We propose a new definition of instance optimality for differentially private estimation algorithms. Our definition requires an optimal algorithm to compete, simultaneously for every dataset $D$, with the best private benchmark algorithm that (a) knows $D$ in advance and (b) is evaluated by its worst-case performance on large subsets of $D$. That is, the benchmark algorithm need not perform well when potentially extreme points are added to $D$; it only has to handle the removal of a small number of real data points that already exist. This makes our benchmark significantly stronger than those proposed in prior work. We nevertheless show, for real-valued datasets, how to construct private algorithms that achieve our notion of instance optimality when estimating a broad class of dataset properties, including means, quantiles, and $\ell_p$-norm minimizers. For means in particular, we provide a detailed analysis and show that our algorithm simultaneously matches or exceeds the asymptotic performance of existing algorithms under a range of distributional assumptions.
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Neural networks often suffer from a feature preference problem, where they tend to overly rely on specific features to solve a task while disregarding other features, even if those neglected features are essential for the task. Feature preference problems have primarily been investigated in classification task. However, we observe that feature preference occurs in high-dimensional regression task, specifically, source separation. To mitigate feature preference in source separation, we propose FEAture BAlancing by Suppressing Easy feature (FEABASE). This approach enables efficient data utilization by learning hidden information about the neglected feature. We evaluate our method in a multi-channel source separation task, where feature preference between spatial feature and timbre feature appears.
We introduce a general random model of a combinatorial optimization problem with geometric structure that encapsulates both linear programming and integer linear programming. Let $Q$ be a bounded set called the feasible set, $E$ be an arbitrary set called the constraint set, and $A$ be a random linear transform. We define and study the $\ell^q$-margin, $M_q := d_q(AQ, E)$. The margin quantifies the feasibility of finding $y \in AQ$ satisfying the constraint $y \in E$. Our contribution is to establish strong concentration of the margin for any $q \in (2,\infty]$, assuming only that $E$ has permutation symmetry. The case of $q = \infty$ is of particular interest in applications -- specifically to combinatorial ``balancing'' problems -- and is markedly out of the reach of the classical isoperimetric and concentration-of-measure tools that suffice for $q \le 2$. Generality is a key feature of this result: we assume permutation symmetry of the constraint set and nothing else. This allows us to encode many optimization problems in terms of the margin, including random versions of: the closest vector problem, integer linear feasibility, perceptron-type problems, $\ell^q$-combinatorial discrepancy for $2 \le q \le \infty$, and matrix balancing. Concentration of the margin implies a host of new sharp threshold results in these models, and also greatly simplifies and extends some key known results.
We consider the problem of sampling from a distribution governed by a potential function. This work proposes an explicit score based MCMC method that is deterministic, resulting in a deterministic evolution for particles rather than a stochastic differential equation evolution. The score term is given in closed form by a regularized Wasserstein proximal, using a kernel convolution that is approximated by sampling. We demonstrate fast convergence on various problems and show improved dimensional dependence of mixing time bounds for the case of Gaussian distributions compared to the unadjusted Langevin algorithm (ULA) and the Metropolis-adjusted Langevin algorithm (MALA). We additionally derive closed form expressions for the distributions at each iterate for quadratic potential functions, characterizing the variance reduction. Empirical results demonstrate that the particles behave in an organized manner, lying on level set contours of the potential. Moreover, the posterior mean estimator of the proposed method is shown to be closer to the maximum a-posteriori estimator compared to ULA and MALA in the context of Bayesian logistic regression. Additional examples demonstrate competitive performance for Bayesian neural network training.
Optimal transport (OT) barycenters are a mathematically grounded way of averaging probability distributions while capturing their geometric properties. In short, the barycenter task is to take the average of a collection of probability distributions w.r.t. given OT discrepancies. We propose a novel algorithm for approximating the continuous Entropic OT (EOT) barycenter for arbitrary OT cost functions. Our approach is built upon the dual reformulation of the EOT problem based on weak OT, which has recently gained the attention of the ML community. Beyond its novelty, our method enjoys several advantageous properties: (i) we establish quality bounds for the recovered solution; (ii) this approach seemlessly interconnects with the Energy-Based Models (EBMs) learning procedure enabling the use of well-tuned algorithms for the problem of interest; (iii) it provides an intuitive optimization scheme avoiding min-max, reinforce and other intricate technical tricks. For validation, we consider several low-dimensional scenarios and image-space setups, including non-Euclidean cost functions. Furthermore, we investigate the practical task of learning the barycenter on an image manifold generated by a pretrained generative model, opening up new directions for real-world applications.
