Wasserstein Barycenter (WB) is one of the most fundamental optimization problems in optimal transportation. Given a set of distributions, the goal of WB is to find a new distribution that minimizes the average Wasserstein distance to them. The problem becomes even harder if we restrict the solution to be ``$k$-sparse''. In this paper, we study the $k$-sparse WB problem in the presence of outliers, which is a more practical setting since real-world data often contains noise. Existing WB algorithms cannot be directly extended to handle the case with outliers, and thus it is urgently needed to develop some novel ideas. First, we investigate the relation between $k$-sparse WB with outliers and the clustering (with outliers) problems. In particular, we propose a clustering based LP method that yields constant approximation factor for the $k$-sparse WB with outliers problem. Further, we utilize the coreset technique to achieve the $(1+\epsilon)$-approximation factor for any $\epsilon>0$, if the dimensionality is not high. Finally, we conduct the experiments for our proposed algorithms and illustrate their efficiencies in practice.

Regression is typically treated as a curve-fitting process where the goal is to fit a prediction function to data. With the help of conditional generative adversarial networks, we propose to solve this age-old problem in a different way; we aim to learn a prediction function whose outputs, when paired with the corresponding inputs, are indistinguishable from feature-label pairs in the training dataset. We show that this approach to regression makes fewer assumptions on the distribution of the data we are fitting to and, therefore, has better representation capabilities. We draw parallels with generalized linear models in statistics and show how our proposal serves as an extension of them to neural networks. We demonstrate the superiority of this new approach to standard regression with experiments on multiple synthetic and publicly available real-world datasets, finding encouraging results, especially with real-world heavy-tailed regression datasets. To make our work more reproducible, we release our source code. Link to repository: https://anonymous.4open.science/r/regressGAN-7B71/

We introduce Contrastive Gaussian Clustering, a novel approach capable of provide segmentation masks from any viewpoint and of enabling 3D segmentation of the scene. Recent works in novel-view synthesis have shown how to model the appearance of a scene via a cloud of 3D Gaussians, and how to generate accurate images from a given viewpoint by projecting on it the Gaussians before $\alpha$ blending their color. Following this example, we train a model to include also a segmentation feature vector for each Gaussian. These can then be used for 3D scene segmentation, by clustering Gaussians according to their feature vectors; and to generate 2D segmentation masks, by projecting the Gaussians on a plane and $\alpha$ blending over their segmentation features. Using a combination of contrastive learning and spatial regularization, our method can be trained on inconsistent 2D segmentation masks, and still learn to generate segmentation masks consistent across all views. Moreover, the resulting model is extremely accurate, improving the IoU accuracy of the predicted masks by $+8\%$ over the state of the art. Code and trained models will be released soon.

With the expanding application of Large Language Models (LLMs) in various domains, it becomes imperative to comprehensively investigate their unforeseen behaviors and consequent outcomes. In this study, we introduce and systematically explore the phenomenon of "glitch tokens", which are anomalous tokens produced by established tokenizers and could potentially compromise the models' quality of response. Specifically, we experiment on seven top popular LLMs utilizing three distinct tokenizers and involving a totally of 182,517 tokens. We present categorizations of the identified glitch tokens and symptoms exhibited by LLMs when interacting with glitch tokens. Based on our observation that glitch tokens tend to cluster in the embedding space, we propose GlitchHunter, a novel iterative clustering-based technique, for efficient glitch token detection. The evaluation shows that our approach notably outperforms three baseline methods on eight open-source LLMs. To the best of our knowledge, we present the first comprehensive study on glitch tokens. Our new detection further provides valuable insights into mitigating tokenization-related errors in LLMs.

Cutting planes (cuts) play an important role in solving mixed-integer linear programs (MILPs), which formulate many important real-world applications. Cut selection heavily depends on (P1) which cuts to prefer and (P2) how many cuts to select. Although modern MILP solvers tackle (P1)-(P2) by human-designed heuristics, machine learning carries the potential to learn more effective heuristics. However, many existing learning-based methods learn which cuts to prefer, neglecting the importance of learning how many cuts to select. Moreover, we observe that (P3) what order of selected cuts to prefer significantly impacts the efficiency of MILP solvers as well. To address these challenges, we propose a novel hierarchical sequence/set model (HEM) to learn cut selection policies. Specifically, HEM is a bi-level model: (1) a higher-level module that learns how many cuts to select, (2) and a lower-level module -- that formulates the cut selection as a sequence/set to sequence learning problem -- to learn policies selecting an ordered subset with the cardinality determined by the higher-level module. To the best of our knowledge, HEM is the first data-driven methodology that well tackles (P1)-(P3) simultaneously. Experiments demonstrate that HEM significantly improves the efficiency of solving MILPs on eleven challenging MILP benchmarks, including two Huawei's real problems.

