Daily Papers

Popular text-to-image (T2I) systems are trained on web-scraped data, which is heavily Amero and Euro-centric, underrepresenting the cultures of the Global South. To analyze these biases, we introduce CuRe, a novel and scalable benchmarking and scoring suite for cultural representativeness that leverages the marginal utility of attribute specification to T2I systems as a proxy for human judgments. Our CuRe benchmark dataset has a novel categorical hierarchy built from the crowdsourced Wikimedia knowledge graph, with 300 cultural artifacts across 32 cultural subcategories grouped into six broad cultural axes (food, art, fashion, architecture, celebrations, and people). Our dataset's categorical hierarchy enables CuRe scorers to evaluate T2I systems by analyzing their response to increasing the informativeness of text conditioning, enabling fine-grained cultural comparisons. We empirically observe much stronger correlations of our class of scorers to human judgments of perceptual similarity, image-text alignment, and cultural diversity across image encoders (SigLIP 2, AIMV2 and DINOv2), vision-language models (OpenCLIP, SigLIP 2, Gemini 2.0 Flash) and state-of-the-art text-to-image systems, including three variants of Stable Diffusion (1.5, XL, 3.5 Large), FLUX.1 [dev], Ideogram 2.0, and DALL-E 3. The code and dataset is open-sourced and available at https://aniketrege.github.io/cure/.

Despite the growing use of transformer models in computer vision, a mechanistic understanding of these networks is still needed. This work introduces a method to reverse-engineer Vision Transformers trained to solve image classification tasks. Inspired by previous research in NLP, we demonstrate how the inner representations at any level of the hierarchy can be projected onto the learned class embedding space to uncover how these networks build categorical representations for their predictions. We use our framework to show how image tokens develop class-specific representations that depend on attention mechanisms and contextual information, and give insights on how self-attention and MLP layers differentially contribute to this categorical composition. We additionally demonstrate that this method (1) can be used to determine the parts of an image that would be important for detecting the class of interest, and (2) exhibits significant advantages over traditional linear probing approaches. Taken together, our results position our proposed framework as a powerful tool for mechanistic interpretability and explainability research.

With the development of Multimodal Large Language Models (MLLMs), the evaluation of multimodal models in the context of mathematical problems has become a valuable research field. Multimodal visual-textual mathematical reasoning serves as a critical indicator for evaluating the comprehension and complex multi-step quantitative reasoning abilities of MLLMs. However, previous multimodal math benchmarks have not sufficiently integrated visual and textual information. To address this gap, we proposed MathScape, a new benchmark that emphasizes the understanding and application of combined visual and textual information. MathScape is designed to evaluate photo-based math problem scenarios, assessing the theoretical understanding and application ability of MLLMs through a categorical hierarchical approach. We conduct a multi-dimensional evaluation on 11 advanced MLLMs, revealing that our benchmark is challenging even for the most sophisticated models. By analyzing the evaluation results, we identify the limitations of MLLMs, offering valuable insights for enhancing model performance.

Understanding how semantic meaning is encoded in the representation spaces of large language models is a fundamental problem in interpretability. In this paper, we study the two foundational questions in this area. First, how are categorical concepts, such as {'mammal', 'bird', 'reptile', 'fish'}, represented? Second, how are hierarchical relations between concepts encoded? For example, how is the fact that 'dog' is a kind of 'mammal' encoded? We show how to extend the linear representation hypothesis to answer these questions. We find a remarkably simple structure: simple categorical concepts are represented as simplices, hierarchically related concepts are orthogonal in a sense we make precise, and (in consequence) complex concepts are represented as polytopes constructed from direct sums of simplices, reflecting the hierarchical structure. We validate these theoretical results on the Gemma large language model, estimating representations for 957 hierarchically related concepts using data from WordNet.

We propose Hier-SLAM++, a comprehensive Neuro-Symbolic semantic 3D Gaussian Splatting SLAM method with both RGB-D and monocular input featuring an advanced hierarchical categorical representation, which enables accurate pose estimation as well as global 3D semantic mapping. The parameter usage in semantic SLAM systems increases significantly with the growing complexity of the environment, making scene understanding particularly challenging and costly. To address this problem, we introduce a novel and general hierarchical representation that encodes both semantic and geometric information in a compact form into 3D Gaussian Splatting, leveraging the capabilities of large language models (LLMs) as well as the 3D generative model. By utilizing the proposed hierarchical tree structure, semantic information is symbolically represented and learned in an end-to-end manner. We further introduce a novel semantic loss designed to optimize hierarchical semantic information through both inter-level and cross-level optimization. Additionally, we propose an improved SLAM system to support both RGB-D and monocular inputs using a feed-forward model. To the best of our knowledge, this is the first semantic monocular Gaussian Splatting SLAM system, significantly reducing sensor requirements for 3D semantic understanding and broadening the applicability of semantic Gaussian SLAM system. We conduct experiments on both synthetic and real-world datasets, demonstrating superior or on-par performance with state-of-the-art NeRF-based and Gaussian-based SLAM systems, while significantly reducing storage and training time requirements.

