In recent Open-set Recognition (OSR) community, a prevailing belief is that enhancing the discriminative boundaries of closed-set classes can improve the robustness of Deep Neural Networks (DNNs) against open data during testing. Typical studies validate this *implicitly* by empirical evidence, without a formalized understanding of *how DNNs help the closed-set features obtain more discriminative boundaries?* For this, we provide an answer from the Neural Collapse (NC) perspective: DNNs align the closed-set with a *Simplex Equiangular Tight Frame* (ETF) structure that has geometric and mathematical interpretability. Regrettably, although NC naturally occurs in DNNs, we discover that typical studies cannot guarantee the features being learned to strictly align with the ETF. Thus, we introduce a novel concept, Fixed ETF Template (FiT), which holds an ideal structure associated with closed-set classes. To force class means and classifier vectors to align with FiT, we further design a Dual ETF (DEF) loss involving two components. Specifically, *F*-DEF loss is designed to align class means with FiT strictly, yielding optimal inter-class separability. Meanwhile, we extend a dual form to classifier vectors, termed *C*-DEF loss, which guides class means and classifier vectors to satisfy self-duality. Our theoretical analysis proves the validity of the proposed approach, and extensive experiments demonstrate that DEF achieves comparable or superior results with reduced computational resources on standard OSR benchmarks.

Neural Collapse (NC) presents an elegant geometric structure that enables individual activations (features), class means and classifier (weights) vectors to reachoptimalinter-class separability during the terminal phase of training on abalanceddataset. Once shifted to imbalanced classification, such an optimal structure of NC can be readily destroyed by the notoriousminority collapse, where the classifier vectors corresponding to the minority classes are squeezed. In response, existing works mainly optimize classifiers in an effort to recover NC. However, we discover that this squeezing phenomenon is not only confined to classifier vectors but also occurs with class means. Consequently, reconstructing NC solely at the classifier aspect may be futile, as the class means remain compressed, leading to the violation of inherentself-dualityin NC (i.e., class means and classifier vectors converge mutually) and incidentally, an unsatisfactory collapse of individual activations towards the corresponding class means. To shake off these dilemmas, we present a unifiedAll-aroundNeuralCollapse framework (AllNC), aiming to comprehensively restore NC across multiple aspects including individual activations, class means and classifier vectors. We thoroughly analyze its effectiveness and verify its performance on multiple benchmark datasets as state-of-the-art in both balanced and imbalanced settings.

In open-set recognition (OSR), a promising strategy is exploiting pseudo-unknown data outside given K known classes as an additional K+1-th class to explicitly model potential open space. However, treating unknown classes without distinction is unequal for them relative to known classes due to the category-agnostic and scale-agnostic of the unknowns. This inevitably not only disrupts the inherent distributions of unknown classes but also incurs both class-wise and instance-wise imbalances between known and unknown classes. Ideally, the OSR problem should model the whole class space as K+∞, but enumerating all unknowns is impractical. Since the core of OSR is to effectively model the boundaries of known classes, this means just focusing on the unknowns nearing the boundaries of targeted known classes seems sufficient. Thus, as a compromise, we convert the open classes from infinite to K, with a novel concept Target-Aware Universum (TAU) and propose a simple yet effective framework Dual Contrastive Learning with Target-Aware Universum (DCTAU). In details, guided by the targeted known classes, TAU automatically expands the unknown classes from the previous 1 to K, effectively alleviating the distribution disruption and the imbalance issues mentioned above. Then, a novel Dual Contrastive (DC) loss is designed, where all instances irrespective of known or TAU are considered as positives to contrast with their respective negatives. Experimental results indicate DCTAU sets a new state-of-the-art.

Logit adjustment is an effective long-tailed visual recognition strategy to encourage a significant margin between rare and dominant labels. Existing methods typically employ the globally fixed label frequencies throughout the training to adjust margins. However, in practice, we observe that the local (in-batch) label frequencies change dynamically or even vanish for some classes (especially the tail classes) in batch-dependent training, which is inconsistent with global ones. Furthermore, our analyses reveal that the intra-classcollinear samplesactually do not contribute to the gradient update, but substantially increase the corresponding local label frequencies. Such contributions are spurious due to over-counting the label frequencies without contributing to the gradient. All of these will cause serious interference in precisely estimating local frequencies of the authentic contribution, leading to inauthentic margins. To simultaneously address the above issues, this paper innovatively proposes Dynamic Learnable Logit Adjustment (DLLA) loss to learn the local label frequencies within dynamic mini-batches precisely. Specifically, DLLA owns two complementary parts: 1)rank-metriceliminates spurious contributions from collinear samples by calculating the algebraic rank of the feature subspace in the mini-batch. 2)class-supplementensures all classes appear in every mini-batch by inserting the corresponding learnable class prototype, for which we resort to neural collapse theory to make them align to the ideal regular simplex structure. Extensive experiments on standard benchmark datasets verify the effectiveness of our method.

BACKGROUND: Generally, SNPs are abundant in the genome; however, they display low power in linkage analysis because of their limited heterozygosity. Haplotype markers, on the other hand, which are composed of many SNPs, greatly increase heterozygosity and have superiority in linkage statistics. RESULTS: Here we developed Haplo2Ped to automatically transform SNP data into haplotype markers and then to compute the logarithm (base 10) of odds (LOD) scores of regional haplotypes that are homozygous within the disease co-segregation haploid group. The results are reported as a hypertext file and a 3D figure to help users to obtain the candidate linkage regions. The hypertext file contains parameters of the disease linked regions, candidate genes, and their links to public databases. The 3D figure clearly displays the linkage signals in each chromosome. We tested Haplo2Ped in a simulated SNP dataset and also applied it to data from a real study. It successfully and accurately located the causative genomic regions. Comparison of Haplo2Ped with other existing software for linkage analysis further indicated the high effectiveness of this software. CONCLUSIONS: Haplo2Ped uses haplotype fragments as mapping markers in whole genome linkage analysis. The advantages of Haplo2Ped over other existing software include straightforward output files, increased accuracy and superior ability to deal with pedigrees showing incomplete penetrance. Haplo2Ped is freely available at: http://bighapmap.big.ac.cn/software.html.