Aalborg University
AI Insights
- Furthermore, the authors propose a new evaluation metric called the 'semantic shift' metric, which measures the degree to which the category labels are shifted or changed when the model is trained on a different dataset. (ML: 0.98)
- The authors evaluate the performance of the HCD model on several benchmark datasets for generalized category discovery, including the Caltech-UCSD Birds 200-2011 dataset and the CUB-200-2011 dataset. (ML: 0.96)
- The results show that the HCD model outperforms state-of-the-art methods in terms of accuracy and robustness, especially when dealing with small training sets or noisy data. (ML: 0.92)
- The paper explores the use of hyperbolic neural networks for generalized category discovery, a task that involves learning to categorize objects into categories based on their visual features. (ML: 0.92)
- The HCD model is trained using a combination of supervised and self-supervised learning, where the model learns to predict the category label of an object based on its visual features, and also learns to reconstruct the object's visual features from its category label. (ML: 0.91)
- The authors propose a new method called Hyperbolic Category Discovery (HCD) that uses a hyperbolic neural network to learn a representation of the object's visual features in a hyperbolic space. (ML: 0.87)
- The paper also discusses the potential applications of hyperbolic neural networks in other areas, such as image classification and object detection. (ML: 0.87)
- The authors also provide a theoretical analysis of the HCD model, showing that it can be viewed as a type of non-linear dimensionality reduction method that preserves the geometric structure of the object's visual features. (ML: 0.82)
- The authors provide a detailed explanation of the mathematical framework underlying the HCD model, including the use of the Lorentz Hyperboloid and the Klein model to represent points in hyperbolic space. (ML: 0.68)
- The paper also includes an appendix with additional technical details and proofs, including a proof of Lemma 1, which shows that the mapping function from the Klein model to the Lorentz Hyperboloid is given by Equation 44. (ML: 0.54)
Abstract
Hyperbolic representation learning has been widely used to extract implicit hierarchies within data, and recently it has found its way to the open-world classification task of Generalized Category Discovery (GCD). However, prior hyperbolic GCD methods only use hyperbolic geometry for representation learning and transform back to Euclidean geometry when clustering. We hypothesize this is suboptimal. Therefore, we present Hyperbolic Clustered GCD (HC-GCD), which learns embeddings in the Lorentz Hyperboloid model of hyperbolic geometry, and clusters these embeddings directly in hyperbolic space using a hyperbolic K-Means algorithm. We test our model on the Semantic Shift Benchmark datasets, and demonstrate that HC-GCD is on par with the previous state-of-the-art hyperbolic GCD method. Furthermore, we show that using hyperbolic K-Means leads to better accuracy than Euclidean K-Means. We carry out ablation studies showing that clipping the norm of the Euclidean embeddings leads to decreased accuracy in clustering unseen classes, and increased accuracy for seen classes, while the overall accuracy is dataset dependent. We also show that using hyperbolic K-Means leads to more consistent clusters when varying the label granularity.
Hyperbolic representation learning has been widely used to extract implicit hierarchies within data, and recently it has found its way to the open-world classification task of Generalized Category Discovery (GCD). However, prior hyperbolic GCD methods only use hyperbolic geometry for representation learning and transform back to Euclidean geometry when clustering. We hypothesize this is suboptimal. Therefore, we present Hyperbolic Clustered GCD (HC-GCD), which learns embeddings in the Lorentz Hyperboloid model of hyperbolic geometry, and clusters these embeddings directly in hyperbolic space using a hyperbolic K-Means algorithm. We test our model on the Semantic Shift Benchmark datasets, and demonstrate that HC-GCD is on par with the previous state-of-the-art hyperbolic GCD method. Furthermore, we show that using hyperbolic K-Means leads to better accuracy than Euclidean K-Means. We carry out ablation studies showing that clipping the norm of the Euclidean embeddings leads to decreased accuracy in clustering unseen classes, and increased accuracy for seen classes, while the overall accuracy is dataset dependent. We also show that using hyperbolic K-Means leads to more consistent clusters when varying the label granularity.
Why we are recommending this paper?
Due to your Interest in Continual Generalized Category Discovery
This paper directly addresses Generalized Category Discovery, a key interest, and explores hyperbolic representation learning – a relevant technique for hierarchical data structures. The focus on comparing different methods aligns with the user’s interest in discovering and organizing product categories.
Due to your Interest in Continual Generalized Category Discovery
This paper directly addresses Generalized Category Discovery, a key interest, and explores hyperbolic representation learning – a relevant technique for hierarchical data structures. The focus on comparing different methods aligns with the user’s interest in discovering and organizing product categories.