The rapid growth and adoption of decentralized finance (DeFi) systems have been accompanied by various threats, notably those emerging from vulnerabilities in their intricate design. In our work, we introduce and define an attack strategy termed as Role-Play Attack, in which the attacker acts as multiple roles concurrently to exploit the DeFi system and cause substantial financial losses. We provide a formal definition of this strategy and demonstrate its potential impacts by revealing the total loss of \$435.1M caused by 14 historical attacks with applying this pattern. Besides, we mathematically analyzed the attacks with top 2 losses and retrofitted the corresponding attack pattern by concrete execution, indicating that this strategy could increase the potential profit for original attacks by \$3.34M (51.4%) and \$3.76M (12.0%), respectively.
We demonstrate possibility for consensus under the model and conditions used by Fischer, Lynch, and Patterson (FLP) to prove impossibility of binary consensus - in complete asynchrony and up to one unannounced process crash-fail. We also show that: i) assembling by every process a dataset containing the initial values of individual processes is an inevitable phase of binary consensus; and ii) agreeing on this dataset is sufficient for a quasi-binary consensus. Key findings: Direct causal relationship between complete asynchrony and the impossibility to solve consensus does not exist. The impossibility to solve consensus is caused only and entirely by the dependence of agreement on the content of the initial values.
Despite the promising progress in multi-modal tasks, current large multi-modal models (LMMs) are prone to hallucinating inconsistent descriptions with respect to the associated image and human instructions. This paper addresses this issue by introducing the first large and diverse visual instruction tuning dataset, named Large-scale Robust Visual (LRV)-Instruction. Our dataset comprises 400k visual instructions generated by GPT4, covering 16 vision-and-language tasks with open-ended instructions and answers. Unlike existing studies that primarily focus on positive instruction samples, we design LRV-Instruction to include both positive and negative instructions for more robust visual instruction tuning. Our negative instructions are designed at three semantic levels: (i) Nonexistent Object Manipulation, (ii) Existent Object Manipulation and (iii) Knowledge Manipulation. To efficiently measure the hallucination generated by LMMs, we propose GPT4-Assisted Visual Instruction Evaluation (GAVIE), a stable approach to evaluate visual instruction tuning like human experts. GAVIE does not require human-annotated groundtruth answers and can adapt to diverse instruction formats. We conduct comprehensive experiments to investigate the hallucination of LMMs. Our results demonstrate existing LMMs exhibit significant hallucinations when presented with our negative instructions, particularly Existent Object and Knowledge Manipulation instructions. Moreover, we successfully mitigate hallucination by finetuning MiniGPT4 and mPLUG-Owl on LRV-Instruction while improving performance on several public datasets compared to state-of-the-art methods. Additionally, we observed that a balanced ratio of positive and negative instances in the training data leads to a more robust model.
Modern sampling-based motion planning algorithms typically take between hundreds of milliseconds to dozens of seconds to find collision-free motions for high degree-of-freedom problems. This paper presents performance improvements of more than 500x over the state-of-the-art, bringing planning times into the range of microseconds and solution rates into the range of kilohertz, without specialized hardware. Our key insight is how to exploit fine-grained parallelism within sampling-based planners, providing generality-preserving algorithmic improvements to any such planner and significantly accelerating critical subroutines, such as forward kinematics and collision checking. We demonstrate our approach over a diverse set of challenging, realistic problems for complex robots ranging from 7 to 14 degrees-of-freedom. Moreover, we show that our approach does not require high-power hardware by also evaluating on a low-power single-board computer. The planning speeds demonstrated are fast enough to reside in the range of control frequencies and open up new avenues of motion planning research.
Knowledge graph embedding, which aims to represent entities and relations as low dimensional vectors (or matrices, tensors, etc.), has been shown to be a powerful technique for predicting missing links in knowledge graphs. Existing knowledge graph embedding models mainly focus on modeling relation patterns such as symmetry/antisymmetry, inversion, and composition. However, many existing approaches fail to model semantic hierarchies, which are common in real-world applications. To address this challenge, we propose a novel knowledge graph embedding model---namely, Hierarchy-Aware Knowledge Graph Embedding (HAKE)---which maps entities into the polar coordinate system. HAKE is inspired by the fact that concentric circles in the polar coordinate system can naturally reflect the hierarchy. Specifically, the radial coordinate aims to model entities at different levels of the hierarchy, and entities with smaller radii are expected to be at higher levels; the angular coordinate aims to distinguish entities at the same level of the hierarchy, and these entities are expected to have roughly the same radii but different angles. Experiments demonstrate that HAKE can effectively model the semantic hierarchies in knowledge graphs, and significantly outperforms existing state-of-the-art methods on benchmark datasets for the link prediction task.
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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