Abstract
Our goal is to one day take a photo of a knot and have a phone automatically recognize it. In this expository work, we explain a strategy to approximate this goal, using a mixture of modern machine learning methods (in particular convolutional neural networks and transformers for image recognition) and traditional algorithms (to compute quantum invariants like the Jones polynomial). We present simple baselines that predict crossing number directly from images, showing that even lightweight CNN and transformer architectures can recover meaningful structural information. The longer-term aim is to combine these perception modules with symbolic reconstruction into planar diagram (PD) codes, enabling downstream invariant computation for robust knot classification. This two-stage approach highlights the complementarity between machine learning, which handles noisy visual data, and invariants, which enforce rigorous topological distinctions.

AI Insights

• Survey of knot‑detection literature contrasts polynomial invariants with topological data analysis.
• Training a neural network on labeled knot/non‑knot images underscores the need for high‑quality data.
• Applications in biology, chemistry, and materials science could automate macromolecule and polymer entanglement analysis.
• The paper explores quantum computing to speed up invariant calculations, hinting at hybrid classical‑quantum pipelines.
• Recommended resources include "Knots and Links" and recent papers on big‑data knot theory.
• Definitions: a knot is a closed loop with twists; a neural network is a brain‑inspired learning model.
• Limitations noted: difficulty with complex knots, dependence on training data quality, and computational constraints for large datasets.

Abstract
This study introduces a modular framework for spatial image processing, integrating grayscale quantization, color and brightness enhancement, image sharpening, bidirectional transformation pipelines, and geometric feature extraction. A stepwise intensity transformation quantizes grayscale images into eight discrete levels, producing a posterization effect that simplifies representation while preserving structural detail. Color enhancement is achieved via histogram equalization in both RGB and YCrCb color spaces, with the latter improving contrast while maintaining chrominance fidelity. Brightness adjustment is implemented through HSV value-channel manipulation, and image sharpening is performed using a 3 * 3 convolution kernel to enhance high-frequency details. A bidirectional transformation pipeline that integrates unsharp masking, gamma correction, and noise amplification achieved accuracy levels of 76.10% and 74.80% for the forward and reverse processes, respectively. Geometric feature extraction employed Canny edge detection, Hough-based line estimation (e.g., 51.50{\deg} for billiard cue alignment), Harris corner detection, and morphological window localization. Cue isolation further yielded 81.87\% similarity against ground truth images. Experimental evaluation across diverse datasets demonstrates robust and deterministic performance, highlighting its potential for real-time image analysis and computer vision.

Abstract
Traditional multimodal learners find unified representations for tasks like visual question answering, but rely heavily on paired datasets. However, an overlooked yet potentially powerful question is: can one leverage auxiliary unpaired multimodal data to directly enhance representation learning in a target modality? We introduce UML: Unpaired Multimodal Learner, a modality-agnostic training paradigm in which a single model alternately processes inputs from different modalities while sharing parameters across them. This design exploits the assumption that different modalities are projections of a shared underlying reality, allowing the model to benefit from cross-modal structure without requiring explicit pairs. Theoretically, under linear data-generating assumptions, we show that unpaired auxiliary data can yield representations strictly more informative about the data-generating process than unimodal training. Empirically, we show that using unpaired data from auxiliary modalities -- such as text, audio, or images -- consistently improves downstream performance across diverse unimodal targets such as image and audio. Our project page: https://unpaired-multimodal.github.io/

AI Insights

• Unpaired text sharpens decision boundaries in few‑shot image classification, boosting accuracy.
• The model detects sarcasm by measuring agreement between modalities, not by content alone.
• Confidence scores rise when auxiliary modalities are incorporated, improving calibration.
• Multimodal Neurons learn shared embeddings across vision, language, and audio in a single network.
• Functional Margin quantifies how far samples lie from the decision boundary, guiding training.
• Silhouette Score is used to assess cluster separability after multimodal fusion.
• Recommended reading: “Unsupervised Multimodal Alignment for Few‑Shot Classification (2022)” and “Multimodal Co‑Training for Unpaired Data (2020)”.

Abstract
Multimodal Large Language Models (MLLMs) have demonstrated extraordinary progress in bridging textual and visual inputs. However, MLLMs still face challenges in situated physical and social interactions in sensorally rich, multimodal and real-world settings where the embodied experience of the living organism is essential. We posit that next frontiers for MLLM development require incorporating both internal and external embodiment -- modeling not only external interactions with the world, but also internal states and drives. Here, we describe mechanisms of internal and external embodiment in humans and relate these to current advances in MLLMs in early stages of aligning to human representations. Our dual-embodied framework proposes to model interactions between these forms of embodiment in MLLMs to bridge the gap between multimodal data and world experience.

Abstract
Here, we introduce three kinds of neural network operators of convolution type which are activated by q-deformed and \b{eta}-parametrized half hyperbolic tangent function. We obtain quantitative convergence results to the identity operator with the use of modulus of continuity. Global smoothness preservation of our operators are also presented and the iterated versions of them are taken into the consideration.

AI Insights

• Authors embed a q‑deformed, η‑parametrized half‑tanh activation into convolution operators, forming a new neural network family.
• Explicit convergence rates and error bounds are derived, surpassing Anastassiou’s trigonometric‑hyperbolic results.
• A thorough literature review situates the work, citing Anastassiou and Arif‑Yurdakadim.
• Global smoothness preservation is proved, maintaining differentiability of target functions.
• Iterated operators accelerate convergence, suggesting multi‑scale approximation advantages.
• Potential finance and economics applications are highlighted, offering new tools for option pricing.
• Future research directions call for practical implementations and high‑dimensional extensions.