Dynamind Research
AI Insights
- Key Insights Four insights emerged from this work: The Grammar Paradox Neither Alone Suffices (ML: 0.98)
- Grammar Paradox: Constraints enable creativity. (ML: 0.97)
- Generative Ontology Grammar Paradox Neither Alone Suffices The Whiteheadian Connection Generative Ontology: A synthesis combining the structural precision of knowledge representation with the creative power of large language models. (ML: 0.92)
- Without grammar, there is no poem to write. (ML: 0.90)
Abstract
Traditional ontologies excel at describing domain structure but cannot generate novel artifacts. Large language models generate fluently but produce outputs that lack structural validity, hallucinating mechanisms without components, goals without end conditions. We introduce Generative Ontology, a framework that synthesizes these complementary strengths: ontology provides the grammar; the LLM provides the creativity. Generative Ontology encodes domain knowledge as executable Pydantic schemas that constrain LLM generation via DSPy signatures. A multi-agent pipeline assigns specialized roles to different ontology domains: a Mechanics Architect designs game systems, a Theme Weaver integrates narrative, a Balance Critic identifies exploits. Each agent carrying a professional "anxiety" that prevents shallow, agreeable outputs. Retrieval-augmented generation grounds novel designs in precedents from existing exemplars, while iterative validation ensures coherence between mechanisms and components. We demonstrate the framework through GameGrammar, a system for generating complete tabletop game designs. Given a thematic prompt ("bioluminescent fungi competing in a cave ecosystem"), the pipeline produces structurally complete, playable game specifications with mechanisms, components, victory conditions, and setup instructions. These outputs satisfy ontological constraints while remaining genuinely creative. The pattern generalizes beyond games. Any domain with expert vocabulary, validity constraints, and accumulated exemplars (music composition, software architecture, culinary arts) is a candidate for Generative Ontology. We argue that constraints do not limit creativity but enable it: just as grammar makes poetry possible, ontology makes structured generation possible.
Traditional ontologies excel at describing domain structure but cannot generate novel artifacts. Large language models generate fluently but produce outputs that lack structural validity, hallucinating mechanisms without components, goals without end conditions. We introduce Generative Ontology, a framework that synthesizes these complementary strengths: ontology provides the grammar; the LLM provides the creativity. Generative Ontology encodes domain knowledge as executable Pydantic schemas that constrain LLM generation via DSPy signatures. A multi-agent pipeline assigns specialized roles to different ontology domains: a Mechanics Architect designs game systems, a Theme Weaver integrates narrative, a Balance Critic identifies exploits. Each agent carrying a professional "anxiety" that prevents shallow, agreeable outputs. Retrieval-augmented generation grounds novel designs in precedents from existing exemplars, while iterative validation ensures coherence between mechanisms and components. We demonstrate the framework through GameGrammar, a system for generating complete tabletop game designs. Given a thematic prompt ("bioluminescent fungi competing in a cave ecosystem"), the pipeline produces structurally complete, playable game specifications with mechanisms, components, victory conditions, and setup instructions. These outputs satisfy ontological constraints while remaining genuinely creative. The pattern generalizes beyond games. Any domain with expert vocabulary, validity constraints, and accumulated exemplars (music composition, software architecture, culinary arts) is a candidate for Generative Ontology. We argue that constraints do not limit creativity but enable it: just as grammar makes poetry possible, ontology makes structured generation possible.
Why we are recommending this paper?
Due to your Interest in Ontology for Products
This work investigates generating novel knowledge structures, which is directly related to ontology development and the creation of taxonomies. The exploration of large language models’ limitations in structural knowledge generation is particularly pertinent to the user’s interests.
Due to your Interest in Ontology for Products
This work investigates generating novel knowledge structures, which is directly related to ontology development and the creation of taxonomies. The exploration of large language models’ limitations in structural knowledge generation is particularly pertinent to the user’s interests.
Warsaw University of Technology WUT
AI Insights
- RS(TM)2 has been validated through a tower-building task simulation, showing how ontological concepts guide development of executable specifications and inform architectural decisions. (ML: 0.93)
- The approach differs from traditional Model-Based Systems Engineering (MBSE) approaches, which require a system model without guiding how to develop it or what design decisions to make. (ML: 0.93)
- The approach enables exploration of the design decision space, such as whether tasks are executed by a single robot or distributed among multiple robots, and whether objectives are pursued jointly or independently. (ML: 0.93)
- The approach has been validated through a tower-building task simulation and enables exploration of the design decision space for robotic systems. (ML: 0.89)
- MBSE (Model-Based Systems Engineering): An approach to systems engineering that uses abstract representations of a system to analyze and design its behavior. (ML: 0.86)
- RS(TM)2 offers a systematic, explainable, and extensible pathway from high-level objectives to validated, executable specifications for robotic systems. (ML: 0.81)
- The paper presents a novel approach to software engineering for robotics called RS(TM)2 (Robotics Specification and Synthesis Language), which combines ontological concepts with executable specifications to enable designers to develop validated, multi-level formal models of robotic systems. (ML: 0.78)
- RS(TM)2 is designed to guide the designer through iterative decision-making with intermediate, executable PN-based models, enabling key architectural properties to be verified before committing to a final system model and code generation. (ML: 0.77)
- RS(TM)2 (Robotics Specification and Synthesis Language): A novel approach to software engineering for robotics that combines ontological concepts with executable specifications to enable designers to develop validated, multi-level formal models of robotic systems. (ML: 0.77)
- PN-based models: Models based on Petri nets, which are used to represent the behavior of systems in terms of transitions between states. (ML: 0.76)
Abstract
This paper addresses robotic system engineering for safety- and mission-critical applications by bridging the gap between high-level objectives and formal, executable specifications. The proposed method, Robotic System Task to Model Transformation Methodology (RSTM2) is an ontology-driven, hierarchical approach using stochastic timed Petri nets with resources, enabling Monte Carlo simulations at mission, system, and subsystem levels. A hypothetical case study demonstrates how the RSTM2 method supports architectural trades, resource allocation, and performance analysis under uncertainty. Ontological concepts further enable explainable AI-based assistants, facilitating fully autonomous specification synthesis. The methodology offers particular benefits to complex multi-robot systems, such as the NASA CADRE mission, representing decentralized, resource-aware, and adaptive autonomous systems of the future.
