Although diffusion models (DMs) have shown promising performances in a number of tasks (e.g., speech synthesis and image generation), they might suffer from error propagation because of their sequential structure. However, this is not certain because some sequential models, such as Conditional Random Field (CRF), are free from this problem. To address this issue, we develop a theoretical framework to mathematically formulate error propagation in the architecture of DMs, The framework contains three elements, including modular error, cumulative error, and propagation equation. The modular and cumulative errors are related by the equation, which interprets that DMs are indeed affected by error propagation. Our theoretical study also suggests that the cumulative error is closely related to the generation quality of DMs. Based on this finding, we apply the cumulative error as a regularization term to reduce error propagation. Because the term is computationally intractable, we derive its upper bound and design a bootstrap algorithm to efficiently estimate the bound for optimization. We have conducted extensive experiments on multiple image datasets, showing that our proposed regularization reduces error propagation, significantly improves vanilla DMs, and outperforms previous baselines.
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Integer linear programming (ILP) models a wide range of practical combinatorial optimization problems and significantly impacts industry and management sectors. This work proposes new characterizations of ILP with the concept of boundary solutions. Motivated by the new characterizations, we develop a new local search algorithm Local-ILP, which is efficient for solving general ILP validated on a large heterogeneous problem dataset. We propose a new local search framework that switches between three modes, namely Search, Improve, and Restore modes. Two new operators are proposed, namely the tight move and the lift move operators, which are associated with appropriate scoring functions. Different modes apply different operators to realize different search strategies and the algorithm switches between three modes according to the current search state. Putting these together, we develop a local search ILP solver called Local-ILP. Experiments conducted on the MIPLIB dataset show the effectiveness of our algorithm in solving large-scale hard ILP problems. In the aspect of finding a good feasible solution quickly, Local-ILP is competitive and complementary to the state-of-the-art commercial solver Gurobi and significantly outperforms the state-of-the-art non-commercial solver SCIP. Moreover, our algorithm establishes new records for 6 MIPLIB open instances. The theoretical analysis of our algorithm is also presented, which shows our algorithm could avoid visiting unnecessary regions.
In contrast with standard classification tasks, strategic classification involves agents strategically modifying their features in an effort to receive favorable predictions. For instance, given a classifier determining loan approval based on credit scores, applicants may open or close their credit cards to fool the classifier. The learning goal is to find a classifier robust against strategic manipulations. Various settings, based on what and when information is known, have been explored in strategic classification. In this work, we focus on addressing a fundamental question: the learnability gaps between strategic classification and standard learning. We essentially show that any learnable class is also strategically learnable: we first consider a fully informative setting, where the manipulation structure (which is modeled by a manipulation graph $G^\star$) is known and during training time the learner has access to both the pre-manipulation data and post-manipulation data. We provide nearly tight sample complexity and regret bounds, offering significant improvements over prior results. Then, we relax the fully informative setting by introducing two natural types of uncertainty. First, following Ahmadi et al. (2023), we consider the setting in which the learner only has access to the post-manipulation data. We improve the results of Ahmadi et al. (2023) and close the gap between mistake upper bound and lower bound raised by them. Our second relaxation of the fully informative setting introduces uncertainty to the manipulation structure. That is, we assume that the manipulation graph is unknown but belongs to a known class of graphs. We provide nearly tight bounds on the learning complexity in various unknown manipulation graph settings. Notably, our algorithm in this setting is of independent interest and can be applied to other problems such as multi-label learning.
In a ring-signature-based anonymous cryptocurrency, signers of a transaction are hidden among a set of potential signers, called a ring, whose size is much smaller than the number of all users. The ring-membership relations specified by the sets of transactions thus induce bipartite transaction graphs, whose distribution is in turn induced by the ring sampler underlying the cryptocurrency. Since efficient graph analysis could be performed on transaction graphs to potentially deanonymise signers, it is crucial to understand the resistance of (the transaction graphs induced by) a ring sampler against graph analysis. Of particular interest is the class of partitioning ring samplers. Although previous works showed that they provide almost optimal local anonymity, their resistance against global, e.g. graph-based, attacks were unclear. In this work, we analyse transaction graphs induced by partitioning ring samplers. Specifically, we show (partly analytically and partly empirically) that, somewhat surprisingly, by setting the ring size to be at least logarithmic in the number of users, a graph-analysing adversary is no better than the one that performs random guessing in deanonymisation up to constant factor of 2.
Multimodal datasets contain observations generated by multiple types of sensors. Most works to date focus on uncovering latent structures in the data that appear in all modalities. However, important aspects of the data may appear in only one modality due to the differences between the sensors. Uncovering modality-specific attributes may provide insights into the sources of the variability of the data. For example, certain clusters may appear in the analysis of genetics but not in epigenetic markers. Another example is hyper-spectral satellite imaging, where various atmospheric and ground phenomena are detectable using different parts of the spectrum. In this paper, we address the problem of uncovering latent structures that are unique to a single modality. Our approach is based on computing a graph representation of datasets from two modalities and analyzing the differences between their connectivity patterns. We provide an asymptotic analysis of the convergence of our approach based on a product manifold model. To evaluate the performance of our method, we test its ability to uncover latent structures in multiple types of artificial and real datasets.
