Reliable confidence estimation is a challenging yet fundamental requirement in many risk-sensitive applications. However, modern deep neural networks are often overconfident for their incorrect predictions, i.e., misclassified samples from known classes, and out-of-distribution (OOD) samples from unknown classes. In recent years, many confidence calibration and OOD detection methods have been developed. In this paper, we find a general, widely existing but actually-neglected phenomenon that most confidence estimation methods are harmful for detecting misclassification errors. We investigate this problem and reveal that popular calibration and OOD detection methods often lead to worse confidence separation between correctly classified and misclassified examples, making it difficult to decide whether to trust a prediction or not. Finally, we propose to enlarge the confidence gap by finding flat minima, which yields state-of-the-art failure prediction performance under various settings including balanced, long-tailed, and covariate-shift classification scenarios. Our study not only provides a strong baseline for reliable confidence estimation but also acts as a bridge between understanding calibration, OOD detection, and failure prediction. The code is available at \url{https://github.com/Impression2805/FMFP}.

Geometry problem solving (GPS) is a challenging mathematical reasoning task requiring multi-modal understanding, fusion and reasoning. Existing neural solvers take GPS as a vision-language task but be short in the representation of geometry diagrams which carry rich and complex layout information. In this paper, we propose a layout-aware neural solver named LANS, integrated with two new modules: multimodal layout-aware pre-trained language model (MLA-PLM) and layout-aware fusion attention (LA-FA). MLA-PLM adopts structural and semantic pre-training (SSP) to implement global relationship modeling, and point matching pre-training (PMP) to achieve alignment between visual points and textual points. LA-FA employs a layout-aware attention mask to realize point-guided cross-modal fusion for further boosting layout awareness of LANS. Extensive experiments on datasets Geometry3K and PGPS9K validate the effectiveness of the layout-aware modules and superior problem solving performance of our LANS solver, over existing symbolic solvers and neural solvers. The code will make public available soon.

Classifying patterns of known classes and rejecting ambiguous and novel (also called as out-of-distribution (OOD)) inputs are involved in open world pattern recognition. Deep neural network models usually excel in closed-set classification while performing poorly in rejecting OOD. To tackle this problem, numerous methods have been designed to perform open set recognition (OSR) or OOD rejection/detection tasks. Previous methods mostly take post-training score transformation or hybrid models to ensure low scores on OOD inputs while separating known classes. In this paper, we attempt to build a unified framework for building open set classifiers for both classification and OOD rejection. We formulate the open set recognition of $ K $-known-class as a $ (K + 1) $-class classification problem with model trained on known-class samples only. By decomposing the $ K $-class problem into $ K $ one-versus-all (OVA) binary classification tasks and binding some parameters, we show that combining the scores of OVA classifiers can give $ (K + 1) $-class posterior probabilities, which enables classification and OOD rejection in a unified framework. To maintain the closed-set classification accuracy of the OVA trained classifier, we propose a hybrid training strategy combining OVA loss and multi-class cross-entropy loss. We implement the OVA framework and hybrid training strategy on the recently proposed convolutional prototype network. Experiments on popular OSR and OOD detection datasets demonstrate that the proposed framework, using a single multi-class classifier, yields competitive performance in closed-set classification, OOD detection, and misclassification detection.

There are ubiquitous distribution shifts in the real world. However, deep neural networks (DNNs) are easily biased towards the training set, which causes severe performance degradation when they receive out-of-distribution data. Many methods are studied to train models that generalize under various distribution shifts in the literature of domain generalization (DG). However, the recent DomainBed and WILDS benchmarks challenged the effectiveness of these methods. Aiming at the problems in the existing research, we propose a new domain generalization task for handwritten Chinese character recognition (HCCR) to enrich the application scenarios of DG method research. We evaluate eighteen DG methods on the proposed PaHCC (Printed and Handwritten Chinese Characters) dataset and show that the performance of existing methods on this dataset is still unsatisfactory. Besides, under a designed dynamic DG setting, we reveal more properties of DG methods and argue that only the leave-one-domain-out protocol is unreliable. We advocate that researchers in the DG community refer to dynamic performance of methods for more comprehensive and reliable evaluation. Our dataset and evaluations bring new perspectives to the community for more substantial progress. We will make our dataset public with the article published to facilitate the study of domain generalization.

Label noise poses a serious threat to deep neural networks (DNNs). Employing robust loss functions which reconcile fitting ability with robustness is a simple but effective strategy to handle this problem. However, the widely-used static trade-off between these two factors contradicts the dynamics of DNNs learning with label noise, leading to inferior performance. Therefore, we propose a dynamics-aware loss (DAL) to solve this problem. Considering that DNNs tend to first learn beneficial patterns, then gradually overfit harmful label noise, DAL strengthens the fitting ability initially, then gradually improves robustness. Moreover, at the later stage, to further reduce the negative impact of label noise and combat underfitting simultaneously, we let DNNs put more emphasis on easy examples than hard ones and introduce a bootstrapping term. Both the detailed theoretical analyses and extensive experimental results demonstrate the superiority of our method. Our source code can be found in https://github.com/XiuchuanLi/DAL.