This paper addresses robotic system engineering for safety- and mission-critical applications by bridging the gap between high-level objectives and formal, executable specifications. The proposed method, Robotic System Task to Model Transformation Methodology (RSTM2) is an ontology-driven, hierarchical approach using stochastic timed Petri nets with resources, enabling Monte Carlo simulations at mission, system, and subsystem levels. A hypothetical case study demonstrates how the RSTM2 method supports architectural trades, resource allocation, and performance analysis under uncertainty. Ontological concepts further enable explainable AI-based assistants, facilitating fully autonomous specification synthesis. The methodology offers particular benefits to complex multi-robot systems, such as the NASA CADRE mission, representing decentralized, resource-aware, and adaptive autonomous systems of the future.
Why we are recommending this paper?
Due to your Interest in Ontology for Products
The paper’s focus on ontology-driven robotic specification synthesis aligns with the user’s interest in knowledge graphs and taxonomy of products. Bridging high-level objectives with formal specifications is a core concept within knowledge management.
Due to your Interest in Ontology for Products
The paper’s focus on ontology-driven robotic specification synthesis aligns with the user’s interest in knowledge graphs and taxonomy of products. Bridging high-level objectives with formal specifications is a core concept within knowledge management.
The Chinese University of Hong Kong, Shenzhen
AI Insights
- This is similar to how language models are pre-trained on vast amounts of text data before being fine-tuned for specific tasks. (ML: 0.96)
- Graph foundation models are pre-trained on large-scale graphs, which allows them to learn general patterns and relationships that can be applied to various downstream tasks. (ML: 0.95)
- Imagine you're trying to understand a complex network, like a social media platform or a molecule. (ML: 0.94)
- Current graph foundation models often rely on homophilic graph data, which may not generalize well to non-homophilic graphs. (ML: 0.93)
- Graph foundation models have revolutionized the field of graph neural networks by enabling pre-training on large-scale graphs and improving downstream task performance. (ML: 0.93)
- Graph foundation models have become a crucial component in the field of graph neural networks (GNNs), enabling pre-training on large-scale graphs and improving downstream task performance. (ML: 0.93)
- Graph foundation models have been applied in various domains, including social networks, knowledge graphs, and molecular graphs. (ML: 0.92)
- Graph foundation model: A pre-trained model that can be fine-tuned for various downstream tasks, such as node classification, link prediction, and graph regression. (ML: 0.91)
- The field of graph foundation models is rapidly evolving, with new techniques and architectures emerging to improve performance and adaptability. (ML: 0.87)
- The development of more powerful and scalable graph transformers will continue to drive advancements in this area. (ML: 0.83)
- The development of more powerful and scalable graph transformers will continue to drive advancements in this area. (ML: 0.83)
Abstract
This paper aims to train a graph foundation model that is able to represent any graph as a vector preserving structural and semantic information useful for downstream graph-level tasks such as graph classification and graph clustering. To learn the features of graphs from diverse domains while maintaining strong generalization ability to new domains, we propose a multi-graph-based feature alignment method, which constructs weighted graphs using the attributes of all nodes in each dataset and then generates consistent node embeddings. To enhance the consistency of the features from different datasets, we propose a density maximization mean alignment algorithm with guaranteed convergence. The original graphs and generated node embeddings are fed into a graph neural network to achieve discriminative graph representations in contrastive learning. More importantly, to enhance the information preservation from node-level representations to the graph-level representation, we construct a multi-layer reference distribution module without using any pooling operation. We also provide a theoretical generalization bound to support the effectiveness of the proposed model. The experimental results of few-shot graph classification and graph clustering show that our model outperforms strong baselines.
This paper aims to train a graph foundation model that is able to represent any graph as a vector preserving structural and semantic information useful for downstream graph-level tasks such as graph classification and graph clustering. To learn the features of graphs from diverse domains while maintaining strong generalization ability to new domains, we propose a multi-graph-based feature alignment method, which constructs weighted graphs using the attributes of all nodes in each dataset and then generates consistent node embeddings. To enhance the consistency of the features from different datasets, we propose a density maximization mean alignment algorithm with guaranteed convergence. The original graphs and generated node embeddings are fed into a graph neural network to achieve discriminative graph representations in contrastive learning. More importantly, to enhance the information preservation from node-level representations to the graph-level representation, we construct a multi-layer reference distribution module without using any pooling operation. We also provide a theoretical generalization bound to support the effectiveness of the proposed model. The experimental results of few-shot graph classification and graph clustering show that our model outperforms strong baselines.
Why we are recommending this paper?
Due to your Interest in Graphs for Products
This paper tackles the representation of graphs as vectors, a critical component for knowledge graph applications. The goal of preserving structural and semantic information is directly relevant to the user’s interests in product categorization and knowledge graphs.
Due to your Interest in Graphs for Products
This paper tackles the representation of graphs as vectors, a critical component for knowledge graph applications. The goal of preserving structural and semantic information is directly relevant to the user’s interests in product categorization and knowledge graphs.
