Payment channel networks (PCNs) are a promising solution to the scalability problem of cryptocurrencies. Any two users connected by a payment channel in the network can theoretically send an unbounded number of instant, costless transactions between them. Users who are not directly connected can also transact with each other in a multi-hop fashion. In this work, we study the incentive structure behind the creation of payment channel networks, particularly from the point of view of a single user that wants to join the network. We define a utility function for a new user in terms of expected revenue, expected fees, and the cost of creating channels, and then provide constant factor approximation algorithms that optimise the utility function given a certain budget. Additionally, we take a step back from a single user to the whole network and examine the parameter spaces under which simple graph topologies form a Nash equilibrium.
State-of-the-art deep neural networks are trained with large amounts (millions or even billions) of data. The expensive computation and memory costs make it difficult to train them on limited hardware resources, especially for recent popular large language models (LLM) and computer vision models (CV). Recent popular dataset distillation methods are thus developed, aiming to reduce the number of training samples via synthesizing small-scale datasets via gradient matching. However, as the gradient calculation is coupled with the specific network architecture, the synthesized dataset is biased and performs poorly when used for training unseen architectures. To address these limitations, we present dataset quantization (DQ), a new framework to compress large-scale datasets into small subsets which can be used for training any neural network architectures. Extensive experiments demonstrate that DQ is able to generate condensed small datasets for training unseen network architectures with state-of-the-art compression ratios for lossless model training. To the best of our knowledge, DQ is the first method that can successfully distill large-scale datasets such as ImageNet-1k with a state-of-the-art compression ratio. Notably, with 60% data from ImageNet and 20% data from Alpaca's instruction tuning data, the models can be trained with negligible or no performance drop for both vision tasks (including classification, semantic segmentation, and object detection) as well as language tasks (including instruction tuning tasks such as BBH and DROP).
Graph neural networks (GNNs) are commonly described as being permutation equivariant with respect to node relabeling in the graph. This symmetry of GNNs is often compared to the translation equivariance symmetry of Euclidean convolution neural networks (CNNs). However, these two symmetries are fundamentally different: The translation equivariance of CNNs corresponds to symmetries of the fixed domain acting on the image signal (sometimes known as active symmetries), whereas in GNNs any permutation acts on both the graph signals and the graph domain (sometimes described as passive symmetries). In this work, we focus on the active symmetries of GNNs, by considering a learning setting where signals are supported on a fixed graph. In this case, the natural symmetries of GNNs are the automorphisms of the graph. Since real-world graphs tend to be asymmetric, we relax the notion of symmetries by formalizing approximate symmetries via graph coarsening. We present a bias-variance formula that quantifies the tradeoff between the loss in expressivity and the gain in the regularity of the learned estimator, depending on the chosen symmetry group. To illustrate our approach, we conduct extensive experiments on image inpainting, traffic flow prediction, and human pose estimation with different choices of symmetries. We show theoretically and empirically that the best generalization performance can be achieved by choosing a suitably larger group than the graph automorphism group, but smaller than the full permutation group.
We show how a neural network can be trained on individual intrusive listening test scores to predict a distribution of scores for each pair of reference and coded input stereo or binaural signals. We nickname this method the Generative Machine Listener (GML), as it is capable of generating an arbitrary amount of simulated listening test data. Compared to a baseline system using regression over mean scores, we observe lower outlier ratios (OR) for the mean score predictions, and obtain easy access to the prediction of confidence intervals (CI). The introduction of data augmentation techniques from the image domain results in a significant increase in CI prediction accuracy as well as Pearson and Spearman rank correlation of mean scores.
Diffusion models have successfully been applied to generative tasks in various continuous domains. However, applying diffusion to discrete categorical data remains a non-trivial task. Moreover, generation in continuous domains often requires clipping in practice, which motivates the need for a theoretical framework for adapting diffusion to constrained domains. Inspired by the mirror Langevin algorithm for the constrained sampling problem, in this theoretical report we propose Mirror Diffusion Models (MDMs). We demonstrate MDMs in the context of simplex diffusion and propose natural extensions to popular domains such as image and text generation.
Traditional problems in computational geometry involve aspects that are both discrete and continuous. One such example is nearest-neighbor searching, where the input is discrete, but the result depends on distances, which vary continuously. In many real-world applications of geometric data structures, it is assumed that query results are continuous, free of jump discontinuities. This is at odds with many modern data structures in computational geometry, which employ approximations to achieve efficiency, but these approximations often suffer from discontinuities. In this paper, we present a general method for transforming an approximate but discontinuous data structure into one that produces a smooth approximation, while matching the asymptotic space efficiencies of the original. We achieve this by adapting an approach called the partition-of-unity method, which smoothly blends multiple local approximations into a single smooth global approximation. We illustrate the use of this technique in a specific application of approximating the distance to the boundary of a convex polytope in $\mathbb{R}^d$ from any point in its interior. We begin by developing a novel data structure that efficiently computes an absolute $\varepsilon$-approximation to this query in time $O(\log (1/\varepsilon))$ using $O(1/\varepsilon^{d/2})$ storage space. Then, we proceed to apply the proposed partition-of-unity blending to guarantee the smoothness of the approximate distance field, establishing optimal asymptotic bounds on the norms of its gradient and Hessian.
