Conformal Prediction (CP) is a popular method for uncertainty quantification that converts a pretrained model's point prediction into a prediction set, with the set size reflecting the model's confidence. Although existing CP methods are guaranteed to achieve marginal coverage, they often exhibit imbalanced coverage across classes under long-tailed label distributions, tending to over cover the head classes at the expense of under covering the remaining tail classes. This under coverage is particularly concerning, as it undermines the reliability of the prediction sets for minority classes, even with coverage ensured on average. In this paper, we propose the Tail-Aware Conformal Prediction (TACP) method to mitigate the under coverage of the tail classes by utilizing the long-tailed structure and narrowing the head-tail coverage gap. Theoretical analysis shows that it consistently achieves a smaller head-tail coverage gap than standard methods. To further improve coverage balance across all classes, we introduce an extension of TACP: soft TACP (sTACP) via a reweighting mechanism. The proposed framework can be combined with various non-conformity scores, and experiments on multiple long-tailed benchmark datasets demonstrate the effectiveness of our methods.

Classical visual coding and Multimodal Large Language Model (MLLM) token technology share the core objective - maximizing information fidelity while minimizing computational cost. Therefore, this paper reexamines MLLM token technology, including tokenization, token compression, and token reasoning, through the established principles of long-developed visual coding area. From this perspective, we (1) establish a unified formulation bridging token technology and visual coding, enabling a systematic, module-by-module comparative analysis; (2) synthesize bidirectional insights, exploring how visual coding principles can enhance MLLM token techniques' efficiency and robustness, and conversely, how token technology paradigms can inform the design of next-generation semantic visual codecs; (3) prospect for promising future research directions and critical unsolved challenges. In summary, this study presents the first comprehensive and structured technology comparison of MLLM token and visual coding, paving the way for more efficient multimodal models and more powerful visual codecs simultaneously.

Conformal prediction, as an emerging uncertainty quantification technique, typically functions as post-hoc processing for the outputs of trained classifiers. To optimize the classifier for maximum predictive efficiency, Conformal Training rectifies the training objective of base classifiers with a regularization that minimizes the average prediction set size at a specific error rate. However, the regularization term inevitably deteriorates the classification accuracy of classifiers, thereby leading to suboptimal efficiency of conformal predictors. To address this issue, we introduce Conformal Adapter (C-Adapter), an adapter-based tuning method to enhance the efficiency of conformal predictors without sacrificing accuracy. In particular, we implement the adapter as a class of intra order-preserving functions and tune it with our proposed loss that maximizes the discriminability of non-conformity scores between correctly and randomly matched data-label pairs. Using C-Adapter, the model tends to produce higher non-conformity scores for incorrect labels than for correct ones, thereby enhancing predictive efficiency across different coverage rates. Extensive experiments demonstrate that C-Adapter can effectively adapt various classifiers for efficient conformal prediction sets, as well as enhance the conformal training method.

Large Language Models (LLMs) with inference-time scaling techniques show promise for code generation, yet face notable efficiency and scalability challenges. Construction-based tree-search methods suffer from rapid growth in tree size, high token consumption, and lack of anytime property. In contrast, improvement-based methods offer better performance but often struggle with uninformative reward signals and inefficient search strategies. In this work, we propose $\textbf{ReLoc}$, a unified local search framework which effectively performs step-by-step code revision. Specifically, ReLoc explores a series of local revisions through four key algorithmic components: initial code drafting, neighborhood code generation, candidate evaluation, and incumbent code updating, each of which can be instantiated with specific decision rules to realize different local search algorithms such as Hill Climbing (HC) or Genetic Algorithm (GA). Furthermore, we develop a specialized revision reward model that evaluates code quality based on revision distance to produce fine-grained preferences that guide the local search toward more promising candidates. Finally, our extensive experimental results demonstrate that our approach achieves superior performance across diverse code generation tasks, significantly outperforming both construction-based tree search as well as the state-of-the-art improvement-based code generation methods.