We propose Hi-SLAM, a semantic 3D Gaussian Splatting SLAM method featuring a novel hierarchical categorical representation, which enables accurate global 3D semantic mapping, scaling-up capability, and explicit semantic label prediction in the 3D world. The parameter usage in semantic SLAM systems increases significantly with the growing complexity of the environment, making it particularly challenging and costly for scene understanding. To address this problem, we introduce a novel hierarchical representation that encodes semantic information in a compact form into 3D Gaussian Splatting, leveraging the capabilities of large language models (LLMs). We further introduce a novel semantic loss designed to optimize hierarchical semantic information through both inter-level and cross-level optimization. Furthermore, we enhance the whole SLAM system, resulting in improved tracking and mapping performance. Our Hi-SLAM outperforms existing dense SLAM methods in both mapping and tracking accuracy, while achieving a 2x operation speed-up. Additionally, it exhibits competitive performance in rendering semantic segmentation in small synthetic scenes, with significantly reduced storage and training time requirements. Rendering FPS impressively reaches 2,000 with semantic information and 3,000 without it. Most notably, it showcases the capability of handling the complex real-world scene with more than 500 semantic classes, highlighting its valuable scaling-up capability.

Object categories are typically organized into a multi-granularity taxonomic hierarchy. When classifying categories at different hierarchy levels, traditional uni-modal approaches focus primarily on image features, revealing limitations in complex scenarios. Recent studies integrating Vision-Language Models (VLMs) with class hierarchies have shown promise, yet they fall short of fully exploiting the hierarchical relationships. These efforts are constrained by their inability to perform effectively across varied granularity of categories. To tackle this issue, we propose a novel framework (HGCLIP) that effectively combines CLIP with a deeper exploitation of the Hierarchical class structure via Graph representation learning. We explore constructing the class hierarchy into a graph, with its nodes representing the textual or image features of each category. After passing through a graph encoder, the textual features incorporate hierarchical structure information, while the image features emphasize class-aware features derived from prototypes through the attention mechanism. Our approach demonstrates significant improvements on 11 diverse visual recognition benchmarks. Our codes are fully available at https://github.com/richard-peng-xia/HGCLIP.

Literature review requires researchers to synthesize a large amount of information and is increasingly challenging as the scientific literature expands. In this work, we investigate the potential of LLMs for producing hierarchical organizations of scientific studies to assist researchers with literature review. We define hierarchical organizations as tree structures where nodes refer to topical categories and every node is linked to the studies assigned to that category. Our naive LLM-based pipeline for hierarchy generation from a set of studies produces promising yet imperfect hierarchies, motivating us to collect CHIME, an expert-curated dataset for this task focused on biomedicine. Given the challenging and time-consuming nature of building hierarchies from scratch, we use a human-in-the-loop process in which experts correct errors (both links between categories and study assignment) in LLM-generated hierarchies. CHIME contains 2,174 LLM-generated hierarchies covering 472 topics, and expert-corrected hierarchies for a subset of 100 topics. Expert corrections allow us to quantify LLM performance, and we find that while they are quite good at generating and organizing categories, their assignment of studies to categories could be improved. We attempt to train a corrector model with human feedback which improves study assignment by 12.6 F1 points. We release our dataset and models to encourage research on developing better assistive tools for literature review.

Markov categories are a recent categorical approach to the mathematical foundations of probability and statistics. Here, this approach is advanced by stating and proving equivalent conditions for second-order stochastic dominance, a widely used way of comparing probability distributions by their spread. Furthermore, we lay foundation for the theory of comparing statistical experiments within Markov categories by stating and proving the classical Blackwell-Sherman-Stein Theorem. Our version not only offers new insight into the proof, but its abstract nature also makes the result more general, automatically specializing to the standard Blackwell-Sherman-Stein Theorem in measure-theoretic probability as well as a Bayesian version that involves prior-dependent garbling. Along the way, we define and characterize representable Markov categories, within which one can talk about Markov kernels to or from spaces of distributions. We do so by exploring the relation between Markov categories and Kleisli categories of probability monads.

In order to avoid well-know paradoxes associated with self-referential definitions, higher-order dependent type theories stratify the theory using a countably infinite hierarchy of universes (also known as sorts), Type_0 : Type_1 : cdots . Such type systems are called cumulative if for any type A we have that A : Type_{i} implies A : Type_{i+1}. The predicative calculus of inductive constructions (pCIC) which forms the basis of the Coq proof assistant, is one such system. In this paper we present and establish the soundness of the predicative calculus of cumulative inductive constructions (pCuIC) which extends the cumulativity relation to inductive types.

Audio-Visual Emotion Recognition (AVER) has garnered increasing attention in recent years for its critical role in creating emotion-ware intelligent machines. Previous efforts in this area are dominated by the supervised learning paradigm. Despite significant progress, supervised learning is meeting its bottleneck due to the longstanding data scarcity issue in AVER. Motivated by recent advances in self-supervised learning, we propose Hierarchical Contrastive Masked Autoencoder (HiCMAE), a novel self-supervised framework that leverages large-scale self-supervised pre-training on vast unlabeled audio-visual data to promote the advancement of AVER. Following prior arts in self-supervised audio-visual representation learning, HiCMAE adopts two primary forms of self-supervision for pre-training, namely masked data modeling and contrastive learning. Unlike them which focus exclusively on top-layer representations while neglecting explicit guidance of intermediate layers, HiCMAE develops a three-pronged strategy to foster hierarchical audio-visual feature learning and improve the overall quality of learned representations. To verify the effectiveness of HiCMAE, we conduct extensive experiments on 9 datasets covering both categorical and dimensional AVER tasks. Experimental results show that our method significantly outperforms state-of-the-art supervised and self-supervised audio-visual methods, which indicates that HiCMAE is a powerful audio-visual emotion representation learner. Codes and models will be publicly available at https://github.com/sunlicai/HiCMAE.

