We consider the problem of Sparse Principal Component Analysis (PCA) when the ratio $d/n \rightarrow c > 0$. There has been a lot of work on optimal rates on sparse PCA in the offline setting, where all the data is available for multiple passes. In contrast, when the population eigenvector is $s$-sparse, streaming algorithms that have $O(d)$ storage and $O(nd)$ time complexity either typically require strong initialization conditions or have a suboptimal error. We show that a simple algorithm that thresholds and renormalizes the output of Oja's algorithm (the Oja vector) obtains a near-optimal error rate. This is very surprising because, without thresholding, the Oja vector has a large error. Our analysis centers around bounding the entries of the unnormalized Oja vector, which involves the projection of a product of independent random matrices on a random initial vector. This is nontrivial and novel since previous analyses of Oja's algorithm and matrix products have been done when the trace of the population covariance matrix is bounded while in our setting, this quantity can be as large as $n$.
Visual navigation requires a whole range of capabilities. A crucial one of these is the ability of an agent to determine its own location and heading in an environment. Prior works commonly assume this information as given, or use methods which lack a suitable inductive bias and accumulate error over time. In this work, we show how the method of slow feature analysis (SFA), inspired by neuroscience research, overcomes both limitations by generating interpretable representations of visual data that encode location and heading of an agent. We employ SFA in a modern reinforcement learning context, analyse and compare representations and illustrate where hierarchical SFA can outperform other feature extractors on navigation tasks.
Retrieval-augmented generation framework can address the limitations of large language models by enabling real-time knowledge updates for more accurate answers. An efficient way in the training phase of retrieval-augmented models is attention distillation, which uses attention scores as a supervision signal instead of manually annotated query-document pairs. Despite its growing popularity, the detailed mechanisms behind the success of attention distillation remain unexplored, particularly the specific patterns it leverages to benefit training. In this paper, we address this gap by conducting a comprehensive review of attention distillation workflow and identifying key factors influencing the learning quality of retrieval-augmented language models. We further propose indicators for optimizing models' training methods and avoiding ineffective training.
Taxonomies represent an arborescence hierarchical structure that establishes relationships among entities to convey knowledge within a specific domain. Each edge in the taxonomy signifies a hypernym-hyponym relationship. Taxonomies find utility in various real-world applications, such as e-commerce search engines and recommendation systems. Consequently, there arises a necessity to enhance these taxonomies over time. However, manually curating taxonomies with neoteric data presents challenges due to limitations in available human resources and the exponential growth of data. Therefore, it becomes imperative to develop automatic taxonomy expansion methods. Traditional supervised taxonomy expansion approaches encounter difficulties stemming from limited resources, primarily due to the small size of existing taxonomies. This scarcity of training data often leads to overfitting. In this paper, we propose FLAME, a novel approach for taxonomy expansion in low-resource environments by harnessing the capabilities of large language models that are trained on extensive real-world knowledge. LLMs help compensate for the scarcity of domain-specific knowledge. Specifically, FLAME leverages prompting in few-shot settings to extract the inherent knowledge within the LLMs, ascertaining the hypernym entities within the taxonomy. Furthermore, it employs reinforcement learning to fine-tune the large language models, resulting in more accurate predictions. Experiments on three real-world benchmark datasets demonstrate the effectiveness of FLAME in real-world scenarios, achieving a remarkable improvement of 18.5% in accuracy and 12.3% in Wu & Palmer metric over eight baselines. Furthermore, we elucidate the strengths and weaknesses of FLAME through an extensive case study, error analysis and ablation studies on the benchmarks.
Linear temporal logic (LTL) is widely used in industrial verification. LTL formulae can be learned from traces. Scaling LTL formula learning is an open problem. We implement the first GPU-based LTL learner using a novel form of enumerative program synthesis. The learner is sound and complete. Our benchmarks indicate that it handles traces at least 2048 times more numerous, and on average at least 46 times faster than existing state-of-the-art learners. This is achieved with, among others, novel branch-free LTL semantics that has $O(\log n)$ time complexity, where $n$ is trace length, while previous implementations are $O(n^2)$ or worse (assuming bitwise boolean operations and shifts by powers of 2 have unit costs -- a realistic assumption on modern processors).
