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We study the representation theory of the increasing monoid. Our results provide a fairly comprehensive picture of the representation category: for example, we describe the Grothendieck group (including the effective cone), classify injective objects, establish properties of injective and projective resolutions, construct a derived auto-duality, and so on. Our work is motivated by numerous connections of this theory to other areas, such as representation stability, commutative algebra, simplicial theory, and shuffle algebras.

Using the theory of ${\\mathbf {FS}} {^\\mathrm {op}}$ modules, we study the asymptotic behavior of the homology of ${\\overline {\\mathcal {M}}_{g,n}}$, the Deligne–Mumford compactification of the moduli space of curves, for $n\\gg 0$. An ${\\mathbf {FS}} {^\\mathrm {op}}$ module is a contravariant functor from the category of finite sets and surjections to vector spaces. Via copies that glue on marked projective lines, we give the homology of ${\\overline {\\mathcal {M}}_{g,n}}$ the structure of an ${\\mathbf {FS}} {^\\mathrm {op}}$ module and bound its degree of generation. As a consequence, we prove that the generating function $\\sum _{n} \\dim (H_i({\\overline {\\mathcal {M}}_{g,n}})) t^n$ is rational, and its denominator has roots in the set $\\{1, 1/2, \\ldots, 1/p(g,i)\\},$ where $p(g,i)$ is a polynomial of order $O(g^2 i^2)$. We also obtain restrictions on the decomposition of the homology of ${\\overline {\\mathcal {M}}_{g,n}}$ into irreducible $\\mathbf {S}_n$ representations.

If D\\mathcal {D} is a category and kk is a commutative ring, the functors from D\\mathcal {D} to Modk\\mathbf {Mod}_{k} can be thought of as representations of D\\mathcal {D}. By definition, D\\mathcal {D} is dimension zero over kk if its finitely generated representations have finite length. We characterize categories of dimension zero in terms of the existence of a “homological modulus” (Definition 1.4) which is combinatorial and linear-algebraic in nature.

Visual category‐selective representations in human ventral occipital temporal cortex (VOTC) seem to emerge early in infancy. Surprisingly, the VOTC of congenitally blind humans features category‐selectivity for auditory and haptic objects. Yet it has been unknown whether VOTC would show category‐selective visual responses if sight were restored in congenitally blind humans. Assuming competition for synaptic space during development, cross‐modal activation of VOTC as a consequence of congenital blindness might interfere with visual processing in sight‐recovery individuals. To test this hypothesis, we investigated adults who had experienced a transient phase of congenital blindness due to bilateral dense cataracts before their sight was restored by cataract‐removal surgery. In a functional magnetic resonance imaging (fMRI) study, participants watched movies of faces, scenes, body parts, and other objects in the visual condition, while in the auditory condition they listened to the corresponding sounds. The most prominent group difference was a reduced face‐selectivity in individuals with reversed congenital cataracts compared with age‐ and sex‐matched normally sighted individuals. In addition, a double dissociation was found: only sight recovery individuals demonstrated significant decoding accuracy of visual categories based on auditory category representations in VOTC, while only normally sighted individuals' VOTC decoded auditory categories based on visual category representations. The present results uncovered the neural mechanisms of previously observed face processing impairments in individuals with reversed congenital blindness. We suggest that lower face‐selectivity in the sight recovery group might arise from selective deficits in the cortical representation of the central visual field in lower‐tier visual areas. Additionally, we speculate that in higher‐order visual areas cross‐modal activity might facilitate—rather than interfere—with visual functional recovery after congenital blindness. Category‐selectivity for faces in ventral occipital cortex depended more on early visual experience than for scenes or body parts. Importantly, auditory activity in higher‐order visual cortex seemed to support—rather than interfere—with the acquisition of the visual category‐selectivity in individuals with reversed congenital cataracts.

Adaptive behavior requires the separation of current from future goals in working memory. We used fMRI of object-selective cortex to determine the representational (dis)similarities of memory representations serving current and prospective perceptual tasks. Participants remembered an object drawn from three possible categories as the target for one of two consecutive visual search tasks. A cue indicated whether the target object should be looked for first (currently relevant), second (prospectively relevant), or if it could be forgotten (irrelevant). Prior to the first search, representations of current, prospective and irrelevant objects were similar, with strongest decoding for current representations compared to prospective (Experiment 1) and irrelevant (Experiment 2). Remarkably, during the first search, prospective representations could also be decoded, but revealed anti-correlated voxel patterns compared to currently relevant representations of the same category. We propose that the brain separates current from prospective memories within the same neuronal ensembles through opposite representational patterns.