High-dimensional decision-making tasks, such as business partner selection, involve evaluating large candidate pools with heterogeneous numerical, categorical, and textual features. While large language models (LLMs) offer strong in-context reasoning capabilities, single-agent or debate-style systems often struggle with scalability and consistency in such settings. We propose PartnerMAS, a hierarchical multi-agent framework that decomposes evaluation into three layers: a Planner Agent that designs strategies, Specialized Agents that perform role-specific assessments, and a Supervisor Agent that integrates their outputs. To support systematic evaluation, we also introduce a curated benchmark dataset of venture capital co-investments, featuring diverse firm attributes and ground-truth syndicates. Across 140 cases, PartnerMAS consistently outperforms single-agent and debate-based multi-agent baselines, achieving up to 10--15\% higher match rates. Analysis of agent reasoning shows that planners are most responsive to domain-informed prompts, specialists produce complementary feature coverage, and supervisors play an important role in aggregation. Our findings demonstrate that structured collaboration among LLM agents can generate more robust outcomes than scaling individual models, highlighting PartnerMAS as a promising framework for high-dimensional decision-making in data-rich domains.

Procedures are inherently hierarchical. To "make videos", one may need to "purchase a camera", which in turn may require one to "set a budget". While such hierarchical knowledge is critical for reasoning about complex procedures, most existing work has treated procedures as shallow structures without modeling the parent-child relation. In this work, we attempt to construct an open-domain hierarchical knowledge-base (KB) of procedures based on wikiHow, a website containing more than 110k instructional articles, each documenting the steps to carry out a complex procedure. To this end, we develop a simple and efficient method that links steps (e.g., "purchase a camera") in an article to other articles with similar goals (e.g., "how to choose a camera"), recursively constructing the KB. Our method significantly outperforms several strong baselines according to automatic evaluation, human judgment, and application to downstream tasks such as instructional video retrieval. A demo with partial data can be found at https://wikihow-hierarchy.github.io. The code and the data are at https://github.com/shuyanzhou/wikihow_hierarchy.

With infinitely many high-quality data points, infinite computational power, an infinitely large foundation model with a perfect training algorithm and guaranteed zero generalization error on the pretext task, can the model be used for everything? This question cannot be answered by the existing theory of representation, optimization or generalization, because the issues they mainly investigate are assumed to be nonexistent here. In this paper, we show that category theory provides powerful machinery to answer this question. We have proved three results. The first one limits the power of prompt-based learning, saying that the model can solve a downstream task with prompts if and only if the task is representable. The second one says fine tuning does not have this limit, as a foundation model with the minimum required power (up to symmetry) can theoretically solve downstream tasks for the category defined by pretext task, with fine tuning and enough resources. Our final result can be seen as a new type of generalization theorem, showing that the foundation model can generate unseen objects from the target category (e.g., images) using the structural information from the source category (e.g., texts). Along the way, we provide a categorical framework for supervised and self-supervised learning, which might be of independent interest.

We give a conceptual treatment of the notion of joints, marginals, and independence in the setting of categorical probability. This is achieved by endowing the usual probability monads (like the Giry monad) with a monoidal and an opmonoidal structure, mutually compatible (i.e. a bimonoidal structure). If the underlying monoidal category is cartesian monoidal, a bimonoidal structure is given uniquely by a commutative strength. However, if the underlying monoidal category is not cartesian monoidal, a strength is not enough to guarantee all the desired properties of joints and marginals. A bimonoidal structure is then the correct requirement for the more general case. We explain the theory and the operational interpretation, with the help of the graphical calculus for monoidal categories. We give a definition of stochastic independence based on the bimonoidal structure, compatible with the intuition and with other approaches in the literature for cartesian monoidal categories. We then show as an example that the Kantorovich monad on the category of complete metric spaces is a bimonoidal monad for a non-cartesian monoidal structure.

We present a novel application of category theory for deep learning. We show how category theory can be used to understand and work with the linear layer functions of group equivariant neural networks whose layers are some tensor power space of R^{n} for the groups S_n, O(n), Sp(n), and SO(n). By using category theoretic constructions, we build a richer structure that is not seen in the original formulation of these neural networks, leading to new insights. In particular, we outline the development of an algorithm for quickly computing the result of a vector that is passed through an equivariant, linear layer for each group in question. The success of our approach suggests that category theory could be beneficial for other areas of deep learning.

Taxonomy is a hierarchically structured knowledge graph that plays a crucial role in machine intelligence. The taxonomy expansion task aims to find a position for a new term in an existing taxonomy to capture the emerging knowledge in the world and keep the taxonomy dynamically updated. Previous taxonomy expansion solutions neglect valuable information brought by the hierarchical structure and evaluate the correctness of merely an added edge, which downgrade the problem to node-pair scoring or mini-path classification. In this paper, we propose the Hierarchy Expansion Framework (HEF), which fully exploits the hierarchical structure's properties to maximize the coherence of expanded taxonomy. HEF makes use of taxonomy's hierarchical structure in multiple aspects: i) HEF utilizes subtrees containing most relevant nodes as self-supervision data for a complete comparison of parental and sibling relations; ii) HEF adopts a coherence modeling module to evaluate the coherence of a taxonomy's subtree by integrating hypernymy relation detection and several tree-exclusive features; iii) HEF introduces the Fitting Score for position selection, which explicitly evaluates both path and level selections and takes full advantage of parental relations to interchange information for disambiguation and self-correction. Extensive experiments show that by better exploiting the hierarchical structure and optimizing taxonomy's coherence, HEF vastly surpasses the prior state-of-the-art on three benchmark datasets by an average improvement of 46.7% in accuracy and 32.3% in mean reciprocal rank.

