In data-driven control and machine learning, a common requirement involves breaking down large matrices into smaller, low-rank factors that possess specific levels of sparsity. This paper introduces an innovative solution to the orthogonal nonnegative matrix factorization (ONMF) problem. The objective is to approximate input data by using two low-rank nonnegative matrices, adhering to both orthogonality and $\ell_0$-norm sparsity constraints. the proposed maximum-entropy-principle based framework ensures orthogonality and sparsity of features or the mixing matrix, while maintaining nonnegativity in both. Additionally, the methodology offers a quantitative determination of the ``true'' number of underlying features, a crucial hyperparameter for ONMF. Experimental evaluation on synthetic and a standard datasets highlights the method's superiority in terms of sparsity, orthogonality, and computational speed compared to existing approaches. Notably, the proposed method achieves comparable or improved reconstruction errors in line with the literature.
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Geometric matching is an important topic in computational geometry and has been extensively studied over decades. In this paper, we study a geometric-matching problem, known as geometric many-to-many matching. In this problem, the input is a set $S$ of $n$ colored points in $\mathbb{R}^d$, which implicitly defines a graph $G = (S,E(S))$ where $E(S) = \{(p,q): p,q \in S \text{ have different colors}\}$, and the goal is to compute a minimum-cost subset $E^* \subseteq E(S)$ of edges that cover all points in $S$. Here the cost of $E^*$ is the sum of the costs of all edges in $E^*$, where the cost of a single edge $e$ is the Euclidean distance (or more generally, the $L_p$-distance) between the two endpoints of $e$. Our main result is a $(1+\varepsilon)$-approximation algorithm with an optimal running time $O_\varepsilon(n \log n)$ for geometric many-to-many matching in any fixed dimension, which works under any $L_p$-norm. This is the first near-linear approximation scheme for the problem in any $d \geq 2$. Prior to this work, only the bipartite case of geometric many-to-many matching was considered in $\mathbb{R}^1$ and $\mathbb{R}^2$, and the best known approximation scheme in $\mathbb{R}^2$ takes $O_\varepsilon(n^{1.5} \cdot \mathsf{poly}(\log n))$ time.
Given the growing significance of reliable, trustworthy, and explainable machine learning, the requirement of uncertainty quantification for anomaly detection systems has become increasingly important. In this context, effectively controlling Type I error rates ($\alpha$) without compromising the statistical power ($1-\beta$) of these systems can build trust and reduce costs related to false discoveries, particularly when follow-up procedures are expensive. Leveraging the principles of conformal prediction emerges as a promising approach for providing respective statistical guarantees by calibrating a model's uncertainty. This work introduces a novel framework for anomaly detection, termed cross-conformal anomaly detection, building upon well-known cross-conformal methods designed for prediction tasks. With that, it addresses a natural research gap by extending previous works in the context of inductive conformal anomaly detection, relying on the split-conformal approach for model calibration. Drawing on insights from conformal prediction, we demonstrate that the derived methods for calculating cross-conformal $p$-values strike a practical compromise between statistical efficiency (full-conformal) and computational efficiency (split-conformal) for uncertainty-quantified anomaly detection on benchmark datasets.
This paper introduces $\infty$-Diff, a generative diffusion model defined in an infinite-dimensional Hilbert space, which can model infinite resolution data. By training on randomly sampled subsets of coordinates and denoising content only at those locations, we learn a continuous function for arbitrary resolution sampling. Unlike prior neural field-based infinite-dimensional models, which use point-wise functions requiring latent compression, our method employs non-local integral operators to map between Hilbert spaces, allowing spatial context aggregation. This is achieved with an efficient multi-scale function-space architecture that operates directly on raw sparse coordinates, coupled with a mollified diffusion process that smooths out irregularities. Through experiments on high-resolution datasets, we found that even at an $8\times$ subsampling rate, our model retains high-quality diffusion. This leads to significant run-time and memory savings, delivers samples with lower FID scores, and scales beyond the training resolution while retaining detail.
Object-oriented programming (OOP) is one of the most popular paradigms used for building software systems. However, despite its industrial and academic popularity, OOP is still missing a formal apparatus similar to $\lambda$-calculus, which functional programming is based on. There were a number of attempts to formalize OOP, but none of them managed to cover all the features available in modern OO programming languages, such as C++ or Java. We have made yet another attempt and created $\varphi$-calculus. We also created EOLANG (also called EO), an experimental programming language based on $\varphi$-calculus.
The idea of decision-aware model learning, that models should be accurate where it matters for decision-making, has gained prominence in model-based reinforcement learning. While promising theoretical results have been established, the empirical performance of algorithms leveraging a decision-aware loss has been lacking, especially in continuous control problems. In this paper, we present a study on the necessary components for decision-aware reinforcement learning models and we showcase design choices that enable well-performing algorithms. To this end, we provide a theoretical and empirical investigation into algorithmic ideas in the field. We highlight that empirical design decisions established in the MuZero line of works, most importantly the use of a latent model, are vital to achieving good performance for related algorithms. Furthermore, we show that the MuZero loss function is biased in stochastic environments and establish that this bias has practical consequences. Building on these findings, we present an overview of which decision-aware loss functions are best used in what empirical scenarios, providing actionable insights to practitioners in the field.
