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The rise of Large Language Models (LLMs) like ChatGPT has advanced natural language processing, yet concerns about cognitive biases are growing. In this paper, we investigate the anchoring effect, a cognitive bias where the mind relies…
It is argued that a dual symmetry is needed to naturally explain experimental limits on color confinement. Since color is an exact symmetry the only possibility is that this symmetry be a dual symmetry, related to non trivial spatial…
Large Language Models (LLMs) frequently produce hallucinated statements that are assigned high likelihood by the model itself, exposing a fundamental limitation of probability-based verification. This suggests that hallucination is often…
Multi-modal knowledge graphs (MKGs) include not only the relation triplets, but also related multi-modal auxiliary data (i.e., texts and images), which enhance the diversity of knowledge. However, the natural incompleteness has…
The "exact subgraph" approach was recently introduced as a hierarchical scheme to get increasingly tight semidefinite programming relaxations of several NP-hard graph optimization problems. Solving these relaxations is a computational…
One of Thomassen's classical results is that every planar graph of girth at least $5$ is 3-choosable. One can wonder if for a planar graph $G$ of girth sufficiently large and a $3$-list-assignment $L$, one can do even better. Can one find…
This paper proposes PoseLecTr, a graph-based encoder-decoder framework that integrates a novel Legendre convolution with attention mechanisms for six-degree-of-freedom (6-DOF) object pose estimation from monocular RGB images. Conventional…
Large Language Models (LLMs) are prone to factual hallucinations, risking their reliability in real-world applications. Existing hallucination detectors mainly extract micro-level intrinsic patterns for uncertainty quantification or elicit…
We evaluate LLMs' language understanding capacities on simple inference tasks that most humans find trivial. Specifically, we target (i) grammatically-specified entailments, (ii) premises with evidential adverbs of uncertainty, and (iii)…
The 1-2-3 Conjecture, posed by Karo\'{n}ski, {\L}uczak and Thomason, asked whether every connected graph $G$ different from $K_2$ can be 3-edge-weighted so that every two adjacent vertices of $G$ get distinct sums of incident weights. The…
Large language models (LLMs) reason over discrete token ID sequences, yet modern subword tokenizers routinely produce non-unique encodings: multiple token ID sequences can detokenize to identical surface strings. This representational…
It is a major challenge to perform addressable and parallel logical operations on constant-rate quantum LDPC (qLDPC) codes. Indeed, the overhead of targeting specific logical qubits represents a crucial bottleneck in many quantum…
Automated theorem proving in first-order logic is an active research area which is successfully supported by machine learning. While there have been various proposals for encoding logical formulas into numerical vectors -- from simple…
In graph embedding, the connectivity information of a graph is used to represent each vertex as a point in a d-dimensional space. Unlike the original, irregular structural information, such a representation can be used for a multitude of…
We present Symbolic Quick Error Detection (Symbolic QED), a structured approach for logic bug detection and localization which can be used both during pre-silicon design verification as well as post-silicon validation and debug. This new…
The single, double, and triple pendulum has served as an illustrative experimental benchmark system for scientists to study dynamical behavior for more than four centuries. The pendulum system exhibits a wide range of interesting behaviors,…
We consider the number of colors for the colorings of links by the symmetric group $S_3$ of degree $3$. For knots, such a coloring corresponds to a Fox 3-coloring, and thus the number of colors must be 1 or 3. However, for links, there are…
Restricted star colouring is a variant of star colouring introduced to design heuristic algorithms to estimate sparse Hessian matrices. For $k\in\mathbb{N}$, a $k$-restricted star colouring ($k$-rs colouring) of a graph $G$ is a function…
Current AI safety relies on behavioral monitoring and post-training alignment, yet empirical measurement shows these approaches produce no detectable pre-commitment signal in a majority of instruction-tuned models tested. We present an…
Motivated by the technological relevance of S-doped few-layer graphene (FLG) in battery applications and in the oxygen reduction reaction, we systematically explore the effect of basal plane S-doping on the electronic properties of mono-,…