Properties such as composability and automatic differentiation made artificial neural networks a pervasive tool in applications. Tackling more challenging problems caused neural networks to progressively become more complex and thus difficult to define from a mathematical perspective. We present a general definition of linear layer arising from a categorical framework based on the notions of integration theory and parametric spans. This definition generalizes and encompasses classical layers (e.g., dense, convolutional), while guaranteeing existence and computability of the layer's derivatives for backpropagation.

We develop Markov categories as a framework for synthetic probability and statistics, following work of Golubtsov as well as Cho and Jacobs. This means that we treat the following concepts in purely abstract categorical terms: conditioning and disintegration; various versions of conditional independence and its standard properties; conditional products; almost surely; sufficient statistics; versions of theorems on sufficient statistics due to Fisher--Neyman, Basu, and Bahadur. Besides the conceptual clarity offered by our categorical setup, its main advantage is that it provides a uniform treatment of various types of probability theory, including discrete probability theory, measure-theoretic probability with general measurable spaces, Gaussian probability, stochastic processes of either of these kinds, and many others.

Generalized Category Discovery (GCD) is an intriguing open-world problem that has garnered increasing attention. Given a dataset that includes both labelled and unlabelled images, GCD aims to categorize all images in the unlabelled subset, regardless of whether they belong to known or unknown classes. In GCD, the common practice typically involves applying a spherical projection operator at the end of the self-supervised pretrained backbone, operating within Euclidean or spherical space. However, both of these spaces have been shown to be suboptimal for encoding samples that possesses hierarchical structures. In contrast, hyperbolic space exhibits exponential volume growth relative to radius, making it inherently strong at capturing the hierarchical structure of samples from both seen and unseen categories. Therefore, we propose to tackle the category discovery challenge in the hyperbolic space. We introduce HypCD, a simple Hyperbolic framework for learning hierarchy-aware representations and classifiers for generalized Category Discovery. HypCD first transforms the Euclidean embedding space of the backbone network into hyperbolic space, facilitating subsequent representation and classification learning by considering both hyperbolic distance and the angle between samples. This approach is particularly helpful for knowledge transfer from known to unknown categories in GCD. We thoroughly evaluate HypCD on public GCD benchmarks, by applying it to various baseline and state-of-the-art methods, consistently achieving significant improvements.

Scientific knowledge is growing rapidly, making it challenging to track progress and high-level conceptual links across broad disciplines. While existing tools like citation networks and search engines make it easy to access a few related papers, they fundamentally lack the flexible abstraction needed to represent the density of activity in various scientific subfields. We motivate SCIENCE HIERARCHOGRAPHY, the goal of organizing scientific literature into a high-quality hierarchical structure that allows for the categorization of scientific work across varying levels of abstraction, from very broad fields to very specific studies. Such a representation can provide insights into which fields are well-explored and which are under-explored. To achieve the goals of SCIENCE HIERARCHOGRAPHY, we develop a range of algorithms. Our primary approach combines fast embedding-based clustering with LLM-based prompting to balance the computational efficiency of embedding methods with the semantic precision offered by LLM prompting. We demonstrate that this approach offers the best trade-off between quality and speed compared to methods that heavily rely on LLM prompting, such as iterative tree construction with LLMs. To better reflect the interdisciplinary and multifaceted nature of research papers, our hierarchy captures multiple dimensions of categorization beyond simple topic labels. We evaluate the utility of our framework by assessing how effectively an LLM-based agent can locate target papers using the hierarchy. Results show that this structured approach enhances interpretability, supports trend discovery, and offers an alternative pathway for exploring scientific literature beyond traditional search methods. Code, data and demo: https://github.com/JHU-CLSP/science-hierarchography{https://github.com/JHU-CLSP/science-hierarchography}

Recent advances in Deep Reinforcement Learning (DRL) have largely focused on improving the performance of agents with the aim of replacing humans in known and well-defined environments. The use of these techniques as a game design tool for video game production, where the aim is instead to create Non-Player Character (NPC) behaviors, has received relatively little attention until recently. Turn-based strategy games like Roguelikes, for example, present unique challenges to DRL. In particular, the categorical nature of their complex game state, composed of many entities with different attributes, requires agents able to learn how to compare and prioritize these entities. Moreover, this complexity often leads to agents that overfit to states seen during training and that are unable to generalize in the face of design changes made during development. In this paper we propose two network architectures which, when combined with a procedural loot generation system, are able to better handle complex categorical state spaces and to mitigate the need for retraining forced by design decisions. The first is based on a dense embedding of the categorical input space that abstracts the discrete observation model and renders trained agents more able to generalize. The second proposed architecture is more general and is based on a Transformer network able to reason relationally about input and input attributes. Our experimental evaluation demonstrates that new agents have better adaptation capacity with respect to a baseline architecture, making this framework more robust to dynamic gameplay changes during development. Based on the results shown in this paper, we believe that these solutions represent a step forward towards making DRL more accessible to the gaming industry.

We enhance the calculus of string diagrams for monoidal categories with hierarchical features in order to capture closed monoidal (and cartesian closed) structure. Using this new syntax we formulate an automatic differentiation algorithm for (applied) simply typed lambda calculus in the style of [Pearlmutter and Siskind 2008] and we prove for the first time its soundness. To give an efficient yet principled implementation of the AD algorithm we define a sound and complete representation of hierarchical string diagrams as a class of hierarchical hypergraphs we call hypernets.

From the Bayesian perspective, the category of conditional probabilities (a variant of the Kleisli category of the Giry monad, whose objects are measurable spaces and arrows are Markov kernels) gives a nice framework for conceptualization and analysis of many aspects of machine learning. Using categorical methods, we construct models for parametric and nonparametric Bayesian reasoning on function spaces, thus providing a basis for the supervised learning problem. In particular, stochastic processes are arrows to these function spaces which serve as prior probabilities. The resulting inference maps can often be analytically constructed in this symmetric monoidal weakly closed category. We also show how to view general stochastic processes using functor categories and demonstrate the Kalman filter as an archetype for the hidden Markov model.