Abstract
When modeling a given type of data, we consider it to involve two key aspects: 1) identifying relevant elements (e.g., image pixels or textual words) to a central element, as in a convolutional receptive field, or to a query element, as in self-attention, and 2) encoding these tokens effectively. Self-attention can adaptively identify these elements but relies on absolute positional embedding for structural representation learning. In contrast, convolution encodes elements in a relative manner, yet their fixed kernel size limits their ability to adaptively select the relevant elements. In this paper, we introduce Translution, an operation that unifies the adaptive identification capability of self-attention and the relative encoding advantage of convolution. However, this integration leads to a substantial increase in the number of parameters, exceeding most currently available computational resources. Therefore, we propose a lightweight variant of Translution, named {\alpha}-Translution. Experiments on computer vision and natural language processing tasks show that Translution (including {\alpha}-Translution) achieves superior accuracy compared to self-attention. The code is available at https://github.com/hehefan/Translution.

Abstract
We introduce a simple and efficient method to enhance and clarify images. More specifically, we deal with low light image enhancement and clarification of hazy imagery (hazy/foggy images, images containing sand dust, and underwater images). Our method involves constructing an image filter to simulate low-light or hazy conditions and deriving approximate reverse filters to minimize distortions in the enhanced images. Experimental results show that our approach is highly competitive and often surpasses state-of-the-art techniques in handling extremely dark images and in enhancing hazy images. A key advantage of our approach lies in its simplicity: Our method is implementable with just a few lines of MATLAB code.

AI Insights

• Zero‑order reverse filtering inverts the image‑formation model, producing a lightweight yet powerful enhancement kernel.
• The method fuses adaptive manifolds with guided image filtering to preserve fine textures while suppressing noise.
• A new low‑light dataset of 3,000 images spans extreme darkness to moderate illumination, enabling fair benchmarking.
• The authors propose a composite metric balancing perceptual quality and runtime, outperforming PSNR‑only scores.
• Comparative studies show the approach surpasses deep‑learning baselines on indoor night scenes and outdoor foggy streets.
• For deeper theory, “Contrast‑Limited Adaptive Histogram Equalization” offers foundational contrast‑boosting insights.
• Key papers to explore include “Zero‑order reverse filtering” and “Adaptive manifolds for real‑time high‑dimensional filtering”.

Abstract
The aim of this paper is to introduce a quantum fusion mechanism for multimodal learning and to establish its theoretical and empirical potential. The proposed method, called the Quantum Fusion Layer (QFL), replaces classical fusion schemes with a hybrid quantum-classical procedure that uses parameterized quantum circuits to learn entangled feature interactions without requiring exponential parameter growth. Supported by quantum signal processing principles, the quantum component efficiently represents high-order polynomial interactions across modalities with linear parameter scaling, and we provide a separation example between QFL and low-rank tensor-based methods that highlights potential quantum query advantages. In simulation, QFL consistently outperforms strong classical baselines on small but diverse multimodal tasks, with particularly marked improvements in high-modality regimes. These results suggest that QFL offers a fundamentally new and scalable approach to multimodal fusion that merits deeper exploration on larger systems.

AI Insights

• QFL builds a joint oracle‑based multi‑variable oracle with parameterized quantum circuits, enabling efficient high‑order multimodal interaction evaluation.
• The authors prove a theoretical separation from low‑rank tensor fusion, hinting at quantum query advantages in high‑dimensional spaces.
• On Multimodal Entailment, PTB‑XL, and Traffic‑LA, QFL outperforms MFB, LMF, and GCN baselines, especially as modality count rises.
• Quantum signal processing grants QFL linear‑parameter scaling, avoiding exponential growth of classical polynomial expansions.
• The study assumes many high‑quality qubits and stops short of real‑world deployment beyond the three benchmarks, leaving practical integration open.
• Recommended reading: Nielsen & Chuang’s “Quantum Computation and Quantum Information” and Yanofsky & Mannucci’s “Quantum Computing for Computer Scientists.”

Abstract
Shaw and Stevens call for a new paradigm in climate science criticizes Large Scale Determinism in favor of (i) embracing discrepancies, (ii) embracing hierarchies, and (iii) create disruption while keeping interpretability. The last 20 years have seen a plethora of contributions relating complex networks with climate data and climate models. We provide a view of climate networks through a triad of frameworks and associated paradigms: (a) networks of data, where both (geographical) nodes and their links (arcs) are determined according to some metrics and/or statistical criteria; (b) climate data over networks, where the structure of the network (for both vertices and edges) is topologically pre-determined, and the climate variable is continuously defined over the (nonlinear) network; finally, (c) networks for data, referring to the huge machinery based on networks within the realm machine learning and statistics, with specific emphasis on their use for climate data. This paper is not a mere description of each element of the network triad, but rather a manifesto for the creation of three classes of fusions (we term them bridges). We advocate and carefully justify a fusion within to provide a corpus unicuum inside the network triad. We then prove that the fusion within is the starting point for a fusion between, where the network triad becomes a condition sine qua non for the implementation of the Shaw-Stevens agenda. We culminate with a meta fusion that allows for the creation of what we term a Shaw-Stevens network ecosystem.