evaluation on language modeling tasks, we demonstrate that T6 surpasses or matches the performance of standard Transformer baselines including Multi-Head Attention (MHA), Multi-Query Attention (MQA), Grouped-Query Attention (GQA), and Multi-Head Latent Attention (MLA) across various metrics, including perplexity and a range of established evaluation benchmarks. Notably, TPA's memory efficiency and computational efficiency at decoding stage enables processing longer sequences under fixed resource constraints, addressing a critical scalability challenge in modern language models. Project Page: https://github.com/tensorgi/TPA.

Contrastive learning is a powerful self-supervised learning method, but we have a limited theoretical understanding of how it works and why it works. In this paper, we prove that contrastive learning with the standard InfoNCE loss is equivalent to spectral clustering on the similarity graph. Using this equivalence as the building block, we extend our analysis to the CLIP model and rigorously characterize how similar multi-modal objects are embedded together. Motivated by our theoretical insights, we introduce the Kernel-InfoNCE loss, incorporating mixtures of kernel functions that outperform the standard Gaussian kernel on several vision datasets.

In this paper, we conduct a comprehensive analysis of two dual-branch (Siamese architecture) self-supervised learning approaches, namely Barlow Twins and spectral contrastive learning, through the lens of matrix mutual information. We prove that the loss functions of these methods implicitly optimize both matrix mutual information and matrix joint entropy. This insight prompts us to further explore the category of single-branch algorithms, specifically MAE and U-MAE, for which mutual information and joint entropy become the entropy. Building on this intuition, we introduce the Matrix Variational Masked Auto-Encoder (M-MAE), a novel method that leverages the matrix-based estimation of entropy as a regularizer and subsumes U-MAE as a special case. The empirical evaluations underscore the effectiveness of M-MAE compared with the state-of-the-art methods, including a 3.9% improvement in linear probing ViT-Base, and a 1% improvement in fine-tuning ViT-Large, both on ImageNet.

The maximum entropy encoding framework provides a unified perspective for many non-contrastive learning methods like SimSiam, Barlow Twins, and MEC. Inspired by this framework, we introduce Matrix-SSL, a novel approach that leverages matrix information theory to interpret the maximum entropy encoding loss as matrix uniformity loss. Furthermore, Matrix-SSL enhances the maximum entropy encoding method by seamlessly incorporating matrix alignment loss, directly aligning covariance matrices in different branches. Experimental results reveal that Matrix-SSL outperforms state-of-the-art methods on the ImageNet dataset under linear evaluation settings and on MS-COCO for transfer learning tasks. Specifically, when performing transfer learning tasks on MS-COCO, our method outperforms previous SOTA methods such as MoCo v2 and BYOL up to 3.3% with only 400 epochs compared to 800 epochs pre-training. We also try to introduce representation learning into the language modeling regime by fine-tuning a 7B model using matrix cross-entropy loss, with a margin of 3.1% on the GSM8K dataset over the standard cross-entropy loss.

Since the proposal of Granger causality, many researchers have followed the idea and developed extensions to the original algorithm. The classic Granger causality test aims to detect the existence of the static causal relationship. Notably, a fundamental assumption underlying most previous studies is the stationarity of causality, which requires the causality between variables to keep stable. However, this study argues that it is easy to break in real-world scenarios. Fortunately, our paper presents an essential observation: if we consider a sufficiently short window when discovering the rapidly changing causalities, they will keep approximately static and thus can be detected using the static way correctly. In light of this, we develop EffCause, bringing dynamics into classic Granger causality. Specifically, to efficiently examine the causalities on different sliding window lengths, we design two optimization schemes in EffCause and demonstrate the advantage of EffCause through extensive experiments on both simulated and real-world datasets. The results validate that EffCause achieves state-of-the-art accuracy in continuous causal discovery tasks while achieving faster computation. Case studies from cloud system failure analysis and traffic flow monitoring show that EffCause effectively helps us understand real-world time-series data and solve practical problems.

In the current landscape of explanation methodologies, most predominant approaches, such as SHAP and LIME, employ removal-based techniques to evaluate the impact of individual features by simulating various scenarios with specific features omitted. Nonetheless, these methods primarily emphasize efficiency in the original context, often resulting in general inconsistencies. In this paper, we demonstrate that such inconsistency is an inherent aspect of these approaches by establishing the Impossible Trinity Theorem, which posits that interpretability, efficiency, and consistency cannot hold simultaneously. Recognizing that the attainment of an ideal explanation remains elusive, we propose the utilization of interpretation error as a metric to gauge inefficiencies and inconsistencies. To this end, we present two novel algorithms founded on the standard polynomial basis, aimed at minimizing interpretation error. Our empirical findings indicate that the proposed methods achieve a substantial reduction in interpretation error, up to 31.8 times lower when compared to alternative techniques.

This letter addresses the challenge of multiplying large real-numbered matrices$\mathbf {A}$and$\mathbf {B}$in on-device edge computing environments with a master node and$N$worker nodes. To ensure accuracy and mitigate adversarial behavior, existing approaches rely on polynomial coding techniques. However, polynomial decoding on real numbers is numerically unstable, leading prior works to employ finite fields or complex number fields. Nevertheless, computing on finite fields may encounter computation overflows. In this letter, we propose a novel, numerically stable coded matrix multiplication scheme on real number fields. Our approach detects malicious workers and mitigates the impact of slower workers (stragglers), all while operating solely on real number fields.