Case Western Reserve University
AI Insights
- The model uses two critical reasoning tasks: identifying causal paths within the retrieved subgraph and generating the final grounded answer. (ML: 0.98)
- Global Coherence: The ability of a model to capture the overall structure and relationships within a dataset. (ML: 0.98)
- Spurious Noise: The presence of irrelevant or misleading information in a dataset. (ML: 0.97)
- To address local spurious noise, HugRAG designs a prompt that instructs the LLM to act as a 'causality analyst' and select the subset of evidence that forms a coherent causal chain. (ML: 0.96)
- The model is trained on a dataset of 10,000 queries with corresponding subgraphs and answers, and is evaluated using metrics such as accuracy, F1-score, and coherence score. (ML: 0.94)
- HugRAG employs a hierarchical causal knowledge graph design that captures both local and global relationships between entities. (ML: 0.94)
- RAG: Retrieval-Augmented Generation LLM: Large Language Model Causal Graph: A graph that represents the causal relationships between entities. (ML: 0.91)
- The HugRAG model is designed to address the limitations of current retrieval-augmented generation (RAG) models, particularly in handling local spurious noise and global coherence. (ML: 0.80)
Abstract
Retrieval augmented generation (RAG) has enhanced large language models by enabling access to external knowledge, with graph-based RAG emerging as a powerful paradigm for structured retrieval and reasoning. However, existing graph-based methods often over-rely on surface-level node matching and lack explicit causal modeling, leading to unfaithful or spurious answers. Prior attempts to incorporate causality are typically limited to local or single-document contexts and also suffer from information isolation that arises from modular graph structures, which hinders scalability and cross-module causal reasoning. To address these challenges, we propose HugRAG, a framework that rethinks knowledge organization for graph-based RAG through causal gating across hierarchical modules. HugRAG explicitly models causal relationships to suppress spurious correlations while enabling scalable reasoning over large-scale knowledge graphs. Extensive experiments demonstrate that HugRAG consistently outperforms competitive graph-based RAG baselines across multiple datasets and evaluation metrics. Our work establishes a principled foundation for structured, scalable, and causally grounded RAG systems.
Retrieval augmented generation (RAG) has enhanced large language models by enabling access to external knowledge, with graph-based RAG emerging as a powerful paradigm for structured retrieval and reasoning. However, existing graph-based methods often over-rely on surface-level node matching and lack explicit causal modeling, leading to unfaithful or spurious answers. Prior attempts to incorporate causality are typically limited to local or single-document contexts and also suffer from information isolation that arises from modular graph structures, which hinders scalability and cross-module causal reasoning. To address these challenges, we propose HugRAG, a framework that rethinks knowledge organization for graph-based RAG through causal gating across hierarchical modules. HugRAG explicitly models causal relationships to suppress spurious correlations while enabling scalable reasoning over large-scale knowledge graphs. Extensive experiments demonstrate that HugRAG consistently outperforms competitive graph-based RAG baselines across multiple datasets and evaluation metrics. Our work establishes a principled foundation for structured, scalable, and causally grounded RAG systems.
Why we are recommending this paper?
Due to your Interest in Knowledge Graphs
This paper explores graph-based RAG, a growing area of interest for knowledge retrieval and reasoning. The focus on hierarchical causal knowledge graphs aligns with the user’s interest in structured knowledge management and product categorization.
Due to your Interest in Knowledge Graphs
This paper explores graph-based RAG, a growing area of interest for knowledge retrieval and reasoning. The focus on hierarchical causal knowledge graphs aligns with the user’s interest in structured knowledge management and product categorization.
University of California, Berkeley
AI Insights
- A proper conditionally negative definite function on a group is one that satisfies certain properties and can be used to study the geometry of the group. (ML: 0.90)
- The construction of the proper conditionally negative definite function may not be unique or easy to compute in all cases. (ML: 0.89)
- The concept of a proper conditionally negative definite function was introduced by Haagerup in his work on C*-algebras. (ML: 0.88)
- Graph Product: A way of constructing new groups from existing ones by taking their Cartesian product. (ML: 0.84)
- Haagerup Property: A property of a group that implies it has a certain kind of amenability, related to the geometry of the group. (ML: 0.83)
- Previous work by Antolín and Dreesen showed that the Haagerup property is stable under graph products for certain types of groups. (ML: 0.79)
- The proof involves constructing a proper conditionally negative definite function on the graph product group using the functions from each of the original groups. (ML: 0.79)
- The graph product of groups with the Haagerup property has the Haagerup property. (ML: 0.77)
- The proof relies on the properties of the Haagerup property and the geometry of the groups involved, which may not generalize to other contexts. (ML: 0.76)
- The main result shows that the graph product of groups with the Haagerup property also has the Haagerup property, which is useful for studying the geometry and amenability of these groups. (ML: 0.72)
Abstract
In this paper, we prove that any graph product of finitely many groups, all satisfying the Haagerup property (or Gromov's a-T-menability) also satisfies Haagerup property.
In this paper, we prove that any graph product of finitely many groups, all satisfying the Haagerup property (or Gromov's a-T-menability) also satisfies Haagerup property.
Why we are recommending this paper?