Time-series data presents limitations stemming from data quality issues, bias and vulnerabilities, and generalization problem. Integrating universal data synthesis methods holds promise in improving generalization. However, current methods cannot guarantee that the generator's output covers all unseen real data. In this paper, we introduce InfoBoost -- a highly versatile cross-domain data synthesizing framework with time series representation learning capability. We have developed a method based on synthetic data that enables model training without the need for real data, surpassing the performance of models trained with real data. Additionally, we have trained a universal feature extractor based on our synthetic data that is applicable to all time-series data. Our approach overcomes interference from multiple sources rhythmic signal, noise interference, and long-period features that exceed sampling window capabilities. Through experiments, our non-deep-learning synthetic data enables models to achieve superior reconstruction performance and universal explicit representation extraction without the need for real data.
Minimizing social bias strengthens societal bonds, promoting shared understanding and better decision-making. We revisit the definition of bias by discovering new bias types (e.g., societal status) in dynamic environments and describe them relative to context, such as culture, region, time, and personal background. Our framework includes eight hypotheses about bias and a minimizing bias strategy for each assumption as well as five methods as proposed solutions in LLM. The realization of the framework is yet to be completed.
Traditional session-based recommendation (SBR) utilizes session behavior sequences from anonymous users for recommendation. Although this strategy is highly efficient, it sacrifices the inherent semantic information of the items, making it difficult for the model to understand the true intent of the session and resulting in a lack of interpretability in the recommended results. Recently, large language models (LLMs) have flourished across various domains, offering a glimpse of hope in addressing the aforementioned challenges. Inspired by the impact of LLMs, research exploring the integration of LLMs with the Recommender system (RS) has surged like mushrooms after rain. However, constrained by high time and space costs, as well as the brief and anonymous nature of session data, the first LLM recommendation framework suitable for industrial deployment has yet to emerge in the field of SBR. To address the aforementioned challenges, we have proposed the LLM Integration Framework for SBR (LLM4SBR). Serving as a lightweight and plug-and-play framework, LLM4SBR adopts a two-step strategy. Firstly, we transform session data into a bimodal form of text and behavior. In the first step, leveraging the inferential capabilities of LLMs, we conduct inference on session text data from different perspectives and design the component for auxiliary enhancement. In the second step, the SBR model is trained on behavior data, aligning and averaging two modal session representations from different perspectives. Finally, we fuse session representations from different perspectives and modalities as the ultimate session representation for recommendation. We conducted experiments on two real-world datasets, and the results demonstrate that LLM4SBR significantly improves the performance of traditional SBR models and is highly lightweight and efficient, making it suitable for industrial deployment.
The development of artificial intelligence systems with advanced reasoning capabilities represents a persistent and long-standing research question. Traditionally, the primary strategy to address this challenge involved the adoption of symbolic approaches, where knowledge was explicitly represented by means of symbols and explicitly programmed rules. However, with the advent of machine learning, there has been a paradigm shift towards systems that can autonomously learn from data, requiring minimal human guidance. In light of this shift, in latest years, there has been increasing interest and efforts at endowing neural networks with the ability to reason, bridging the gap between data-driven learning and logical reasoning. Within this context, Neural Algorithmic Reasoning (NAR) stands out as a promising research field, aiming to integrate the structured and rule-based reasoning of algorithms with the adaptive learning capabilities of neural networks, typically by tasking neural models to mimic classical algorithms. In this dissertation, we provide theoretical and practical contributions to this area of research. We explore the connections between neural networks and tropical algebra, deriving powerful architectures that are aligned with algorithm execution. Furthermore, we discuss and show the ability of such neural reasoners to learn and manipulate complex algorithmic and combinatorial optimization concepts, such as the principle of strong duality. Finally, in our empirical efforts, we validate the real-world utility of NAR networks across different practical scenarios. This includes tasks as diverse as planning problems, large-scale edge classification tasks and the learning of polynomial-time approximate algorithms for NP-hard combinatorial problems. Through this exploration, we aim to showcase the potential integrating algorithmic reasoning in machine learning models.
Time-series data can represent the behaviors of autonomous systems, such as drones and self-driving cars. The problem of binary and multi-class classification has received a lot of attention in this field. Neural networks represent a popular approach to classifying data; However, they lack interpretability, which poses a significant challenge in extracting meaningful information from them. Signal Temporal Logic (STL) is a formalism to describe the properties of timed behaviors. We propose a method that combines all of the above: neural networks that represent STL specifications for multi-class classification of time-series data. We offer two key contributions: 1) We introduce a notion of margin for multi-class classification, and 2) we introduce the use of STL-based attributes for enhancing the interpretability of the results. We evaluate our method on two datasets and compare with state-of-the-art baselines.