Enhancing the intelligibility and interpretability of machine learning is a crucial task in responding to the demand for Explicability as an AI principle, and in promoting the better social implementation of AI. The aim of our research is to contribute to this improvement by reformulating machine learning models through the lens of category theory, thereby developing a semantic framework for structuring and understanding AI systems. Our categorical modeling in this paper clarifies and formalizes the structural interplay between residuals and parameters in supervised learning. The present paper focuses on the multiple linear regression model, which represents the most basic form of supervised learning. By defining two concrete categories corresponding to parameters and data, along with an adjoint pair of functors between them, we introduce our categorical formulation of supervised learning. We show that the essential structure of this framework is captured by what we call the Gauss-Markov Adjunction. Within this setting, the dual flow of information can be explicitly described as a correspondence between variations in parameters and residuals. The ordinary least squares estimator for the parameters and the minimum residual are related via the preservation of limits by the right adjoint functor. Furthermore, we position this formulation as an instance of extended denotational semantics for supervised learning, and propose applying a semantic perspective developed in theoretical computer science as a formal foundation for Explicability in AI.

We consider three monads on Top, the category of topological spaces, which formalize topological aspects of probability and possibility in categorical terms. The first one is the Hoare hyperspace monad H, which assigns to every space its space of closed subsets equipped with the lower Vietoris topology. The second is the monad V of continuous valuations, also known as the extended probabilistic powerdomain. We construct both monads in a unified way in terms of double dualization. This reveals a close analogy between them, and allows us to prove that the operation of taking the support of a continuous valuation is a morphism of monads from V to H. In particular, this implies that every H-algebra (topological complete semilattice) is also a V-algebra. Third, we show that V can be restricted to a submonad of tau-smooth probability measures on Top. By composing these two morphisms of monads, we obtain that taking the support of a tau-smooth probability measure is also a morphism of monads.

Hierarchical classification is a crucial task in many applications, where objects are organized into multiple levels of categories. However, conventional classification approaches often neglect inherent inter-class relationships at different hierarchy levels, thus missing important supervisory signals. Thus, we propose two novel hierarchical contrastive learning (HMLC) methods. The first, leverages a Gaussian Mixture Model (G-HMLC) and the second uses an attention mechanism to capture hierarchy-specific features (A-HMLC), imitating human processing. Our approach explicitly models inter-class relationships and imbalanced class distribution at higher hierarchy levels, enabling fine-grained clustering across all hierarchy levels. On the competitive CIFAR100 and ModelNet40 datasets, our method achieves state-of-the-art performance in linear evaluation, outperforming existing hierarchical contrastive learning methods by 2 percentage points in terms of accuracy. The effectiveness of our approach is backed by both quantitative and qualitative results, highlighting its potential for applications in computer vision and beyond.

People can categorize the same entity at multiple taxonomic levels, such as basic (bear), superordinate (animal), and subordinate (grizzly bear). While prior research has focused on basic-level categories, this study is the first attempt to examine the organization of categories by analyzing exemplars produced at the subordinate level. We present a new Italian psycholinguistic dataset of human-generated exemplars for 187 concrete words. We then use these data to evaluate whether textual and vision LLMs produce meaningful exemplars that align with human category organization across three key tasks: exemplar generation, category induction, and typicality judgment. Our findings show a low alignment between humans and LLMs, consistent with previous studies. However, their performance varies notably across different semantic domains. Ultimately, this study highlights both the promises and the constraints of using AI-generated exemplars to support psychological and linguistic research.

We provide a construction for categorical representation learning and introduce the foundations of "categorifier". The central theme in representation learning is the idea of everything to vector. Every object in a dataset S can be represented as a vector in R^n by an encoding map E: Obj(S)toR^n. More importantly, every morphism can be represented as a matrix E: Hom(S)toR^{n}_{n}. The encoding map E is generally modeled by a deep neural network. The goal of representation learning is to design appropriate tasks on the dataset to train the encoding map (assuming that an encoding is optimal if it universally optimizes the performance on various tasks). However, the latter is still a set-theoretic approach. The goal of the current article is to promote the representation learning to a new level via a category-theoretic approach. As a proof of concept, we provide an example of a text translator equipped with our technology, showing that our categorical learning model outperforms the current deep learning models by 17 times. The content of the current article is part of the recent US patent proposal (patent application number: 63110906).

Hierarchical organization is fundamental to biological systems and human societies, yet artificial intelligence systems often rely on monolithic architectures that limit adaptability and scalability. Current hierarchical reinforcement learning (HRL) approaches typically restrict hierarchies to two levels or require centralized training, which limits their practical applicability. We introduce TAME Agent Framework (TAG), a framework for constructing fully decentralized hierarchical multi-agent systems.TAG enables hierarchies of arbitrary depth through a novel LevelEnv concept, which abstracts each hierarchy level as the environment for the agents above it. This approach standardizes information flow between levels while preserving loose coupling, allowing for seamless integration of diverse agent types. We demonstrate the effectiveness of TAG by implementing hierarchical architectures that combine different RL agents across multiple levels, achieving improved performance over classical multi-agent RL baselines on standard benchmarks. Our results show that decentralized hierarchical organization enhances both learning speed and final performance, positioning TAG as a promising direction for scalable multi-agent systems.

