This study targets the mixed-integer black-box optimization (MI-BBO) problem where continuous and integer variables should be optimized simultaneously. The CMA-ES, our focus in this study, is a population-based stochastic search method that samples solution candidates from a multivariate Gaussian distribution (MGD), which shows excellent performance in continuous BBO. The parameters of MGD, mean and (co)variance, are updated based on the evaluation value of candidate solutions in the CMA-ES. If the CMA-ES is applied to the MI-BBO with straightforward discretization, however, the variance corresponding to the integer variables becomes much smaller than the granularity of the discretization before reaching the optimal solution, which leads to the stagnation of the optimization. In particular, when binary variables are included in the problem, this stagnation more likely occurs because the granularity of the discretization becomes wider, and the existing integer handling for the CMA-ES does not address this stagnation. To overcome these limitations, we propose a simple integer handling for the CMA-ES based on lower-bounding the marginal probabilities associated with the generation of integer variables in the MGD. The numerical experiments on the MI-BBO benchmark problems demonstrate the efficiency and robustness of the proposed method. Furthermore, in order to demonstrate the generality of the idea of the proposed method, in addition to the single-objective optimization case, we incorporate it into multi-objective CMA-ES and verify its performance on bi-objective mixed-integer benchmark problems.
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The increasing use of complex and opaque black box models requires the adoption of interpretable measures, one such option is extractive rationalizing models, which serve as a more interpretable alternative. These models, also known as Explain-Then-Predict models, employ an explainer model to extract rationales and subsequently condition the predictor with the extracted information. Their primary objective is to provide precise and faithful explanations, represented by the extracted rationales. In this paper, we take a semi-supervised approach to optimize for the plausibility of extracted rationales. We adopt a pre-trained natural language inference (NLI) model and further fine-tune it on a small set of supervised rationales ($10\%$). The NLI predictor is leveraged as a source of supervisory signals to the explainer via entailment alignment. We show that, by enforcing the alignment agreement between the explanation and answer in a question-answering task, the performance can be improved without access to ground truth labels. We evaluate our approach on the ERASER dataset and show that our approach achieves comparable results with supervised extractive models and outperforms unsupervised approaches by $> 100\%$.
In the field of intelligent multimedia analysis, ultra-fine-grained visual categorization (Ultra-FGVC) plays a vital role in distinguishing intricate subcategories within broader categories. However, this task is inherently challenging due to the complex granularity of category subdivisions and the limited availability of data for each category. To address these challenges, this work proposes CSDNet, a pioneering framework that effectively explores contrastive learning and self-distillation to learn discriminative representations specifically designed for Ultra-FGVC tasks. CSDNet comprises three main modules: Subcategory-Specific Discrepancy Parsing (SSDP), Dynamic Discrepancy Learning (DDL), and Subcategory-Specific Discrepancy Transfer (SSDT), which collectively enhance the generalization of deep models across instance, feature, and logit prediction levels. To increase the diversity of training samples, the SSDP module introduces adaptive augmented samples to spotlight subcategory-specific discrepancies. Simultaneously, the proposed DDL module stores historical intermediate features by a dynamic memory queue, which optimizes the feature learning space through iterative contrastive learning. Furthermore, the SSDT module effectively distills subcategory-specific discrepancies knowledge from the inherent structure of limited training data using a self-distillation paradigm at the logit prediction level. Experimental results demonstrate that CSDNet outperforms current state-of-the-art Ultra-FGVC methods, emphasizing its powerful efficacy and adaptability in addressing Ultra-FGVC tasks.
Recently, various parameter-efficient fine-tuning (PEFT) strategies for application to language models have been proposed and successfully implemented. However, this raises the question of whether PEFT, which only updates a limited set of model parameters, constitutes security vulnerabilities when confronted with weight-poisoning backdoor attacks. In this study, we show that PEFT is more susceptible to weight-poisoning backdoor attacks compared to the full-parameter fine-tuning method, with pre-defined triggers remaining exploitable and pre-defined targets maintaining high confidence, even after fine-tuning. Motivated by this insight, we developed a Poisoned Sample Identification Module (PSIM) leveraging PEFT, which identifies poisoned samples through confidence, providing robust defense against weight-poisoning backdoor attacks. Specifically, we leverage PEFT to train the PSIM with randomly reset sample labels. During the inference process, extreme confidence serves as an indicator for poisoned samples, while others are clean. We conduct experiments on text classification tasks, five fine-tuning strategies, and three weight-poisoning backdoor attack methods. Experiments show near 100% success rates for weight-poisoning backdoor attacks when utilizing PEFT. Furthermore, our defensive approach exhibits overall competitive performance in mitigating weight-poisoning backdoor attacks.
We examine the possibility of approximating Maximum Vertex-Disjoint Shortest Paths. In this problem, the input is an edge-weighted (directed or undirected) $n$-vertex graph $G$ along with $k$ terminal pairs $(s_1,t_1),(s_2,t_2),\ldots,(s_k,t_k)$. The task is to connect as many terminal pairs as possible by pairwise vertex-disjoint paths such that each path is a shortest path between the respective terminals. Our work is anchored in the recent breakthrough by Lochet [SODA '21], which demonstrates the polynomial-time solvability of the problem for a fixed value of $k$. Lochet's result implies the existence of a polynomial-time $ck$-approximation for Maximum Vertex-Disjoint Shortest Paths, where $c \leq 1$ is a constant. Our first result suggests that this approximation algorithm is, in a sense, the best we can hope for. More precisely, assuming the gap-ETH, we exclude the existence of an $o(k)$-approximations within $f(k) \cdot $poly($n$) time for any function $f$ that only depends on $k$. Our second result demonstrates the infeasibility of achieving an approximation ratio of $n^{\frac{1}{2}-\varepsilon}$ in polynomial time, unless P = NP. It is not difficult to show that a greedy algorithm selecting a path with the minimum number of arcs results in a $\lceil\sqrt{\ell}\rceil$-approximation, where $\ell$ is the number of edges in all the paths of an optimal solution. Since $\ell \leq n$, this underscores the tightness of the $n^{\frac{1}{2}-\varepsilon}$-inapproximability bound. Additionally, we establish that Maximum Vertex-Disjoint Shortest Paths is fixed-parameter tractable when parameterized by $\ell$ but does not admit a polynomial kernel. Our hardness results hold for undirected graphs with unit weights, while our positive results extend to scenarios where the input graph is directed and features arbitrary (non-negative) edge weights.