ABSTRACT In scenarios with heavy smog, the accuracy of object detection in low‐light visible polarization images significantly decreases. To address this issue, we propose a dual‐branch enhancement and multi‐modal fusion network for object detection in low‐light visible polarization images in dense smog environments. Specifically, the network consists of an image enhancement stage and an object detection stage. In the image enhancement stage, a dual‐branch enhancement structure comprising greyscale feature map prediction and atmospheric light transmission network is proposed to remove noise from the images and enhance texture information, jointly generating enhanced visible polarization images. In the object detection stage, feature maps of the enhanced visible polarization images and the degree of visible polarization images are fused, and their fused texture‐enhanced feature maps are fed into the detection module for object detection. Additionally, we have collected a dataset of low‐light visible polarization images under real smog conditions. Extensive experiments demonstrate that our method can generate visually improved enhanced images and significantly increase detection accuracy and the number of detected objects in low‐light and dense smog environments.

Conformal prediction (CP) is a powerful statistical framework that generates prediction intervals or sets with guaranteed coverage probability. While CP algorithms have evolved beyond traditional classifiers and regressors to sophisticated deep learning models like deep neural networks (DNNs), graph neural networks (GNNs), and large language models (LLMs), existing CP libraries often lack the model support and scalability for large-scale deep learning (DL) scenarios. This paper introduces TorchCP, a PyTorch-native library designed to integrate state-of-the-art CP algorithms into DL techniques, including DNN-based classifiers/regressors, GNNs, and LLMs. Released under the LGPL-3.0 license, TorchCP comprises about 16k lines of code, validated with 100% unit test coverage and detailed documentation. Notably, TorchCP enables CP-specific training algorithms, online prediction, and GPU-accelerated batch processing, achieving up to 90% reduction in inference time on large datasets. With its low-coupling design, comprehensive suite of advanced methods, and full GPU scalability, TorchCP empowers researchers and practitioners to enhance uncertainty quantification across cutting-edge applications.

Conformal prediction is a statistical framework that generates prediction sets containing ground-truth labels with a desired coverage guarantee. The predicted probabilities produced by machine learning models are generally miscalibrated, leading to large prediction sets in conformal prediction. To address this issue, we propose a novel algorithm named $\textit{Sorted Adaptive Prediction Sets}$ (SAPS), which discards all the probability values except for the maximum softmax probability. The key idea behind SAPS is to minimize the dependence of the non-conformity score on the probability values while retaining the uncertainty information. In this manner, SAPS can produce compact prediction sets and communicate instance-wise uncertainty. Extensive experiments validate that SAPS not only lessens the prediction sets but also broadly enhances the conditional coverage rate of prediction sets.

Graph Neural Networks have achieved remarkable accuracy in semi-supervised node classification tasks. However, these results lack reliable uncertainty estimates. Conformal prediction methods provide a theoretical guarantee for node classification tasks, ensuring that the conformal prediction set contains the ground-truth label with a desired probability (e.g., 95\%). In this paper, we empirically show that for each node, aggregating the non-conformity scores of nodes with the same label can improve the efficiency of conformal prediction sets while maintaining valid marginal coverage. This observation motivates us to propose a novel algorithm named $\textit{Similarity-Navigated Adaptive Prediction Sets}$ (SNAPS), which aggregates the non-conformity scores based on feature similarity and structural neighborhood. The key idea behind SNAPS is that nodes with high feature similarity or direct connections tend to have the same label. By incorporating adaptive similar nodes information, SNAPS can generate compact prediction sets and increase the singleton hit ratio (correct prediction sets of size one). Moreover, we theoretically provide a finite-sample coverage guarantee of SNAPS. Extensive experiments demonstrate the superiority of SNAPS, improving the efficiency of prediction sets and singleton hit ratio while maintaining valid coverage.