We apply category theory to extract multimodal document structure which leads us to develop information theoretic measures, content summarization and extension, and self-supervised improvement of large pretrained models. We first develop a mathematical representation of a document as a category of question-answer pairs. Second, we develop an orthogonalization procedure to divide the information contained in one or more documents into non-overlapping pieces. The structures extracted in the first and second steps lead us to develop methods to measure and enumerate the information contained in a document. We also build on those steps to develop new summarization techniques, as well as to develop a solution to a new problem viz. exegesis resulting in an extension of the original document. Our question-answer pair methodology enables a novel rate distortion analysis of summarization techniques. We implement our techniques using large pretrained models, and we propose a multimodal extension of our overall mathematical framework. Finally, we develop a novel self-supervised method using RLVR to improve large pretrained models using consistency constraints such as composability and closure under certain operations that stem naturally from our category theoretic framework.

Modelling compositionality has been a longstanding area of research in the field of vector space semantics. The categorical approach to compositionality maps grammar onto vector spaces in a principled way, but comes under fire for requiring the formation of very high-dimensional matrices and tensors, and therefore being computationally infeasible. In this paper I show how a linear simplification of recursive neural tensor network models can be mapped directly onto the categorical approach, giving a way of computing the required matrices and tensors. This mapping suggests a number of lines of research for both categorical compositional vector space models of meaning and for recursive neural network models of compositionality.

Markov categories are a recent category-theoretic approach to the foundations of probability and statistics. Here we develop this approach further by treating infinite products and the Kolmogorov extension theorem. This is relevant for all aspects of probability theory in which infinitely many random variables appear at a time. These infinite tensor products bigotimes_{i in J} X_i come in two versions: a weaker but more general one for families of objects (X_i)_{i in J} in semicartesian symmetric monoidal categories, and a stronger but more specific one for families of objects in Markov categories. As a first application, we state and prove versions of the zero-one laws of Kolmogorov and Hewitt-Savage for Markov categories. This gives general versions of these results which can be instantiated not only in measure-theoretic probability, where they specialize to the standard ones in the setting of standard Borel spaces, but also in other contexts.

Markov categories are a novel framework to describe and treat problems in probability and information theory. In this work we combine the categorical formalism with the traditional quantitative notions of entropy, mutual information, and data processing inequalities. We show that several quantitative aspects of information theory can be captured by an enriched version of Markov categories, where the spaces of morphisms are equipped with a divergence or even a metric. As it is customary in information theory, mutual information can be defined as a measure of how far a joint source is from displaying independence of its components. More strikingly, Markov categories give a notion of determinism for sources and channels, and we can define entropy exactly by measuring how far a source or channel is from being deterministic. This recovers Shannon and R\'enyi entropies, as well as the Gini-Simpson index used in ecology to quantify diversity, and it can be used to give a conceptual definition of generalized entropy.

Knowledge graphs are useful tools to organize, recommend and sort data. Hierarchies in knowledge graphs provide significant benefit in improving understanding and compartmentalization of the data within a knowledge graph. This work leverages large language models to generate and augment hierarchies in an existing knowledge graph. For small (<100,000 node) domain-specific KGs, we find that a combination of few-shot prompting with one-shot generation works well, while larger KG may require cyclical generation. We present techniques for augmenting hierarchies, which led to coverage increase by 98% for intents and 99% for colors in our knowledge graph.

The reverse derivative is a fundamental operation in machine learning and automatic differentiation. This paper gives a direct axiomatization of a category with a reverse derivative operation, in a similar style to that given by Cartesian differential categories for a forward derivative. Intriguingly, a category with a reverse derivative also has a forward derivative, but the converse is not true. In fact, we show explicitly what a forward derivative is missing: a reverse derivative is equivalent to a forward derivative with a dagger structure on its subcategory of linear maps. Furthermore, we show that these linear maps form an additively enriched category with dagger biproducts.

We propose a categorical semantics of gradient-based machine learning algorithms in terms of lenses, parametrised maps, and reverse derivative categories. This foundation provides a powerful explanatory and unifying framework: it encompasses a variety of gradient descent algorithms such as ADAM, AdaGrad, and Nesterov momentum, as well as a variety of loss functions such as as MSE and Softmax cross-entropy, shedding new light on their similarities and differences. Our approach to gradient-based learning has examples generalising beyond the familiar continuous domains (modelled in categories of smooth maps) and can be realized in the discrete setting of boolean circuits. Finally, we demonstrate the practical significance of our framework with an implementation in Python.

We introduce Reverse Derivative Ascent: a categorical analogue of gradient based methods for machine learning. Our algorithm is defined at the level of so-called reverse differential categories. It can be used to learn the parameters of models which are expressed as morphisms of such categories. Our motivating example is boolean circuits: we show how our algorithm can be applied to such circuits by using the theory of reverse differential categories. Note our methodology allows us to learn the parameters of boolean circuits directly, in contrast to existing binarised neural network approaches. Moreover, we demonstrate its empirical value by giving experimental results on benchmark machine learning datasets.

Visuomotor policy learning has witnessed substantial progress in robotic manipulation, with recent approaches predominantly relying on generative models to model the action distribution. However, these methods often overlook the critical coupling between visual perception and action prediction. In this work, we introduce Triply-Hierarchical Diffusion Policy~(H^{\mathbf{3}DP}), a novel visuomotor learning framework that explicitly incorporates hierarchical structures to strengthen the integration between visual features and action generation. H^{3}DP contains 3 levels of hierarchy: (1) depth-aware input layering that organizes RGB-D observations based on depth information; (2) multi-scale visual representations that encode semantic features at varying levels of granularity; and (3) a hierarchically conditioned diffusion process that aligns the generation of coarse-to-fine actions with corresponding visual features. Extensive experiments demonstrate that H^{3}DP yields a +27.5% average relative improvement over baselines across 44 simulation tasks and achieves superior performance in 4 challenging bimanual real-world manipulation tasks. Project Page: https://lyy-iiis.github.io/h3dp/.