Collision-resistant hashing, a fundamental primitive in modern cryptography, ensures that there is no efficient way to find distinct inputs that produce the same hash value. This property underpins the security of various cryptographic applications, making it crucial to understand its complexity. The complexity of this problem is well-understood in the classical setting and $\Theta(N^{1/2})$ queries are needed to find a collision. However, the advent of quantum computing has introduced new challenges since quantum adversaries $\unicode{x2013}$ equipped with the power of quantum queries $\unicode{x2013}$ can find collisions much more efficiently. Brassard, H\"oyer and Tapp and Aaronson and Shi established that full-scale quantum adversaries require $\Theta(N^{1/3})$ queries to find a collision, prompting a need for longer hash outputs, which impacts efficiency in terms of the key lengths needed for security. This paper explores the implications of quantum attacks in the Noisy-Intermediate Scale Quantum (NISQ) era. In this work, we investigate three different models for NISQ algorithms and achieve tight bounds for all of them: (1) A hybrid algorithm making adaptive quantum or classical queries but with a limited quantum query budget, or (2) A quantum algorithm with access to a noisy oracle, subject to a dephasing or depolarizing channel, or (3) A hybrid algorithm with an upper bound on its maximum quantum depth; i.e., a classical algorithm aided by low-depth quantum circuits. In fact, our results handle all regimes between NISQ and full-scale quantum computers. Previously, only results for the pre-image search problem were known for these models by Sun and Zheng, Rosmanis, Chen, Cotler, Huang and Li while nothing was known about the collision finding problem.
Model editing aims to precisely modify the behaviours of large language models (LLMs) on specific knowledge while keeping irrelevant knowledge unchanged. It has been proven effective in resolving hallucination and out-of-date issues in LLMs. As a result, it can boost the application of LLMs in many critical domains (e.g., medical domain), where the hallucination is not tolerable. In this paper, we propose two model editing studies and validate them in the medical domain: (1) directly editing the factual medical knowledge and (2) editing the explanations to facts. Meanwhile, we observed that current model editing methods struggle with the specialization and complexity of medical knowledge. Therefore, we propose MedLaSA, a novel Layer-wise Scalable Adapter strategy for medical model editing. It employs causal tracing to identify the precise location of knowledge in neurons and then introduces scalable adapters into the dense layers of LLMs. These adapters are assigned scaling values based on the corresponding specific knowledge. To evaluate the editing impact, we build two benchmark datasets and introduce a series of challenging and comprehensive metrics. Extensive experiments on medical LLMs demonstrate the editing efficiency of MedLaSA, without affecting irrelevant knowledge that is not edited.
Large Language Models (LLMs) have shown excellent generalization capabilities that have led to the development of numerous models. These models propose various new architectures, tweaking existing architectures with refined training strategies, increasing context length, using high-quality training data, and increasing training time to outperform baselines. Analyzing new developments is crucial for identifying changes that enhance training stability and improve generalization in LLMs. This survey paper comprehensively analyses the LLMs architectures and their categorization, training strategies, training datasets, and performance evaluations and discusses future research directions. Moreover, the paper also discusses the basic building blocks and concepts behind LLMs, followed by a complete overview of LLMs, including their important features and functions. Finally, the paper summarizes significant findings from LLM research and consolidates essential architectural and training strategies for developing advanced LLMs. Given the continuous advancements in LLMs, we intend to regularly update this paper by incorporating new sections and featuring the latest LLM models.
Existing knowledge graph (KG) embedding models have primarily focused on static KGs. However, real-world KGs do not remain static, but rather evolve and grow in tandem with the development of KG applications. Consequently, new facts and previously unseen entities and relations continually emerge, necessitating an embedding model that can quickly learn and transfer new knowledge through growth. Motivated by this, we delve into an expanding field of KG embedding in this paper, i.e., lifelong KG embedding. We consider knowledge transfer and retention of the learning on growing snapshots of a KG without having to learn embeddings from scratch. The proposed model includes a masked KG autoencoder for embedding learning and update, with an embedding transfer strategy to inject the learned knowledge into the new entity and relation embeddings, and an embedding regularization method to avoid catastrophic forgetting. To investigate the impacts of different aspects of KG growth, we construct four datasets to evaluate the performance of lifelong KG embedding. Experimental results show that the proposed model outperforms the state-of-the-art inductive and lifelong embedding baselines.
Residual networks (ResNets) have displayed impressive results in pattern recognition and, recently, have garnered considerable theoretical interest due to a perceived link with neural ordinary differential equations (neural ODEs). This link relies on the convergence of network weights to a smooth function as the number of layers increases. We investigate the properties of weights trained by stochastic gradient descent and their scaling with network depth through detailed numerical experiments. We observe the existence of scaling regimes markedly different from those assumed in neural ODE literature. Depending on certain features of the network architecture, such as the smoothness of the activation function, one may obtain an alternative ODE limit, a stochastic differential equation or neither of these. These findings cast doubts on the validity of the neural ODE model as an adequate asymptotic description of deep ResNets and point to an alternative class of differential equations as a better description of the deep network limit.
High spectral dimensionality and the shortage of annotations make hyperspectral image (HSI) classification a challenging problem. Recent studies suggest that convolutional neural networks can learn discriminative spatial features, which play a paramount role in HSI interpretation. However, most of these methods ignore the distinctive spectral-spatial characteristic of hyperspectral data. In addition, a large amount of unlabeled data remains an unexploited gold mine for efficient data use. Therefore, we proposed an integration of generative adversarial networks (GANs) and probabilistic graphical models for HSI classification. Specifically, we used a spectral-spatial generator and a discriminator to identify land cover categories of hyperspectral cubes. Moreover, to take advantage of a large amount of unlabeled data, we adopted a conditional random field to refine the preliminary classification results generated by GANs. Experimental results obtained using two commonly studied datasets demonstrate that the proposed framework achieved encouraging classification accuracy using a small number of data for training.
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