Extracting extrusion cylinders from raw 3D geometry has been extensively researched in computer vision, while the processing of 3D data through neural networks has remained a bottleneck.

In this paper, we show that this task can be addressed effectively by leveraging instead 2D pre-trained models for instance segmentation.

State-of-the-art word embeddings presume a linear vector space, but this approach does not easily incorporate the nonlinearity that is necessary to represent polysemy. We thus propose a novel semantic FIeld REepresentation, called FIRE, which is a $D$-dimensional field in which every word is represented as a set of its locations and a nonlinear function covering the field. The strength of a word's relation to another word at a certain location is measured as the function value at that location. With FIRE, compositionality is represented via functional additivity, whereas polysemy is represented via the set of points and the function's multimodality. By implementing FIRE for English and comparing it with previous representation methods via word and sentence similarity tasks, we show that FIRE produces comparable or even better results. In an evaluation of polysemy to predict the number of word senses, FIRE greatly outperformed BERT and Word2vec, providing evidence of how FIRE represents polysemy. The code is available at https://github.com/kduxin/firelang.

Embedding spaces are fundamental to modern AI, translating raw data into high-dimensional vectors that encode rich semantic relationships. Y et, their internal structures remain opaque, with existing approaches often sacrificing semantic coherence for structural regularity or incurring high computational overhead to improve interpretability. To address these challenges, we introduce the Semantic Field Subspace (SFS), a geometry-preserving, context-aware representation that captures local semantic neighborhoods within the embedding space. We also propose SAF ARI (SemAntic Field subspAce deteRmInation), an unsupervised, modality-agnostic algorithm that uncovers hierarchical semantic structures using a novel metric called Semantic Shift, which quantifies how semantics evolve as SFSes evolve. To ensure scalability, we develop an efficient approximation of Semantic Shift that replaces costly SVD computations, achieving a 15 30 speedup with average errors below 0.01. Extensive evaluations across six real-world text and image datasets show that SFSes outperform standard classifiers not only in classification but also in nuanced tasks such as political bias detection, while SAF ARI consistently reveals interpretable and generalizable semantic hierarchies. This work presents a unified framework for structuring, analyzing, and scaling semantic understanding in embedding spaces.

Despite massive investments in scale, deep models for click-through rate (CTR) prediction often exhibit rapidly diminishing returns - a stark contrast to the smooth, predictable gains seen in large language models. We identify the root cause as a structural misalignment: Transformers assume sequential compositionality, while CTR data demand combinatorial reasoning over high-cardinality semantic fields. Unstructured attention spreads capacity indiscriminately, amplifying noise under extreme sparsity and breaking scalable learning. To restore alignment, we introduce the Field-Aware Transformer (FAT), which embeds field-based interaction priors into attention through decomposed content alignment and cross-field modulation. This design ensures model complexity scales with the number of fields F, not the total vocabulary size n >> F, leading to tighter generalization and, critically, observed power-law scaling in AUC as model width increases. We present the first formal scaling law for CTR models, grounded in Rademacher complexity, that explains and predicts this behavior. On large-scale benchmarks, FAT improves AUC by up to +0.51% over state-of-the-art methods. Deployed online, it delivers +2.33% CTR and +0.66% RPM. Our work establishes that effective scaling in recommendation arises not from size, but from structured expressivity-architectural coherence with data semantics.

Work in psychology has highlighted that the geometric model of similarity standard in deep learning is not psychologically plausible because its metric properties such as symmetry do not align with human perception of similarity. In contrast, Tversky (1977) proposed an axiomatic theory of similarity with psychological plausibility based on a representation of objects as sets of features, and their similarity as a function of their common and distinctive features. This model of similarity has not been used in deep learning before, in part because of the challenge of incorporating discrete set operations. In this paper, we develop a differentiable parameterization of Tversky's similarity that is learnable through gradient descent, and derive basic neural network building blocks such as the Tversky projection layer, which unlike the linear projection layer can model non-linear functions such as XOR. Through experiments with image recognition and language modeling neural networks, we show that the Tversky projection layer is a beneficial replacement for the linear projection layer. For instance, on the NABirds image classification task, a frozen ResNet-50 adapted with a Tversky projection layer achieves a 24.7% relative accuracy improvement over the linear layer adapter baseline. With Tversky projection layers, GPT-2's perplexity on PTB decreases by 7.8%, and its parameter count by 34.8%. Finally, we propose a unified interpretation of both types of projection layers as computing similarities of input stimuli to learned prototypes for which we also propose a novel visualization technique highlighting the interpretability of Tversky projection layers. Our work offers a new paradigm for thinking about the similarity model implicit in modern deep learning, and designing neural networks that are interpretable under an established theory of psychological similarity.

This essay develops a theoretical framework for a semantic Artificial General Intelligence (AGI) based on the notion of semantic attractors in complex-valued meaning spaces. Departing from current transformer-based language models, which operate on statistical next-token prediction, we explore a model in which meaning is not inferred probabilistically but formed through recursive tensorial transformation. Using cyclic operations involving the imaginary unit \emph{i}, we describe a rotational semantic structure capable of modeling irony, homonymy, and ambiguity. At the center of this model, however, is a semantic attractor -- a teleological operator that, unlike statistical computation, acts as an intentional agent (Microvitum), guiding meaning toward stability, clarity, and expressive depth. Conceived in terms of gradient flows, tensor deformations, and iterative matrix dynamics, the attractor offers a model of semantic transformation that is not only mathematically suggestive, but also philosophically significant. We argue that true meaning emerges not from simulation, but from recursive convergence toward semantic coherence, and that this requires a fundamentally new kind of cognitive architecture -- one designed to shape language, not just predict it.