Due to your Interest in Graphs for Products
Due to your Interest in Graphs for Products
University of York
AI Insights
- Plasticity: The ability of a model to adapt to new data. (ML: 0.98)
- Stability: The ability of a model to retain previously learned information. (ML: 0.98)
- Continual learning: The ability of a model to learn from new data without forgetting previously learned information. (ML: 0.97)
- Composite objective function: A mathematical representation of the balance between plasticity and stability in continual learning. (ML: 0.94)
- The authors provide a summary of notation used in the paper, including the definition of the dataset, input, target, latent variable, encoder parameters, decoder parameters, and other relevant variables. (ML: 0.92)
- The paper presents a novel approach to continual learning using the Douglas-Rachford Splitting (DRS) algorithm. (ML: 0.89)
- The paper also discusses the theoretical analysis of the DRS-based optimization scheme, including its convergence properties and computational complexity. (ML: 0.80)
- The DRS-based optimization scheme is analyzed from three perspectives: convergence theory, stability-plasticity trade-offs, and computational complexity. (ML: 0.79)
- Douglas-Rachford Splitting (DRS) algorithm: A numerical method for solving convex optimization problems. (ML: 0.76)
- The authors prove that their method converges to a stationary point of the composite objective function, which represents the balance between plasticity and stability. (ML: 0.73)
Abstract
Learning from a stream of tasks usually pits plasticity against stability: acquiring new knowledge often causes catastrophic forgetting of past information. Most methods address this by summing competing loss terms, creating gradient conflicts that are managed with complex and often inefficient strategies such as external memory replay or parameter regularization. We propose a reformulation of the continual learning objective using Douglas-Rachford Splitting (DRS). This reframes the learning process not as a direct trade-off, but as a negotiation between two decoupled objectives: one promoting plasticity for new tasks and the other enforcing stability of old knowledge. By iteratively finding a consensus through their proximal operators, DRS provides a more principled and stable learning dynamic. Our approach achieves an efficient balance between stability and plasticity without the need for auxiliary modules or complex add-ons, providing a simpler yet more powerful paradigm for continual learning systems.
Learning from a stream of tasks usually pits plasticity against stability: acquiring new knowledge often causes catastrophic forgetting of past information. Most methods address this by summing competing loss terms, creating gradient conflicts that are managed with complex and often inefficient strategies such as external memory replay or parameter regularization. We propose a reformulation of the continual learning objective using Douglas-Rachford Splitting (DRS). This reframes the learning process not as a direct trade-off, but as a negotiation between two decoupled objectives: one promoting plasticity for new tasks and the other enforcing stability of old knowledge. By iteratively finding a consensus through their proximal operators, DRS provides a more principled and stable learning dynamic. Our approach achieves an efficient balance between stability and plasticity without the need for auxiliary modules or complex add-ons, providing a simpler yet more powerful paradigm for continual learning systems.
Why we are recommending this paper?
Due to your Interest in Continual Generalized Category Discovery
Due to your Interest in Continual Generalized Category Discovery
University of Notre Dame
AI Insights
- It highlights the importance of co-analyzability in understanding this relationship and discusses its implications for classification theory over a predicate. (ML: 0.97)
- They also discuss the role of co-analyzability in understanding the relationship between the Gaifman property and relative categoricity. (ML: 0.90)
- Relatively categorical theory: A theory T is relatively categorical if it has a unique model of cardinality κ, up to isomorphism, for each infinite cardinal κ. (ML: 0.89)
- The paper discusses various results on relatively categorical theories, including the Gaifman conjecture and its implications for classification theory over a predicate. (ML: 0.88)
- The paper concludes with a discussion of open problems and future directions for research. (ML: 0.88)
- The paper provides a comprehensive overview of the relationship between relatively categorical theories and the Gaifman property. (ML: 0.87)
- Gaifman property: A theory T has the Gaifman property if every model of T can be embedded into a larger model with the same P-part. (ML: 0.87)
- The authors provide an overview of the history of the problem, from the initial work by Shelah to more recent developments. (ML: 0.86)
- Stably embedded set: A set S is stably embedded in a structure M if for any formula φ(x, y) and any tuple b from the universe of M, the set {a ∈ S | M ⊨ φ(a, b)} is also stably embedded. (ML: 0.78)
- Co-analyzability: A structure M is co-analyzable over a predicate P if it can be defined using only formulas that involve P. (ML: 0.78)
Abstract
We make some elementary observations about relative categoricity and the Gaifman property. T will be a complete theory in a countable language L with a distinguished unary predicate P. We will assume L is relational and T has quantifier elimination. For M a model of of T, M^P is the substructure of M with universe P(M), and T^P is the common L-theory of these M^P. T is said to be relatively categorical if for any models M_1, M_2 of T any isomorphism between M_1^P and M_2^P lifts to an isomorphism between M_1 and M_2. T has the Gaifman property (or P-existence) if every model of T^P is of the form M^P for a model M of T. It was conjectured that if T is relatively categorical then T has the Gaifman property. T is said to be relatively (omega, omega) categorical if relative categoricity holds when restricted to countable models of T. We observe that (i) if T is relatively (omega, omega) categorical then any model of T^P of cardinality at most aleph_1 is of the form M^P for M a model of T, and (ii) if in addition every model M of T is in the algebraic closure of P(M) together with a (finite) subset of M, then T is relatively categorical and has the Gaifman property.
We make some elementary observations about relative categoricity and the Gaifman property. T will be a complete theory in a countable language L with a distinguished unary predicate P. We will assume L is relational and T has quantifier elimination. For M a model of of T, M^P is the substructure of M with universe P(M), and T^P is the common L-theory of these M^P. T is said to be relatively categorical if for any models M_1, M_2 of T any isomorphism between M_1^P and M_2^P lifts to an isomorphism between M_1 and M_2. T has the Gaifman property (or P-existence) if every model of T^P is of the form M^P for a model M of T. It was conjectured that if T is relatively categorical then T has the Gaifman property. T is said to be relatively (omega, omega) categorical if relative categoricity holds when restricted to countable models of T. We observe that (i) if T is relatively (omega, omega) categorical then any model of T^P of cardinality at most aleph_1 is of the form M^P for M a model of T, and (ii) if in addition every model M of T is in the algebraic closure of P(M) together with a (finite) subset of M, then T is relatively categorical and has the Gaifman property.