Data privacy is becoming increasingly important as data becomes more valuable, as evidenced by the enactment of right-to-be-forgotten laws and regulations. However, in a federated learning (FL) system, simply deleting data from the database when a user requests data revocation is not sufficient, as the training data is already implicitly contained in the parameter distribution of the models trained with it. Furthermore, the global model in the FL system is vulnerable to data poisoning attacks by malicious nodes. Exploring a reliable data poisoning reversal method can effectively counter such attacks. In this article, we analyze the necessity of decoupling the processes of unlearning and training and propose a training-agnostic and efficient method that can effectively perform two types of unlearning tasks: 1) client revocation and 2) category removal. Specifically, we decompose the unlearning process into two steps: 1) knowledge erasure and 2) memory guidance. We first propose a novel knowledge erasure strategy called momentum degradation (MoDe) which realizes the erasure of implicit knowledge in the model and ensures that the model can move smoothly to the early state of the retrained model. To mitigate the performance degradation caused by the first step, the memory guidance strategy implements guided fine-tuning of the model on different data points, which can effectively restore the discriminability of the model on the remaining data points. Extensive experiments demonstrate that our method outperforms the existing task-specific algorithms and matches the performance of retraining, accelerating the execution time by 5–20 times compared to retraining on different data sets.

Driven by the huge demand to explore oceans, underwater wireless communications have been rapidly developed in the past few decades. Due to the complex physical characteristics of water, acoustic wave is the only media available for underwater wireless communication at any distance. As a result, underwater acoustic communication (UAC) is the major research field in underwater wireless communication. In this paper, characteristics of underwater acoustic channels are first introduced and compared with terrestrial communication to demonstrate the difficulties in UAC research. To give a general impression of the UAC, current important research areas are mentioned. Furthermore, different principal modulation-based schemes for short- and medium-range communications with high data rates are investigated and summarized. To evaluate the performance of UAC systems in general, three criteria are presented based on the research publications and our years of experience in high-rate short- to medium-range communications. These three criteria provide useful tools to generally guide the design and evaluate the performance of underwater acoustic communication systems.

This study proposes a novel approach to joint channel estimation and detection of orthogonal frequency division multiplexing transmission over underwater acoustic (UWA) multipath channels exhibiting cluster sparsity. Unlike most sparse channel estimations, the authors exploit the cluster‐sparsity characteristic of UWA channels without additional prior information. They adopt a modified spike‐and‐slab prior model in their non‐parametric Bayesian learning framework. To avoid the need for a closed‐form Bayesian estimate, they apply the Markov chain Monte Carlo technique to joint achieve channel estimation and signal detection. The proposed solution is amenable to being integrated with soft‐input soft‐output decoding to improve the performance through turbo iteration. Simulation results demonstrate improved bit error rate of the proposed algorithm over existing algorithms.

Complex kernel-based adaptive algorithms have been recently introduced for complex-valued nonlinear system identification. These algorithms are built upon the same framework as complex linear adaptive filtering techniques and Wirtinger's calculus in complex reproducing kernel Hilbert spaces. In this paper, we study the convergence behavior of the augmented complex Gaussian KLMS algorithm. Simulation results illustrate the accuracy of the analysis.

Single-carrier with frequency domain equalization (SC-FDE) has been considered for bandwidth efficiency underwater acoustic (UWA) communication recently due to its reduced computational complexity and low peak-to-average power ratio. A multi-channel time-frequency domain equalization method for pseudurandom noise (PN) based SC-FDE is proposed in this paper. The proposed equalizer includes a multi-channel frequency domain equalizer followed by a low order multi-channel adaptive time domain decision feedback equalizer (DFE). The proposed algorithm is applied to the real data receiving from a lake test conducted in November 2011. It is demonstrated that the uncoded error-free data rates of around 1500 and 3000 bps are achieved using one transmitter and six-channel receiving hydrophone array at a distance of 1.8 km. Experiment results shows that the performance can be enhanced by 4.5-5.5 dB in terms of output signal-to-noise ratio (SNR).