Geometry problem solving (GPS) is a high-level mathematical reasoning requiring the capacities of multi-modal fusion and geometric knowledge application. Recently, neural solvers have shown great potential in GPS but still be short in diagram presentation and modal fusion. In this work, we convert diagrams into basic textual clauses to describe diagram features effectively, and propose a new neural solver called PGPSNet to fuse multi-modal information efficiently. Combining structural and semantic pre-training, data augmentation and self-limited decoding, PGPSNet is endowed with rich knowledge of geometry theorems and geometric representation, and therefore promotes geometric understanding and reasoning. In addition, to facilitate the research of GPS, we build a new large-scale and fine-annotated GPS dataset named PGPS9K, labeled with both fine-grained diagram annotation and interpretable solution program. Experiments on PGPS9K and an existing dataset Geometry3K validate the superiority of our method over the state-of-the-art neural solvers. Our code, dataset and appendix material are available at \url{https://github.com/mingliangzhang2018/PGPS}.

Reliable confidence estimation for deep neural classifiers is a challenging yet fundamental requirement in high-stakes applications. Unfortunately, modern deep neural networks are often overconfident for their erroneous predictions. In this work, we exploit the easily available outlier samples, i.e., unlabeled samples coming from non-target classes, for helping detect misclassification errors. Particularly, we find that the well-known Outlier Exposure, which is powerful in detecting out-of-distribution (OOD) samples from unknown classes, does not provide any gain in identifying misclassification errors. Based on these observations, we propose a novel method called OpenMix, which incorporates open-world knowledge by learning to reject uncertain pseudo-samples generated via outlier transformation. OpenMix significantly improves confidence reliability under various scenarios, establishing a strong and unified framework for detecting both misclassified samples from known classes and OOD samples from unknown classes. The code is publicly available at https://github.com/Impression2805/OpenMix.

Reliable confidence estimation for the predictions is important in many safety-critical applications. However, modern deep neural networks are often overconfident for their incorrect predictions. Recently, many calibration methods have been proposed to alleviate the overconfidence problem. With calibrated confidence, a primary and practical purpose is to detect misclassification errors by filtering out low-confidence predictions (known as failure prediction). In this paper, we find a general, widely-existed but actually-neglected phenomenon that most confidence calibration methods are useless or harmful for failure prediction. We investigate this problem and reveal that popular confidence calibration methods often lead to worse confidence separation between correct and incorrect samples, making it more difficult to decide whether to trust a prediction or not. Finally, inspired by the natural connection between flat minima and confidence separation, we propose a simple hypothesis: flat minima is beneficial for failure prediction. We verify this hypothesis via extensive experiments and further boost the performance by combining two different flat minima techniques.

Detecting Out-of-distribution (OOD) inputs have been a critical issue for neural networks in the open world. However, the unstable behavior of OOD detection along the optimization trajectory during training has not been explored clearly. In this paper, we first find the performance of OOD detection suffers from overfitting and instability during training: 1) the performance could decrease when the training error is near zero, and 2) the performance would vary sharply in the final stage of training. Based on our findings, we propose Average of Pruning (AoP), consisting of model averaging and pruning, to mitigate the unstable behaviors. Specifically, model averaging can help achieve a stable performance by smoothing the landscape, and pruning is certified to eliminate the overfitting by eliminating redundant features. Comprehensive experiments on various datasets and architectures are conducted to verify the effectiveness of our method.

Representation is a core issue in artificial intelligence. Humans use discrete language to communicate and learn from each other, while machines use continuous features (like vector, matrix, or tensor in deep neural networks) to represent cognitive patterns. Discrete symbols are low-dimensional, decoupled, and have strong reasoning ability, while continuous features are high-dimensional, coupled, and have incredible abstracting capabilities. In recent years, deep learning has developed the idea of continuous representation to the extreme, using millions of parameters to achieve high accuracies. Although this is reasonable from the statistical perspective, it has other major problems like lacking interpretability, poor generalization, and is easy to be attacked. Since both paradigms have strengths and weaknesses, a better choice is to seek reconciliation. In this paper, we make an initial attempt towards this direction. Specifically, we propose to combine symbolism and connectionism principles by using neural networks to derive a discrete representation. This process is highly similar to human language, which is a natural combination of discrete symbols and neural systems, where the brain processes continuous signals and represents intelligence via discrete language. To mimic this functionality, we denote our approach as machine language. By designing an interactive environment and task, we demonstrated that machines could generate a spontaneous, flexible, and semantic language through cooperation. Moreover, through experiments we show that discrete language representation has several advantages compared with continuous feature representation, from the aspects of interpretability, generalization, and robustness.