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Numerous theorems, such as those in geometry, are often presented in multimodal forms (e.g., diagrams). Humans benefit from visual reasoning in such settings, using diagrams to gain intuition and guide the proof process. Modern Multimodal…
Domain of mathematical logic in computers is dominated by automated theorem provers (ATP) and interactive theorem provers (ITP). Both of these are hard to access by AI from the human-imitation approach: ATPs often use human-unfriendly…
The potential of multimodal generative artificial intelligence (mAI) to replicate human grounded language understanding, including the pragmatic, context-rich aspects of communication, remains to be clarified. Humans are known to use…
Graph Neural Networks (GNNs) have been widely adopted for Protein Representation Learning (PRL), as residue interaction networks can be naturally represented as graphs. Current GNN-based PRL methods typically rely on single-perspective…
Recent advances in Multimodal Large Language Models (MLLMs) have achieved remarkable progress in general domains and demonstrated promise in multimodal mathematical reasoning. However, applying MLLMs to geometry problem solving (GPS)…
In this preprint we present an outline of the multidimensional version of topological Galois theory. The theory studies topological obstruction to solvability of equations "in finite terms" (i.e. to their solvability by radicals, by…
This position statement looks back on two decades of work on shallow embeddings of non-classical logics in classical higher-order logic (HOL), a line of research that expanded into a range of logic embeddings in HOL and inspired the LogiKEy…
Large language models (LLMs) have shown impressive performance on complex reasoning by leveraging chain-of-thought (CoT) prompting to generate intermediate reasoning chains as the rationale to infer the answer. However, existing CoT studies…
Visual generation models have made remarkable progress in creating realistic images from text prompts, yet struggle with complex prompts that specify multiple objects with precise spatial relationships and attributes. Effective handling of…
Multimodal large language models (MLLMs) have exhibited remarkable performance in various visual tasks, yet still struggle with spatial reasoning. Recent efforts mitigate this by injecting geometric features from 3D foundation models, but…
We introduce a class of iterated integrals, defined through a set of linearly independent integration kernels on elliptic curves. As a direct generalisation of multiple polylogarithms, we construct our set of integration kernels ensuring…
Recent advances in multi-modal large language models (MLLMs) have significantly improved object-level grounding and region captioning. However, they remain limited in visual relation understanding, struggling even with binary relation…
Pre-trained language models (PLMs) have made significant advances in natural language inference (NLI) tasks, however their sensitivity to textual perturbations and dependence on large datasets indicate an over-reliance on shallow…
Establishing common ground, a shared set of beliefs and mutually recognized facts, is fundamental to collaboration, yet remains a challenge for current AI systems, especially in multimodal, multiparty settings, where the collaborators bring…
Next Point-of-Interest (POI) prediction is a fundamental task in location-based services, especially critical for large-scale navigation platforms like AMAP that serve billions of users across diverse lifestyle scenarios. While recent POI…
Multiparticle correlations is a hallmark measurement characterizing the behaviour of the assumed Quark Gluon Plasma in heavy ion collisions. In these proceedings an alternative, microscopic approach is resented, based on interacting strings…
In this paper, we present a novel method for solving multiobjective linear programming problems (MOLPP) that overcomes the need to calculate the optimal value of each objective function. This method is a follow-up to our previous work on…
Girard's Geometry of Interaction (GoI), a semantics designed for linear logic proofs, has been also successfully applied to programming language semantics. One way is to use abstract machines that pass a token on a fixed graph along a path…
We present a neuro-mathematical model for geometrical optical illusions (GOIs), a class of illusory phenomena that consists in a mismatch of geometrical properties of the visual stimulus and its associated percept. They take place in the…
Recent advancements in Multimodal Large Language Models (MLLMs) have incentivized models to ``think with images'' by actively invoking visual tools during multi-turn reasoning. The common Reinforcement Learning (RL) practice of relying on…