Online Unsupervised Domain Adaptation (OUDA) for person Re-Identification (Re-ID) is the task of continuously adapting a model trained on a well-annotated source domain dataset to a target domain observed as a data stream. In OUDA, person Re-ID models face two main challenges: catastrophic forgetting and domain shift. In this work, we propose a new Source-guided Similarity Preservation (S2P) framework to alleviate these two problems. Our framework is based on the extraction of a support set composed of source images that maximizes the similarity with the target data. This support set is used to identify feature similarities that must be preserved during the learning process. S2P can incorporate multiple existing UDA methods to mitigate catastrophic forgetting. Our experiments show that S2P outperforms previous state-of-the-art methods on multiple real-to-real and synthetic-to-real challenging OUDA benchmarks.
A new moving mesh scheme based on the Lagrange-Galerkin method for the approximation of the one-dimensional convection-diffusion equation is studied. The mesh movement, which is prescribed by a discretized dynamical system for the nodal points, follows the direction of convection. It is shown that under a restriction of the time increment the mesh movement cannot lead to an overlap of the elements and therefore an invalid mesh. For the linear element, optimal error estimates in the $\ell^\infty(L^2) \cap \ell^2(H_0^1)$ norm are proved in case of both, a first-order backward Euler method and a second-order two-step method in time. These results are based on new estimates of the time dependent interpolation operator derived in this work. Preservation of the total mass is verified for both choices of the time discretization. Numerical experiments are presented that confirm the error estimates and demonstrate that the proposed moving mesh scheme can circumvent limitations that the Lagrange-Galerkin method on a fixed mesh exhibits.
We propose a novel data-driven linear inverse model, called Colored-LIM, to extract the linear dynamics and diffusion matrix that define a linear stochastic process driven by an Ornstein-Uhlenbeck colored-noise. The Colored-LIM is a new variant of the classical linear inverse model (LIM) which relies on the white noise assumption. Similar to LIM, the Colored-LIM approximates the linear dynamics from a finite realization of a stochastic process and then solves the diffusion matrix based on, for instance, a generalized fluctuation-dissipation relation, which can be done by solving a system of linear equations. The main difficulty is that in practice, the colored-noise process can be hardly observed while it is correlated to the stochastic process of interest. Nevertheless, we show that the local behavior of the correlation function of the observable encodes the dynamics of the stochastic process and the diffusive behavior of the colored-noise. In this article, we review the classical LIM and develop Colored-LIM with a mathematical background and rigorous derivations. In the numerical experiments, we examine the performance of both LIM and Colored-LIM. Finally, we discuss some false attempts to build a linear inverse model for colored-noise driven processes, and investigate the potential misuse and its consequence of LIM in the appendices.
Transformer-based models have significantly improved performance across a range of multimodal understanding tasks, such as visual question answering and action recognition. However, multimodal Transformers significantly suffer from a quadratic complexity of the multi-head attention with the input sequence length, especially as the number of modalities increases. To address this, we introduce Low-Cost Multimodal Transformer (LoCoMT), a novel multimodal attention mechanism that aims to reduce computational cost during training and inference with minimal performance loss. Specifically, by assigning different multimodal attention patterns to each attention head, LoCoMT can flexibly control multimodal signals and theoretically ensures a reduced computational cost compared to existing multimodal Transformer variants. Experimental results on two multimodal datasets, namely Audioset and MedVidCL demonstrate that LoCoMT not only reduces GFLOPs but also matches or even outperforms established models.
Few-shot Knowledge Graph (KG) completion is a focus of current research, where each task aims at querying unseen facts of a relation given its few-shot reference entity pairs. Recent attempts solve this problem by learning static representations of entities and references, ignoring their dynamic properties, i.e., entities may exhibit diverse roles within task relations, and references may make different contributions to queries. This work proposes an adaptive attentional network for few-shot KG completion by learning adaptive entity and reference representations. Specifically, entities are modeled by an adaptive neighbor encoder to discern their task-oriented roles, while references are modeled by an adaptive query-aware aggregator to differentiate their contributions. Through the attention mechanism, both entities and references can capture their fine-grained semantic meanings, and thus render more expressive representations. This will be more predictive for knowledge acquisition in the few-shot scenario. Evaluation in link prediction on two public datasets shows that our approach achieves new state-of-the-art results with different few-shot sizes.
Multi-relation Question Answering is a challenging task, due to the requirement of elaborated analysis on questions and reasoning over multiple fact triples in knowledge base. In this paper, we present a novel model called Interpretable Reasoning Network that employs an interpretable, hop-by-hop reasoning process for question answering. The model dynamically decides which part of an input question should be analyzed at each hop; predicts a relation that corresponds to the current parsed results; utilizes the predicted relation to update the question representation and the state of the reasoning process; and then drives the next-hop reasoning. Experiments show that our model yields state-of-the-art results on two datasets. More interestingly, the model can offer traceable and observable intermediate predictions for reasoning analysis and failure diagnosis.
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