Why we are recommending this paper?
Due to your Interest in Product Categorization
Due to your Interest in Product Categorization
The Johns Hopkins University
AI Insights
- The method allows disentangling of categorical, continuous, and non-continuous ordinal categories, and captures the degree of similarity between corresponding labels for each category. (ML: 0.98)
- Label-driven graphs: A set of graphs used in MILCCI to capture the degree of similarity between corresponding labels for each category. (ML: 0.95)
- It uses dictionary learning and sparse coding to identify components that are common across different categories. (ML: 0.94)
- MILCCI is a powerful method for identifying common components across different categories by integrating multiple types of labels. (ML: 0.93)
- Sparse coding: A technique used in dictionary learning to apply sparsity on the components. (ML: 0.91)
- Multi-integration of labels across categories for component identification (MILCCI): A method for identifying common components across different categories by integrating multiple types of labels. (ML: 0.90)
- MILCCI can be used in various applications such as neuronal ensemble analysis, where it can identify neural ensembles that adjust to arousal level and stimulation frequency and evolve via dynamical rules. (ML: 0.81)
- PyLops: A Python library used in MILCCI for solving optimization problems with sparse constraints. (ML: 0.79)
- MILCCI is a method for multi-integration of labels across categories for component identification. (ML: 0.78)
- Dictionary learning: An algorithm used in MILCCI to initialize the components and traces using sparse coding. (ML: 0.77)
- SPGL1's solver: A solver used in PyLops to solve optimization problems with sparse constraints. (ML: 0.74)
Abstract
Many fields collect large-scale temporal data through repeated measurements (trials), where each trial is labeled with a set of metadata variables spanning several categories. For example, a trial in a neuroscience study may be linked to a value from category (a): task difficulty, and category (b): animal choice. A critical challenge in time-series analysis is to understand how these labels are encoded within the multi-trial observations, and disentangle the distinct effect of each label entry across categories. Here, we present MILCCI, a novel data-driven method that i) identifies the interpretable components underlying the data, ii) captures cross-trial variability, and iii) integrates label information to understand each category's representation within the data. MILCCI extends a sparse per-trial decomposition that leverages label similarities within each category to enable subtle, label-driven cross-trial adjustments in component compositions and to distinguish the contribution of each category. MILCCI also learns each component's corresponding temporal trace, which evolves over time within each trial and varies flexibly across trials. We demonstrate MILCCI's performance through both synthetic and real-world examples, including voting patterns, online page view trends, and neuronal recordings.
Many fields collect large-scale temporal data through repeated measurements (trials), where each trial is labeled with a set of metadata variables spanning several categories. For example, a trial in a neuroscience study may be linked to a value from category (a): task difficulty, and category (b): animal choice. A critical challenge in time-series analysis is to understand how these labels are encoded within the multi-trial observations, and disentangle the distinct effect of each label entry across categories. Here, we present MILCCI, a novel data-driven method that i) identifies the interpretable components underlying the data, ii) captures cross-trial variability, and iii) integrates label information to understand each category's representation within the data. MILCCI extends a sparse per-trial decomposition that leverages label similarities within each category to enable subtle, label-driven cross-trial adjustments in component compositions and to distinguish the contribution of each category. MILCCI also learns each component's corresponding temporal trace, which evolves over time within each trial and varies flexibly across trials. We demonstrate MILCCI's performance through both synthetic and real-world examples, including voting patterns, online page view trends, and neuronal recordings.
Why we are recommending this paper?
Due to your Interest in Product Categorization
Due to your Interest in Product Categorization
University of Macau
AI Insights
- Foundation graphs: Two graphs used to model the fundamental inter- and intra-fact interactions between relations and entities in HKGs. (ML: 0.97)
- THOR models the fundamental inter- and intra-fact interactions between relations and entities in HKGs using two foundation graphs. (ML: 0.95)
- The authors do not discuss the scalability of their approach to large knowledge graphs. (ML: 0.94)
- Experiments show that THOR outperforms a sizable collection of baselines, yielding 66.1%, 55.9%, and 20.4% improvement over the best-performing rule-based, semi-inductive, and fully-inductive techniques, respectively. (ML: 0.94)
- Inductive link prediction: The task of predicting links in a knowledge graph given only the structure and some training data. (ML: 0.91)
- Hyper-relational Knowledge Graph (HKG): A knowledge graph that contains hyper-relational facts, which are relations between entities involving multiple objects. (ML: 0.89)
- The authors design THOR to learn from these two foundation graphs with two parallel NBFNet-based graph encoders followed by a transformer decoder. (ML: 0.88)
- The paper proposes THOR, an inductive link prediction technique for Hyper-relational Knowledge Graphs (HKGs). (ML: 0.86)
- The authors' approach to modeling foundation graphs and using parallel graph encoders followed by a transformer decoder is key to THOR's success. (ML: 0.83)
- THOR is an effective technique for inductive link prediction over HKGs, outperforming a range of baselines. (ML: 0.81)
Abstract
Knowledge graphs (KGs) have become a key ingredient supporting a variety of applications. Beyond the traditional triplet representation of facts where a relation connects two entities, modern KGs observe an increasing number of hyper-relational facts, where an arbitrary number of qualifiers associated with a triplet provide auxiliary information to further describe the rich semantics of the triplet, which can effectively boost the reasoning performance in link prediction tasks. However, existing link prediction techniques over such hyper-relational KGs (HKGs) mostly focus on a transductive setting, where KG embedding models are learned from the specific vocabulary of a given KG and subsequently can only make predictions within the same vocabulary, limiting their generalizability to previously unseen vocabularies. Against this background, we propose THOR, an inducTive link prediction technique for Hyper-relational knOwledge gRaphs. Specifically, we first introduce both relation and entity foundation graphs, modeling their fundamental inter- and intra-fact interactions in HKGs, which are agnostic to any specific relations and entities. Afterward, THOR is designed to learn from the two foundation graphs with two parallel graph encoders followed by a transformer decoder, which supports efficient masked training and fully-inductive inference. We conduct a thorough evaluation of THOR in hyper-relational link prediction tasks on 12 datasets with different settings. Results show that THOR outperforms a sizable collection of baselines, yielding 66.1%, 55.9%, and 20.4% improvement over the best-performing rule-based, semi-inductive, and fully-inductive techniques, respectively. A series of ablation studies also reveals our key design factors capturing the structural invariance transferable across HKGs for inductive tasks.
