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Map environments provide a fundamental medium for representing spatial structure. Understanding how foundation model (FM) agents understand and act in such environments is therefore critical for enabling reliable map-based reasoning and…
Large Language Models (LLMs) excel at generating natural language answers, yet their outputs often remain unverifiable and difficult to trace. Knowledge Graphs (KGs) offer a complementary strength by representing entities and their…
BGG-operators form sequences of invariant differential operators and the first of these is overdetermined. Interesting equations in conformal geometry described by these operators are those for Einstein scales, conformal Killing forms and…
We study the standard tractor bundle and the standard cotractor bundle of an almost Grassmann structure: We provide explicit formulae for their splitting operators, first BGG operators as well as prolongation connections. We characterize…
Neural operators are increasingly used as drop-in accelerators inside classical numerical methods, but it is rarely clear which architectural ingredients matter for which role. We answer this question for one important role: the…
A recent work has shown that transformers are able to "reason" with facts and rules in a limited setting where the rules are natural language expressions of conjunctions of conditions implying a conclusion. Since this suggests that…
Transformers architecture apply self-attention to tokens represented as vectors, before a fully connected (neuronal network) layer. These two parts can be layered many times. Traditionally, self-attention is seen as a mechanism for…
How can the semantic interpretation of a formal symbol system be made intrinsic to the system, rather than just parasitic on the meanings in our heads? How can the meanings of the meaningless symbol tokens, manipulated solely on the basis…
We consider algorithms for the factorization of linear partial differential operators. We introduce several new theoretical notions in order to simplify such considerations. We define an obstacle and a ring of obstacles to factorizations.…
Dormant pruning, or the removal of unproductive portions of a tree while a tree is not actively growing, is an important orchard task to help maintain yield, requiring years to build expertise. Because of long training periods and an…
Key to tasks that require reasoning about natural language in visual contexts is grounding words and phrases to image regions. However, observing this grounding in contemporary models is complex, even if it is generally expected to take…
In this preliminary note, we will illustrate our ideas on automated mechanisms for termination and non-termination reasoning.
In order to interpret the communicative intents of an utterance, it needs to be grounded in something that is outside of language; that is, grounded in world modalities. In this paper, we argue that dialogue clarification mechanisms make…
In this note we consider weighted conditional type operators between different Orlicz spaces and generalized conditional type Holder inequality that we defined in [2]. Then we give some necessary and sufficient conditions for boundedness of…
We consider generalized gradients in the general context of $G$-structures. They are natural first order differential operators acting on sections of vector bundles associated to irreducible $G$-representations. We study their geometric…
Intelligent physical systems as embodied cognitive systems must perform high-level reasoning while concurrently managing an underlying control architecture. The link between cognition and control must manage the problem of converting…
Circuit representations are becoming the lingua franca to express and reason about tractable generative and discriminative models. In this paper, we show how complex inference scenarios for these models that commonly arise in machine…
Explaining neural network computation in terms of probabilistic/fuzzy logical operations has attracted much attention due to its simplicity and high interpretability. Different choices of logical operators such as AND, OR and XOR give rise…
Without the assumption of complete, shared awareness, it is necessary to consider communication between agents who may entertain different representations of the world. A syntactic (language-based) approach provides powerful tools to…
The fundamental assumption of the Event Calculus is overly simplistic when it comes to organizations in which time-varying properties have to be actively maintained and managed in order to continue to hold and termination by another action…