Modern deep learning-based recommendation systems exploit hundreds to thousands of different categorical features, each with millions of different categories ranging from clicks to posts. To respect the natural diversity within the categorical data, embeddings map each category to a unique dense representation within an embedded space. Since each categorical feature could take on as many as tens of millions of different possible categories, the embedding tables form the primary memory bottleneck during both training and inference. We propose a novel approach for reducing the embedding size in an end-to-end fashion by exploiting complementary partitions of the category set to produce a unique embedding vector for each category without explicit definition. By storing multiple smaller embedding tables based on each complementary partition and combining embeddings from each table, we define a unique embedding for each category at smaller memory cost. This approach may be interpreted as using a specific fixed codebook to ensure uniqueness of each category's representation. Our experimental results demonstrate the effectiveness of our approach over the hashing trick for reducing the size of the embedding tables in terms of model loss and accuracy, while retaining a similar reduction in the number of parameters.

The U.S. Securities and Exchange Commission (SEC) requires that public companies file financial reports tagging numbers with the machine readable inline eXtensible Business Reporting Language (iXBRL) standard. However, the highly complex and highly granular taxonomy defined by iXBRL limits label transferability across domains. In this paper, we introduce the Hierarchical Financial Key Performance Indicator (HiFi-KPI) dataset, designed to facilitate numerical KPI extraction at specified levels of granularity from unstructured financial text. Our approach organizes a 218,126-label hierarchy using a taxonomy based grouping method, investigating which taxonomy layer provides the most meaningful structure. HiFi-KPI comprises ~1.8M paragraphs and ~5M entities, each linked to a label in the iXBRL-specific calculation and presentation taxonomies. We provide baselines using encoder-based approaches and structured extraction using Large Language Models (LLMs). To simplify LLM inference and evaluation, we additionally release HiFi-KPI Lite, a manually curated subset with four expert-mapped labels. We publicly release all artifacts

This work addresses two important questions pertinent to Relation Extraction (RE). First, what are all possible relations that could exist between any two given entity types? Second, how do we define an unambiguous taxonomical (is-a) hierarchy among the identified relations? To address the first question, we use three resources Wikipedia Infobox, Wikidata, and DBpedia. This study focuses on relations between person, organization and location entity types. We exploit Wikidata and DBpedia in a data-driven manner, and Wikipedia Infobox templates manually to generate lists of relations. Further, to address the second question, we canonicalize, filter, and combine the identified relations from the three resources to construct a taxonomical hierarchy. This hierarchy contains 623 canonical relations with highest contribution from Wikipedia Infobox followed by DBpedia and Wikidata. The generated relation list subsumes an average of 85% of relations from RE datasets when entity types are restricted.

There is a recently discovered and intriguing phenomenon called Neural Collapse: at the terminal phase of training a deep neural network for classification, the within-class penultimate feature means and the associated classifier vectors of all flat classes collapse to the vertices of a simplex Equiangular Tight Frame (ETF). Recent work has tried to exploit this phenomenon by fixing the related classifier weights to a pre-computed ETF to induce neural collapse and maximize the separation of the learned features when training with imbalanced data. In this work, we propose to fix the linear classifier of a deep neural network to a Hierarchy-Aware Frame (HAFrame), instead of an ETF, and use a cosine similarity-based auxiliary loss to learn hierarchy-aware penultimate features that collapse to the HAFrame. We demonstrate that our approach reduces the mistake severity of the model's predictions while maintaining its top-1 accuracy on several datasets of varying scales with hierarchies of heights ranging from 3 to 12. Code: https://github.com/ltong1130ztr/HAFrame

We introduce the category of information structures, whose objects are suitable diagrams of measurable sets that encode the possible outputs of a given family of observables and their mutual relationships of refinement; they serve as mathematical models of contextuality in classical and quantum settings. Each information structure can be regarded as a ringed site with trivial topology; the structure ring is generated by the observables themselves and its multiplication corresponds to joint measurement. We extend Baudot and Bennequin's definition of information cohomology to this setting, as a derived functor in the category of modules over the structure ring, and show explicitly that the bar construction gives a projective resolution in that category, recovering in this way the cochain complexes previously considered in the literature. Finally, we study the particular case of a one-parameter family of coefficients made of functions of probability distributions. The only 1-cocycles are Shannon entropy or Tsallis alpha-entropy, depending on the value of the parameter.

Hierarchical Text Classification (HTC) aims to assign texts to structured label hierarchies; however, it faces challenges due to data scarcity and model complexity. This study explores the feasibility of using black box Large Language Models (LLMs) accessed via APIs for HTC, as an alternative to traditional machine learning methods that require extensive labeled data and computational resources. We evaluate three prompting strategies -- Direct Leaf Label Prediction (DL), Direct Hierarchical Label Prediction (DH), and Top-down Multi-step Hierarchical Label Prediction (TMH) -- in both zero-shot and few-shot settings, comparing the accuracy and cost-effectiveness of these strategies. Experiments on two datasets show that a few-shot setting consistently improves classification accuracy compared to a zero-shot setting. While a traditional machine learning model achieves high accuracy on a dataset with a shallow hierarchy, LLMs, especially DH strategy, tend to outperform the machine learning model on a dataset with a deeper hierarchy. API costs increase significantly due to the higher input tokens required for deeper label hierarchies on DH strategy. These results emphasize the trade-off between accuracy improvement and the computational cost of prompt strategy. These findings highlight the potential of black box LLMs for HTC while underscoring the need to carefully select a prompt strategy to balance performance and cost.