This article introduces a generative model of category representation that uses computer vision methods to extract category-consistent features (CCFs) directly from images of category exemplars. The model was trained on 4,800 images of common objects, and CCFs were obtained for 68 categories spanning subordinate, basic, and superordinate levels in a category hierarchy. When participants searched for these same categories, targets cued at the subordinate level were preferentially fixated, but fixated targets were verified faster when they followed a basic-level cue. The subordinate-level advantage in guidance is explained by the number of target-category CCFs, a measure of category specificity that decreases with movement up the category hierarchy. The basic-level advantage in verification is explained by multiplying the number of CCFs by sibling distance, a measure of category distinctiveness. With this model, the visual representations of real-world object categories, each learned from the vast numbers of image exemplars accumulated throughout everyday experience, can finally be studied.

Hélie, Shamloo, & Ell (2017) showed that regular classification learning instructions (A/B) promote between-category knowledge in rule-based categorization whereas conceptual learning instructions (YES/NO) promote learning within-category knowledge with the same categories. Here we explore how these tasks affect brain activity using fMRI. Participants learned two sets of two categories. Computational models were fit to the behavioral data to determine the type of knowledge learned by each participant. fMRI contrasts were computed to compare BOLD signal between the tasks and between the types of knowledge. The results show that participants in the YES/NO task had more activity in the pre-supplementary motor area, prefrontal cortex, and the angular/supramarginal gyrus. These brain areas are related to working memory and part of the dorsal attention network, which showed increased task-based functional connectivity with the medial temporal lobes. In contrast, participants in the A/B task had more activity in the thalamus and caudate. These results suggest that participants in the YES/NO task used bivalent rules and may have treated each contextual question as a separate task, switching task each time the question changed. Activity in the A/B condition was more consistent with participants applying direct Stimulus → Response rules. With regards to knowledge representation, there was a large shared network of brain areas, but participants learning between-category information showed additional posterior parietal activity, which may be related to the inhibition of incorrect motor programs.

Human neuroimaging studies suggest that areas in temporal cortex respond preferentially to certain biologically relevant stimulus categories such as faces and bodies. Single-cell studies in monkeys have reported cells in inferior temporal cortex that respond selectively to faces, hands, and bodies but provide little evidence of large clusters of category-specific cells that would form \"areas.\" We probed the category selectivity of macaque temporal cortex for representations of monkey faces and monkey body parts relative to man-made objects using function MRI in animals trained to fixate. Two face-selective areas were activated bilaterally in the posterior and anterior superior temporal sulcus exhibiting different degrees of category selectivity. The posterior face area was more extensively activated in the right hemisphere than in the left hemisphere. Immediately adjacent to the face areas, regions were activated bilaterally responding preferentially to body parts. Our findings suggest a category-selective organization for faces and body parts in macaque temporal cortex.

Semantic segmentation of novel object categories with limited labeled data remains a challenging problem in computer vision. Few-shot segmentation methods aim to address this problem by recognizing objects from specific target classes with a few provided examples. Previous approaches for few-shot semantic segmentation typically represent target classes using class prototypes. These prototypes are matched with the features of the query set to get segmentation results. However, class prototypes are usually obtained by applying global average pooling on masked support images. Global pooling discards much structural information, which may reduce the accuracy of model predictions. To address this issue, we propose a Category-Guided Frequency Modulation (CGFM) method. CGFM is designed to learn category-specific information in the frequency space and leverage it to provide a two-stage guidance for the segmentation process. First, to self-adaptively activate class-relevant frequency bands while suppressing irrelevant ones, we leverage the Dual-Perception Gaussian Band Pre-activation (DPGBP) module to generate Gaussian filters using class embedding vectors. Second, to further enhance category-relevant frequency components in activated bands, we design a Support-Guided Category Response Enhancement (SGCRE) module to effectively introduce support frequency components into the modulation of query frequency features. Experiments on the and datasets demonstrate the promising performance of our model. The code will be released at accessed on 17 February 2025.