Nonlinear adaptive filtering with kernels has become a topic of high interest over the last decade. A characteristics of kernel-based techniques is that they deal with kernel expansions whose number of terms is equal to the number of input data, making them unsuitable for online applications. Kernel-based adaptive filtering algorithms generally rely on a two-stage process at each iteration: a model order control stage that limits the increase in the number of terms by including only valuable kernels into the so-called dictionary, and a filter parameter update stage. It is surprising to note that most existing strategies for dictionary update can only incorporate new elements into the dictionary. This unfortunately means that they cannot discard obsolete kernel functions, within the context of a time-varying environment in particular. Recently, to remedy this drawback, it has been proposed to associate an ℓ1-norm regularization criterion with the mean-square error criterion. The aim of this paper is to provide theoretical results on the convergence of this approach.

In this paper, we consider the problem of power constrained partially coherent distributed detection over fading multi-access channel. The deflection coefficient maximization (DCM) is used to optimize the performance of detectors. Two cases of the channel gain information are considered separately at the fusion center, one case with perfect channel gain (the corresponding method is referred to as PC-DCM, with PC being the abbreviation for “partially coherent”), the other case with statistical information of channel gain (the corresponding method is referred to as PC-DCM-CS, with CS being the abbreviation for “channel statistics”). We derive the closed-form solutions to the considered problems. Monte-Carlo simulations are carried out to verify the performance of the proposed methods. Simulation results show that the proposed new methods could significantly improve the detection performance of the fusion system at low signal-to-noise ratio (SNR).

In this paper, we propose a robust sparse spectrum fitting method (RSpSF) for Directions-Of-Arrival (DOA) and power estimation in the presence of general form of modeling errors in the array manifold matrix. By exploiting the group sparsity between the power spectrum and the modeling errors, RSpSF formulates the estimator as a convex optimization program. Then, in order to reduce its computational complexity, we apply a beam-space technique to RSpSF and obtain another convex estimator, the beam-space RSpSF (BMRSpSF). Simulation examples are presented to demonstrate the robustness of the proposed methods to off-grid DOAs and to random array calibration errors.

A new generalized eigenstructure-based 3-dimensional joint estimator (GETJE) for the direction, frequency, and time-delay of multiple sources is presented. For 2-dimensional joint parameter estimation, we proposed an ESPRIT-based algorithm (Qunfei Zhang and Jianguo Huang, Int. Conf. On ASSP, 1999). Now we extend it to the 3-dimensional estimator. Using a single echo wave, the bearings, frequencies and time-delays of multiple reflectors are jointly estimated. We construct 2 sub-arrays like ESPRIT, and then conduct generalized eigen-decomposition for their auto-correlation matrix and cross-correlation matrix. Bearing parameters can be estimated from eigenvalues, while frequency parameters can also be obtained from corresponding eigenvectors. After modifying the time-delay vectors of the envelop of the emitting signal according to the estimated frequencies, the time-delay parameters can be obtained simultaneously. Computer simulations show that the GETJE can carry out the 3-dimensional joint parameter estimation without additional pairing in the case of lower SNR. Preferable results are also obtained in water tank experiments, which indicate that the GETJE is robust for sensor array errors and has potential applications.

A new Gibbs sampling DOA estimator based on Bayesian method (GSDB) is proposed to estimate the directions of multiple sources. The estimator combines the Gibbs sampler and the Bayesian high-resolution method. The formulation of the proposed Gibbs sampling DOA estimator based on the Bayesian method is derived. The new method not only possesses the performance of the high-resolution direction finding in the original Bayesian method but also provides reduced computational complexity to the original one from O(L/sup K/) to O(K/spl times/J/spl times/N/sub s/). Comparison with MUSIC shows that the new estimator has higher resolution and better performance in low SNR.