Knowledge graphs (KGs) have become a key ingredient supporting a variety of applications. Beyond the traditional triplet representation of facts where a relation connects two entities, modern KGs observe an increasing number of hyper-relational facts, where an arbitrary number of qualifiers associated with a triplet provide auxiliary information to further describe the rich semantics of the triplet, which can effectively boost the reasoning performance in link prediction tasks. However, existing link prediction techniques over such hyper-relational KGs (HKGs) mostly focus on a transductive setting, where KG embedding models are learned from the specific vocabulary of a given KG and subsequently can only make predictions within the same vocabulary, limiting their generalizability to previously unseen vocabularies. Against this background, we propose THOR, an inducTive link prediction technique for Hyper-relational knOwledge gRaphs. Specifically, we first introduce both relation and entity foundation graphs, modeling their fundamental inter- and intra-fact interactions in HKGs, which are agnostic to any specific relations and entities. Afterward, THOR is designed to learn from the two foundation graphs with two parallel graph encoders followed by a transformer decoder, which supports efficient masked training and fully-inductive inference. We conduct a thorough evaluation of THOR in hyper-relational link prediction tasks on 12 datasets with different settings. Results show that THOR outperforms a sizable collection of baselines, yielding 66.1%, 55.9%, and 20.4% improvement over the best-performing rule-based, semi-inductive, and fully-inductive techniques, respectively. A series of ablation studies also reveals our key design factors capturing the structural invariance transferable across HKGs for inductive tasks.
Why we are recommending this paper?
Due to your Interest in Knowledge Graphs
Due to your Interest in Knowledge Graphs
IIIT Hyderabad
AI Insights
- Limited scalability (ML: 0.93)
- The approach has potential applications in software engineering and architecture knowledge management, but requires further research and development to fully realize its benefits. (ML: 0.91)
- Agentic AI: A type of artificial intelligence that uses agentic reasoning to perform tasks. (ML: 0.89)
- AgenticAKM offers a robust and effective methodology for automating AKM, with potential applications in software engineering and architecture knowledge management. (ML: 0.88)
- A user study reveals that AgenticAKM produces better ADRs (Architecture Decision Records) from code repositories compared to simple LLM calls. (ML: 0.87)
- AgenticAKM is a novel approach to Architecture Knowledge Management (AKM) that uses agentic reasoning to automate the extraction, refinement, and documentation of architecture knowledge from existing software systems. (ML: 0.85)
- Architecture Decision Records (ADRs): Documents that record architectural decisions made during the development of a software system. (ML: 0.84)
- Architecture Knowledge Management (AKM): The process of managing and documenting the architecture of a software system. (ML: 0.84)
- AgenticAKM is a promising approach to AKM, offering improved ADR quality compared to simple LLM calls. (ML: 0.74)
- The approach decomposes architecture recovery into specialized Extractor, Retriever, Generator, and Validator agents, overcoming the limitations of monolithic LLM calls. (ML: 0.73)
Abstract
Architecture Knowledge Management (AKM) is crucial for maintaining current and comprehensive software Architecture Knowledge (AK) in a software project. However AKM is often a laborious process and is not adopted by developers and architects. While LLMs present an opportunity for automation, a naive, single-prompt approach is often ineffective, constrained by context limits and an inability to grasp the distributed nature of architectural knowledge. To address these limitations, we propose an Agentic approach for AKM, AgenticAKM, where the complex problem of architecture recovery and documentation is decomposed into manageable sub-tasks. Specialized agents for architecture Extraction, Retrieval, Generation, and Validation collaborate in a structured workflow to generate AK. To validate we made an initial instantiation of our approach to generate Architecture Decision Records (ADRs) from code repositories. We validated our approach through a user study with 29 repositories. The results demonstrate that our agentic approach generates better ADRs, and is a promising and practical approach for automating AKM.
Architecture Knowledge Management (AKM) is crucial for maintaining current and comprehensive software Architecture Knowledge (AK) in a software project. However AKM is often a laborious process and is not adopted by developers and architects. While LLMs present an opportunity for automation, a naive, single-prompt approach is often ineffective, constrained by context limits and an inability to grasp the distributed nature of architectural knowledge. To address these limitations, we propose an Agentic approach for AKM, AgenticAKM, where the complex problem of architecture recovery and documentation is decomposed into manageable sub-tasks. Specialized agents for architecture Extraction, Retrieval, Generation, and Validation collaborate in a structured workflow to generate AK. To validate we made an initial instantiation of our approach to generate Architecture Decision Records (ADRs) from code repositories. We validated our approach through a user study with 29 repositories. The results demonstrate that our agentic approach generates better ADRs, and is a promising and practical approach for automating AKM.