Assessing the quality of summarizers poses significant challenges. In response, we propose a novel task-oriented evaluation approach that assesses summarizers based on their capacity to produce summaries that are useful for downstream tasks, while preserving task outcomes. We theoretically establish a direct relationship between the resulting error probability of these tasks and the mutual information between source texts and generated summaries. We introduce $\texttt{COSMIC}$ as a practical implementation of this metric, demonstrating its strong correlation with human judgment-based metrics and its effectiveness in predicting downstream task performance. Comparative analyses against established metrics like $\texttt{BERTScore}$ and $\texttt{ROUGE}$ highlight the competitive performance of $\texttt{COSMIC}$.
The performance gap between memory and processor has grown rapidly. Consequently, the energy and wall-clock time costs associated with moving data between the CPU and main memory predominate the overall computational cost. The Processing-in-Memory (PIM) paradigm emerges as a promising architecture that mitigates the need for extensive data movements by strategically positioning computing units proximate to the memory. Despite the abundant efforts devoted to building a robust and highly-available PIM system, identifying PIM-friendly segments of applications poses significant challenges due to the lack of a comprehensive tool to evaluate the intrinsic memory access pattern of the segment. To tackle this challenge, we propose A$^3$PIM: an Automated, Analytic and Accurate Processing-in-Memory offloader. We systematically consider the cross-segment data movement and the intrinsic memory access pattern of each code segment via static code analyzer. We evaluate A$^3$PIM across a wide range of real-world workloads including GAP and PrIM benchmarks and achieve an average speedup of 2.63x and 4.45x (up to 7.14x and 10.64x) when compared to CPU-only and PIM-only executions, respectively.
Click-through rate (CTR) prediction plays a critical role in recommender systems and online advertising. The data used in these applications are multi-field categorical data, where each feature belongs to one field. Field information is proved to be important and there are several works considering fields in their models. In this paper, we proposed a novel approach to model the field information effectively and efficiently. The proposed approach is a direct improvement of FwFM, and is named as Field-matrixed Factorization Machines (FmFM, or $FM^2$). We also proposed a new explanation of FM and FwFM within the FmFM framework, and compared it with the FFM. Besides pruning the cross terms, our model supports field-specific variable dimensions of embedding vectors, which acts as soft pruning. We also proposed an efficient way to minimize the dimension while keeping the model performance. The FmFM model can also be optimized further by caching the intermediate vectors, and it only takes thousands of floating-point operations (FLOPs) to make a prediction. Our experiment results show that it can out-perform the FFM, which is more complex. The FmFM model's performance is also comparable to DNN models which require much more FLOPs in runtime.
Graph convolution networks (GCN) are increasingly popular in many applications, yet remain notoriously hard to train over large graph datasets. They need to compute node representations recursively from their neighbors. Current GCN training algorithms suffer from either high computational costs that grow exponentially with the number of layers, or high memory usage for loading the entire graph and node embeddings. In this paper, we propose a novel efficient layer-wise training framework for GCN (L-GCN), that disentangles feature aggregation and feature transformation during training, hence greatly reducing time and memory complexities. We present theoretical analysis for L-GCN under the graph isomorphism framework, that L-GCN leads to as powerful GCNs as the more costly conventional training algorithm does, under mild conditions. We further propose L^2-GCN, which learns a controller for each layer that can automatically adjust the training epochs per layer in L-GCN. Experiments show that L-GCN is faster than state-of-the-arts by at least an order of magnitude, with a consistent of memory usage not dependent on dataset size, while maintaining comparable prediction performance. With the learned controller, L^2-GCN can further cut the training time in half. Our codes are available at //github.com/Shen-Lab/L2-GCN.
Network representation learning in low dimensional vector space has attracted considerable attention in both academic and industrial domains. Most real-world networks are dynamic with addition/deletion of nodes and edges. The existing graph embedding methods are designed for static networks and they cannot capture evolving patterns in a large dynamic network. In this paper, we propose a dynamic embedding method, dynnode2vec, based on the well-known graph embedding method node2vec. Node2vec is a random walk based embedding method for static networks. Applying static network embedding in dynamic settings has two crucial problems: 1) Generating random walks for every time step is time consuming 2) Embedding vector spaces in each timestamp are different. In order to tackle these challenges, dynnode2vec uses evolving random walks and initializes the current graph embedding with previous embedding vectors. We demonstrate the advantages of the proposed dynamic network embedding by conducting empirical evaluations on several large dynamic network datasets.
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