The clinical trial process, also known as drug development, is an indispensable step toward the development of new treatments. The major objective of interventional clinical trials is to assess the safety and effectiveness of drug-based treatment in treating certain diseases in the human body. However, clinical trials are lengthy, labor-intensive, and costly. The duration of a clinical trial is a crucial factor that influences overall expenses. Therefore, effective management of the timeline of a clinical trial is essential for controlling the budget and maximizing the economic viability of the research. To address this issue, We propose TrialDura, a machine learning-based method that estimates the duration of clinical trials using multimodal data, including disease names, drug molecules, trial phases, and eligibility criteria. Then, we encode them into Bio-BERT embeddings specifically tuned for biomedical contexts to provide a deeper and more relevant semantic understanding of clinical trial data. Finally, the model's hierarchical attention mechanism connects all of the embeddings to capture their interactions and predict clinical trial duration. Our proposed model demonstrated superior performance with a mean absolute error (MAE) of 1.04 years and a root mean square error (RMSE) of 1.39 years compared to the other models, indicating more accurate clinical trial duration prediction. Publicly available code can be found at https://anonymous.4open.science/r/TrialDura-F196

A pressing issue in the adoption of AI models is the increasing demand for more human-centric explanations of their predictions. To advance towards more human-centric explanations, understanding how humans produce and select explanations has been beneficial. In this work, inspired by insights of human cognition we propose and test the incorporation of two novel biases to enhance the search for effective counterfactual explanations. Central to our methodology is the application of diffusion distance, which emphasizes data connectivity and actionability in the search for feasible counterfactual explanations. In particular, diffusion distance effectively weights more those points that are more interconnected by numerous short-length paths. This approach brings closely connected points nearer to each other, identifying a feasible path between them. We also introduce a directional coherence term that allows the expression of a preference for the alignment between the joint and marginal directional changes in feature space to reach a counterfactual. This term enables the generation of counterfactual explanations that align with a set of marginal predictions based on expectations of how the outcome of the model varies by changing one feature at a time. We evaluate our method, named Coherent Directional Counterfactual Explainer (CoDiCE), and the impact of the two novel biases against existing methods such as DiCE, FACE, Prototypes, and Growing Spheres. Through a series of ablation experiments on both synthetic and real datasets with continuous and mixed-type features, we demonstrate the effectiveness of our method.

Quantum computers have the potential to outperform classical computers for some complex computational problems. However, current quantum computers (e.g., from IBM and Google) have inherent noise that results in errors in the outputs of quantum software executing on the quantum computers, affecting the reliability of quantum software development. The industry is increasingly interested in machine learning (ML)--based error mitigation techniques, given their scalability and practicality. However, existing ML-based techniques have limitations, such as only targeting specific noise types or specific quantum circuits. This paper proposes a practical ML-based approach, called Q-LEAR, with a novel feature set, to mitigate noise errors in quantum software outputs. We evaluated Q-LEAR on eight quantum computers and their corresponding noisy simulators, all from IBM, and compared Q-LEAR with a state-of-the-art ML-based approach taken as baseline. Results show that, compared to the baseline, Q-LEAR achieved a 25% average improvement in error mitigation on both real quantum computers and simulators. We also discuss the implications and practicality of Q-LEAR, which, we believe, is valuable for practitioners.

In this paper, we introduce Selective-distillation for Class and Architecture-agnostic unleaRning (SCAR), a novel approximate unlearning method. SCAR efficiently eliminates specific information while preserving the model's test accuracy without using a retain set, which is a key component in state-of-the-art approximate unlearning algorithms. Our approach utilizes a modified Mahalanobis distance to guide the unlearning of the feature vectors of the instances to be forgotten, aligning them to the nearest wrong class distribution. Moreover, we propose a distillation-trick mechanism that distills the knowledge of the original model into the unlearning model with out-of-distribution images for retaining the original model's test performance without using any retain set. Importantly, we propose a self-forget version of SCAR that unlearns without having access to the forget set. We experimentally verified the effectiveness of our method, on three public datasets, comparing it with state-of-the-art methods. Our method obtains performance higher than methods that operate without the retain set and comparable w.r.t the best methods that rely on the retain set.

The Neural Tangent Kernel (NTK) has emerged as a fundamental concept in the study of wide Neural Networks. In particular, it is known that the positivity of the NTK is directly related to the memorization capacity of sufficiently wide networks, i.e., to the possibility of reaching zero loss in training, via gradient descent. Here we will improve on previous works and obtain a sharp result concerning the positivity of the NTK of feedforward networks of any depth. More precisely, we will show that, for any non-polynomial activation function, the NTK is strictly positive definite. Our results are based on a novel characterization of polynomial functions which is of independent interest.