Complex hierarchical structures composed of simple nanoscale building blocks form the basis of most biological materials. Here we demonstrate how analogies between seemingly different fields enable the understanding of general principles by which functional properties in hierarchical systems emerge, similar to an analogy learning process. Specifically, natural hierarchical materials like spider silk exhibit properties comparable to classical music in terms of their hierarchical structure and function. As a comparative tool here we apply hierarchical ontology logs (olog) that follow a rigorous mathematical formulation based on category theory to provide an insightful system representation by expressing knowledge in a conceptual map. We explain the process of analogy creation, draw connections at several levels of hierarchy and identify similar patterns that govern the structure of the hierarchical systems silk and music and discuss the impact of the derived analogy for nanotechnology.

This paper discusses a simple and explicit toy-model example of the categorical Hopfield equations introduced in previous work of Manin and the author. These describe dynamical assignments of resources to networks, where resources are objects in unital symmetric monoidal categories and assignments are realized by summing functors. The special case discussed here is based on computational resources (computational models of neurons) as objects in a category of DNNs, with a simple choice of the endofunctors defining the Hopfield equations that reproduce the usual updating of the weights in DNNs by gradient descent.

In this work we take a Category Theoretic perspective on the relationship between probabilistic modeling and function approximation. We begin by defining two extensions of function composition to stochastic process subordination: one based on the co-Kleisli category under the comonad (Omega x -) and one based on the parameterization of a category with a Lawvere theory. We show how these extensions relate to the category Stoch and other Markov Categories. Next, we apply the Para construction to extend stochastic processes to parameterized statistical models and we define a way to compose the likelihood functions of these models. We conclude with a demonstration of how the Maximum Likelihood Estimation procedure defines an identity-on-objects functor from the category of statistical models to the category of Learners. Code to accompany this paper can be found at https://github.com/dshieble/Categorical_Stochastic_Processes_and_Likelihood

Categorical encoders transform categorical features into numerical representations that are indispensable for a wide range of machine learning models. Existing encoder benchmark studies lack generalizability because of their limited choice of (1) encoders, (2) experimental factors, and (3) datasets. Additionally, inconsistencies arise from the adoption of varying aggregation strategies. This paper is the most comprehensive benchmark of categorical encoders to date, including an extensive evaluation of 32 configurations of encoders from diverse families, with 36 combinations of experimental factors, and on 50 datasets. The study shows the profound influence of dataset selection, experimental factors, and aggregation strategies on the benchmark's conclusions -- aspects disregarded in previous encoder benchmarks.

In an unpublished preprint batanin, Batanin conjectures that it is possible to take `slices' of a globular operad, thereby isolating the algebraic structure in each dimension. It was further hypothesised that the slices of a globular operad for some theory of higher category contain essential information about those higher categories, namely whether or not they are equivalent to the fully weak variety. In this paper, we use the theory of presentations for globular operads developed in Me to provide a concrete definition of slices, and calculate the slices for several key theories of n-category.

Hierarchical classification offers an approach to incorporate the concept of mistake severity by leveraging a structured, labeled hierarchy. However, decoding in such settings frequently relies on heuristic decision rules, which may not align with task-specific evaluation metrics. In this work, we propose a framework for the optimal decoding of an output probability distribution with respect to a target metric. We derive optimal decision rules for increasingly complex prediction settings, providing universal algorithms when candidates are limited to the set of nodes. In the most general case of predicting a subset of nodes, we focus on rules dedicated to the hierarchical hF_{beta} scores, tailored to hierarchical settings. To demonstrate the practical utility of our approach, we conduct extensive empirical evaluations, showcasing the superiority of our proposed optimal strategies, particularly in underdetermined scenarios. These results highlight the potential of our methods to enhance the performance and reliability of hierarchical classifiers in real-world applications. The code is available at https://github.com/RomanPlaud/hierarchical_decision_rules

Over the past two decades machine learning has permeated almost every realm of technology. At the same time, many researchers have begun using category theory as a unifying language, facilitating communication between different scientific disciplines. It is therefore unsurprising that there is a burgeoning interest in applying category theory to machine learning. We aim to document the motivations, goals and common themes across these applications. We touch on gradient-based learning, probability, and equivariant learning.

Emotions have played an important part in many sectors, including psychology, medicine, mental health, computer science, and so on, and categorizing them has proven extremely useful in separating one emotion from another. Emotions can be classified using the following two methods: (1) The supervised method's efficiency is strongly dependent on the size and domain of the data collected. A categorization established using relevant data from one domain may not work well in another. (2) An unsupervised method that uses either domain expertise or a knowledge base of emotion types already exists. Though this second approach provides a suitable and generic categorization of emotions and is cost-effective, the literature doesn't possess a publicly available knowledge base that can be directly applied to any emotion categorization-related task. This pushes us to create a knowledge base that can be used for emotion classification across domains, and ontology is often used for this purpose. In this study, we provide TONE, an emotion-based ontology that effectively creates an emotional hierarchy based on Dr. Gerrod Parrot's group of emotions. In addition to ontology development, we introduce a semi-automated vocabulary construction process to generate a detailed collection of terms for emotions at each tier of the hierarchy. We also demonstrate automated methods for establishing three sorts of dependencies in order to develop linkages between different emotions. Our human and automatic evaluation results show the ontology's quality. Furthermore, we describe three distinct use cases that demonstrate the applicability of our ontology.