Nested Episodic State Topology (NEST): A Graph-Theoretic Architecture of Cognitive States

We present NEST (Nested Episodic State Topology), a foundational graph-theoretic representational ontology for modeling cognition as structured state formation and transformation rather than as a finished empirical model. Concepts, episodes, percepts, and task contexts are represented as typed, weighted graphs whose nodes may carry internal subgraph payloads; edges are typed under six relation classes -- causal, containment, temporal, associative, evidential, and spatial. Durable belief graphs are separated from capacity-limited working-memory graphs that may host transient non-belief content. WM-belief grounding, conflict catalogs, and belief-update operators specify how transient structure is tested against stored knowledge and how belief is revised. A reusable operator toolkit -- activation, graph-property functionals, working-memory transitions, awareness and trajectory functionals, and belief update -- organizes the formal core. Derived diagnostics such as fragmentation, involvement, signed evaluation, coherence, and active conflict define familiar phenomena in the same ontology; self-related processing is modeled through designated self-image subgraphs within belief. Subsequent sections instantiate this core without new primitives: phenomena signatures, a task-instantiation schema for action selection and failure modes, and compatibility mappings that embed ACT-R, Soar, Sigma, the Common Model of Cognition, Global Workspace Theory, semantic networks, Theory-Theory, and chunking as constrained regions of one language. Mappings constitute the culminating technical section; discussion addresses scope, limitations, and open research directions. The contribution is intentionally foundational: a transparent representational substrate for later empirical, computational, and domain-specific work.

Controllable Hand Grasp Generation for HOI and Efficient Evaluation Methods

Controllable affordance Hand-Object Interaction (HOI) generation has become an increasingly important area of research in computer vision. In HOI generation, the hand grasp generation is a crucial step for effectively controlling the geometry of the hand. Current hand grasp generation methods rely on 3D information for both the hand and the object. In addition, these methods lack controllability concerning the hand's location and orientation. We treat the hand pose as the discrete graph structure and exploit the geometric priors. It is well established that higher order contextual dependency among the points improves the quality of the results in general. We propose a framework of higher order geometric representations (HOR's) inspired by spectral graph theory and vector algebra to improve the quality of generated hand poses. We demonstrate the effectiveness of our proposed HOR's in devising a controllable novel diffusion method (based on 2D information) for hand grasp generation that outperforms the state of the art (SOTA). Overcoming the limitations of existing methods: like lacking of controllability and dependency on 3D information. Once we have the generated pose, it is very natural to evaluate them using a metric. Popular metrics like FID and MMD are biased and inefficient for evaluating the generated hand poses. Using our proposed HOR's, we introduce an efficient and stable framework of evaluation metrics for grasp generation methods, addressing inefficiencies and biases in FID and MMD.