Joint estimation of direction of arrival (DOA) and time-delay plays a great role in source localization, which attracts many researchers not only in the areas of radar, sonar, geological exploration but also in wireless communication. M. Wax (see IEEE Trans. on SP, vol.45, no.10, p.2477-84, 1997) applies approximate MLE with iteration algorithm, which convert a 2-D search into two or three 1-D search. A.J. van der Veen (see IEEE Trans. on SP, vol.46, no.2, p.405-18, 1998) use 2-D ESPRIT to conduct joint estimation. Both of them show good performance at a cost of large computation. Both of them require deconvolution in the frequency domain to transfer time-delay into phase. The deconvolution lends to two problems. One is blowing up noise, the other is leading to spurious peak if the emitted signal is non-minimum phase. In this paper, a simple method using 1-D ESPRIT is presented to complete joint estimation of DOA and time-delay, which requires no deconvolution. It is suitable for active underwater localization where a non-minimum phase signal is frequently employed. The method can estimate parameters of three reflectors with big difference between amplitudes as large as 12 dB. The statistical performance of new estimators and the probability of correct pairing are given by computer simulations. It shows that better performance of the new method can be achieved for multiple source localization even in low SNR.

A novel and practical approach of array calibration in underwater high-resolution direction finding is presented to alleviate the effect of different errors generated in underwater array processing system. It is different from other algorithms in that the array manifold used in subspace-based methods is obtained through automatic measurement instead of using the theoretical value. It can efficiently calibrate the errors of gain, phase, mutual-coupling, position of sensors, and other errors generated by the array and sensors even if they are direction dependent. A spatial smoothing technique is employed and so the method is effective no matter if the sources are correlated or uncorrelated. It is also proved by the experiment that spatial smoothing is beneficial to reduce some errors. Several experimental results are provided to verify the efficiency of the new calibration method.

A novel method based on the phase information of continuous wavelet transform to estimate the instantaneous parameter of an AM-FM signal is introduced, and some strategies, including the determination of initial value in the iteration and post-processing to the estimated results, to improve the performance of the algorithm are proposed. Compared to several other instantaneous parameter estimators, such as CDF, Teager-Kaiser energy operator, and some TFR-based estimators, the proposed method has the advantages of noise resistance and accuracy by exploiting the time-scale localization of the wavelet transform. Simulation results testify that the proposed strategies improve the performance of the CWT based iteration algorithm greatly, and the method has excellent performance including robustness and accuracy in noisy conditions.

An easy and efficient method to classify the underwater sources for passive sonar by extracting the poles of the AR model as the feature of source emitted noise is proposed. Our research demonstrates that the poles of the AR model can represent the intrinsic spectral characteristic of the sources, and a simple statistical classifiers can be used to obtain excellent recognition performance due to the good cluster property and robustness of the poles corresponding to the different sources. It is more important that the poles of the low order AR model can represent the basic feature of the source, thus the computation burden will be reduced significantly. Real data are processed and classification results show the efficiency even for short data records.

A formalism for frequency estimation of multiple sinusoids in noise using dynamic programming is derived. A dynamic-programming-type algorithm for the frequency estimation of two close sinusoids in noise is proposed. Computer simulation results show an improvement over the periodogram.>

An approximate maximum-likelihood estimator is derived for ARMA (autoregressive moving-average) processes and is shown to correspond to least-squares fitting of the estimated cepstrum of the process by the model cepstrum. Experiments with several simple ARMA

A method for autoregressive (AR) modeling of stationary stochastic signals has been proposed based upon fitting the model auto-correlation function to the estimated (biased) autocorrelation in the least-squares sense over more than the minimum number of autocorrelation values (Ref. 7). In this paper, the method is extended to the case of autoregressive-moving-average (ARMA) models, including the special case of AR signals in white noise, and both AR and ARMA examples are presented. This method differs from the well known method of overdetermined normal equations in that fitting error, not equation error, is minimized. The bias in the estimated correlation values is also readily compensated without amplifying the higher (noisy) correlation lags. Iterative algorithms are derived to solve the resulting nonlinear equations.