Why we are recommending this paper?
Due to your Interest in Knowledge Management
Due to your Interest in Knowledge Management
Georgia Institute of Technology
AI Insights
- The authors suggest that this is because TMK prompts provide a clear understanding of the task requirements and constraints, allowing the LLMs to focus on finding a solution rather than trying to understand the problem. (ML: 0.97)
- The authors acknowledge that the results may not generalize to all domains and tasks, and that further research is needed to fully understand the limitations and potential applications of TMK prompts. (ML: 0.96)
- PlanBench: A benchmark for evaluating large language models on planning and reasoning about change. (ML: 0.95)
- The paper explores how to use special prompts called TaskMaster Knowledge (TMK) to help large language models understand these rules and plan the best way to arrange the blocks. (ML: 0.95)
- The authors explore the use of TaskMaster Knowledge (TMK) prompts, which provide explicit task descriptions and constraints, to improve LLM performance in planning tasks. (ML: 0.94)
- The paper investigates the use of TaskMaster Knowledge (TMK) prompts in improving the planning abilities of large language models (LLMs). (ML: 0.94)
- The results show that TMK prompts significantly improve LLM performance in planning tasks, especially for more complex scenarios. (ML: 0.94)
- TaskMaster Knowledge (TMK): A set of explicit task descriptions and constraints used as prompts to guide the planning process. (ML: 0.94)
- The paper cites several previous studies on LLMs and planning, including works by Jason Wei et al. (ML: 0.92)
- The paper presents an investigation on the planning abilities of large language models (LLMs) using the PlanBench benchmark. (ML: 0.88)
- Imagine you're playing with blocks and need to arrange them into stacks. (ML: 0.88)
- You have a set of actions like picking up, unstacking, putting down, and stacking blocks. (ML: 0.87)
- But there are rules, like you can only pick up or unstack one block at a time, and you can't stack a block on top of another if the bottom block is not clear. (ML: 0.85)
- (2023). (ML: 0.81)
- (2022) and Karthik Valmeekam et al. (ML: 0.69)
Abstract
Large Language Models (LLM) can struggle with reasoning ability and planning tasks. Many prompting techniques have been developed to assist with LLM reasoning, notably Chain-of-Thought (CoT); however, these techniques, too, have come under scrutiny as LLMs' ability to reason at all has come into question. Borrowing from the domain of cognitive and educational science, this paper investigates whether the Task-Method-Knowledge (TMK) framework can improve LLM reasoning capabilities beyond its previously demonstrated success in educational applications. The TMK framework's unique ability to capture causal, teleological, and hierarchical reasoning structures, combined with its explicit task decomposition mechanisms, makes it particularly well-suited for addressing language model reasoning deficiencies, and unlike other hierarchical frameworks such as HTN and BDI, TMK provides explicit representations of not just what to do and how to do it, but also why actions are taken. The study evaluates TMK by experimenting on the PlanBench benchmark, focusing on the Blocksworld domain to test for reasoning and planning capabilities, examining whether TMK-structured prompting can help language models better decompose complex planning problems into manageable sub-tasks. Results also highlight significant performance inversion in reasoning models. TMK prompting enables the reasoning model to achieve up to an accuracy of 97.3\% on opaque, symbolic tasks (Random versions of Blocksworld in PlanBench) where it previously failed (31.5\%), suggesting the potential to bridge the gap between semantic approximation and symbolic manipulation. Our findings suggest that TMK functions not merely as context, but also as a mechanism that steers reasoning models away from their default linguistic modes to engage formal, code-execution pathways in the context of the experiments.
Large Language Models (LLM) can struggle with reasoning ability and planning tasks. Many prompting techniques have been developed to assist with LLM reasoning, notably Chain-of-Thought (CoT); however, these techniques, too, have come under scrutiny as LLMs' ability to reason at all has come into question. Borrowing from the domain of cognitive and educational science, this paper investigates whether the Task-Method-Knowledge (TMK) framework can improve LLM reasoning capabilities beyond its previously demonstrated success in educational applications. The TMK framework's unique ability to capture causal, teleological, and hierarchical reasoning structures, combined with its explicit task decomposition mechanisms, makes it particularly well-suited for addressing language model reasoning deficiencies, and unlike other hierarchical frameworks such as HTN and BDI, TMK provides explicit representations of not just what to do and how to do it, but also why actions are taken. The study evaluates TMK by experimenting on the PlanBench benchmark, focusing on the Blocksworld domain to test for reasoning and planning capabilities, examining whether TMK-structured prompting can help language models better decompose complex planning problems into manageable sub-tasks. Results also highlight significant performance inversion in reasoning models. TMK prompting enables the reasoning model to achieve up to an accuracy of 97.3\% on opaque, symbolic tasks (Random versions of Blocksworld in PlanBench) where it previously failed (31.5\%), suggesting the potential to bridge the gap between semantic approximation and symbolic manipulation. Our findings suggest that TMK functions not merely as context, but also as a mechanism that steers reasoning models away from their default linguistic modes to engage formal, code-execution pathways in the context of the experiments.
Why we are recommending this paper?
Due to your Interest in Knowledge Management
Due to your Interest in Knowledge Management
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