Humans have a natural instinct to identify unknown object instances in their environments. The intrinsic curiosity about these unknown instances aids in learning about them, when the corresponding knowledge is eventually available. This motivates us to propose a novel computer vision problem called: `Open World Object Detection', where a model is tasked to: 1) identify objects that have not been introduced to it as `unknown', without explicit supervision to do so, and 2) incrementally learn these identified unknown categories without forgetting previously learned classes, when the corresponding labels are progressively received. We formulate the problem, introduce a strong evaluation protocol and provide a novel solution, which we call ORE: Open World Object Detector, based on contrastive clustering and energy based unknown identification. Our experimental evaluation and ablation studies analyze the efficacy of ORE in achieving Open World objectives. As an interesting by-product, we find that identifying and characterizing unknown instances helps to reduce confusion in an incremental object detection setting, where we achieve state-of-the-art performance, with no extra methodological effort. We hope that our work will attract further research into this newly identified, yet crucial research direction.
Adversarial attack is a technique for deceiving Machine Learning (ML) models, which provides a way to evaluate the adversarial robustness. In practice, attack algorithms are artificially selected and tuned by human experts to break a ML system. However, manual selection of attackers tends to be sub-optimal, leading to a mistakenly assessment of model security. In this paper, a new procedure called Composite Adversarial Attack (CAA) is proposed for automatically searching the best combination of attack algorithms and their hyper-parameters from a candidate pool of \textbf{32 base attackers}. We design a search space where attack policy is represented as an attacking sequence, i.e., the output of the previous attacker is used as the initialization input for successors. Multi-objective NSGA-II genetic algorithm is adopted for finding the strongest attack policy with minimum complexity. The experimental result shows CAA beats 10 top attackers on 11 diverse defenses with less elapsed time (\textbf{6 $\times$ faster than AutoAttack}), and achieves the new state-of-the-art on $l_{\infty}$, $l_{2}$ and unrestricted adversarial attacks.
Graph neural networks (GNNs) have been widely used in representation learning on graphs and achieved state-of-the-art performance in tasks such as node classification and link prediction. However, most existing GNNs are designed to learn node representations on the fixed and homogeneous graphs. The limitations especially become problematic when learning representations on a misspecified graph or a heterogeneous graph that consists of various types of nodes and edges. In this paper, we propose Graph Transformer Networks (GTNs) that are capable of generating new graph structures, which involve identifying useful connections between unconnected nodes on the original graph, while learning effective node representation on the new graphs in an end-to-end fashion. Graph Transformer layer, a core layer of GTNs, learns a soft selection of edge types and composite relations for generating useful multi-hop connections so-called meta-paths. Our experiments show that GTNs learn new graph structures, based on data and tasks without domain knowledge, and yield powerful node representation via convolution on the new graphs. Without domain-specific graph preprocessing, GTNs achieved the best performance in all three benchmark node classification tasks against the state-of-the-art methods that require pre-defined meta-paths from domain knowledge.
Attention networks in multimodal learning provide an efficient way to utilize given visual information selectively. However, the computational cost to learn attention distributions for every pair of multimodal input channels is prohibitively expensive. To solve this problem, co-attention builds two separate attention distributions for each modality neglecting the interaction between multimodal inputs. In this paper, we propose bilinear attention networks (BAN) that find bilinear attention distributions to utilize given vision-language information seamlessly. BAN considers bilinear interactions among two groups of input channels, while low-rank bilinear pooling extracts the joint representations for each pair of channels. Furthermore, we propose a variant of multimodal residual networks to exploit eight-attention maps of the BAN efficiently. We quantitatively and qualitatively evaluate our model on visual question answering (VQA 2.0) and Flickr30k Entities datasets, showing that BAN significantly outperforms previous methods and achieves new state-of-the-arts on both datasets.
The dominant sequence transduction models are based on complex recurrent or convolutional neural networks in an encoder-decoder configuration. The best performing models also connect the encoder and decoder through an attention mechanism. We propose a new simple network architecture, the Transformer, based solely on attention mechanisms, dispensing with recurrence and convolutions entirely. Experiments on two machine translation tasks show these models to be superior in quality while being more parallelizable and requiring significantly less time to train. Our model achieves 28.4 BLEU on the WMT 2014 English-to-German translation task, improving over the existing best results, including ensembles by over 2 BLEU. On the WMT 2014 English-to-French translation task, our model establishes a new single-model state-of-the-art BLEU score of 41.8 after training for 3.5 days on eight GPUs, a small fraction of the training costs of the best models from the literature. We show that the Transformer generalizes well to other tasks by applying it successfully to English constituency parsing both with large and limited training data.