This article considers the problem of designing adaption and optimisation techniques for training quantum learning machines. To this end, the division algebra of quaternions is used to derive an effective model for representing computation and measurement operations on qubits. In turn, the derived model, serves as the foundation for formulating an adaptive learning problem on principal quantum learning units, thereby establishing quantum information processing units akin to that of neurons in classical approaches. Then, leveraging the modern HR-calculus, a comprehensive training framework for learning on quantum machines is developed. The quaternion-valued model accommodates mathematical tractability and establishment of performance criteria, such as convergence conditions.

Spectral algorithms leverage spectral regularization techniques to analyze and process data, providing a flexible framework for addressing supervised learning problems. To deepen our understanding of their performance in real-world scenarios where the distributions of training and test data may differ, we conduct a rigorous investigation into the convergence behavior of spectral algorithms under distribution shifts, specifically within the framework of reproducing kernel Hilbert spaces. Our study focuses on the case of covariate shift. In this scenario, the marginal distributions of the input data differ between the training and test datasets, while the conditional distribution of the output given the input remains unchanged. Under this setting, we analyze the generalization error of spectral algorithms and show that they achieve minimax optimality when the density ratios between the training and test distributions are uniformly bounded. However, we also identify a critical limitation: when the density ratios are unbounded, the spectral algorithms may become suboptimal. To address this limitation, we propose a weighted spectral algorithm that incorporates density ratio information into the learning process. Our theoretical analysis shows that this weighted approach achieves optimal capacity-independent convergence rates. Furthermore, by introducing a weight clipping technique, we demonstrate that the convergence rates of the weighted spectral algorithm can approach the optimal capacity-dependent convergence rates arbitrarily closely. This improvement resolves the suboptimality issue in unbounded density ratio scenarios and advances the state-of-the-art by refining existing theoretical results.

We investigate the challenge of establishing stochastic-like guarantees when sequentially learning from a stream of i.i.d. data that includes an unknown quantity of clean-label adversarial samples. We permit the learner to abstain from making predictions when uncertain. The regret of the learner is measured in terms of misclassification and abstention error, where we allow the learner to abstain for free on adversarial injected samples. This approach is based on the work of Goel, Hanneke, Moran, and Shetty from arXiv:2306.13119. We explore the methods they present and manage to correct inaccuracies in their argumentation. However, this approach is limited to the realizable setting, where labels are assigned according to some function $f^*$ from the hypothesis space $\mathcal{F}$. Based on similar arguments, we explore methods to make adaptations for the agnostic setting where labels are random. Introducing the notion of a clean-label adversary in the agnostic context, we are the first to give a theoretical analysis of a disagreement-based learner for thresholds, subject to a clean-label adversary with noise.

We develop two classes of variance-reduced fast operator splitting methods to approximate solutions of both finite-sum and stochastic generalized equations. Our approach integrates recent advances in accelerated fixed-point methods, co-hypomonotonicity, and variance reduction. First, we introduce a class of variance-reduced estimators and establish their variance-reduction bounds. This class covers both unbiased and biased instances and comprises common estimators as special cases, including SVRG, SAGA, SARAH, and Hybrid-SGD. Next, we design a novel accelerated variance-reduced forward-backward splitting (FBS) algorithm using these estimators to solve finite-sum and stochastic generalized equations. Our method achieves both $\mathcal{O}(1/k^2)$ and $o(1/k^2)$ convergence rates on the expected squared norm $\mathbb{E}[ \| G_{\lambda}x^k\|^2]$ of the FBS residual $G_{\lambda}$, where $k$ is the iteration counter. Additionally, we establish, for the first time, almost sure convergence rates and almost sure convergence of iterates to a solution in stochastic accelerated methods. Unlike existing stochastic fixed-point algorithms, our methods accommodate co-hypomonotone operators, which potentially include nonmonotone problems arising from recent applications. We further specify our method to derive an appropriate variant for each stochastic estimator -- SVRG, SAGA, SARAH, and Hybrid-SGD -- demonstrating that they achieve the best-known complexity for each without relying on enhancement techniques. Alternatively, we propose an accelerated variance-reduced backward-forward splitting (BFS) method, which attains similar convergence rates and oracle complexity as our FBS method. Finally, we validate our results through several numerical experiments and compare their performance.

Current sign language machine translation systems rely on recognizing hand movements, facial expressions and body postures, and natural language processing, to convert signs into text. Recent approaches use Transformer architectures to model long-range dependencies via positional encoding. However, they lack accuracy in recognizing fine-grained, short-range temporal dependencies between gestures captured at high frame rates. Moreover, their high computational complexity leads to inefficient training. To mitigate these issues, we propose an Adaptive Transformer (ADAT), which incorporates components for enhanced feature extraction and adaptive feature weighting through a gating mechanism to emphasize contextually relevant features while reducing training overhead and maintaining translation accuracy. To evaluate ADAT, we introduce MedASL, the first public medical American Sign Language dataset. In sign-to-gloss-to-text experiments, ADAT outperforms the encoder-decoder transformer, improving BLEU-4 accuracy by 0.1% while reducing training time by 14.33% on PHOENIX14T and 3.24% on MedASL. In sign-to-text experiments, it improves accuracy by 8.7% and reduces training time by 2.8% on PHOENIX14T and achieves 4.7% higher accuracy and 7.17% faster training on MedASL. Compared to encoder-only and decoder-only baselines in sign-to-text, ADAT is at least 6.8% more accurate despite being up to 12.1% slower due to its dual-stream structure.

This invited paper introduces the concept of "proof-carrying neuro-symbolic code" and explains its meaning and value, from both the "neural" and the "symbolic" perspectives. The talk outlines the first successes and challenges that this new area of research faces. Keywords: Neural Networks Cyber-Physical System Verification Programming Languages Neuro-Symbolic Programs. 1 Neuro-Symbolic Proofs and Programs Proof Carrying Code is a long tradition within programming language research, broadly referring to methods that interleave verification with executable code, thus avoiding the inevitable discrepancies that arise when the code and the proofs are handled in different languages. Although the term was coined by Necula [50] almost three decades ago, with time, it grew to encompass any languages that are powerful enough to handle both the coding and the proving. Examples are dependently-typed (Agda, Idris, Coq/Rocq) and refinement-typed (F*, Liquid Haskell) languages.

Image decomposition offers deep insights into the imaging factors of visual data and significantly enhances various advanced computer vision tasks. In this work, we introduce a novel approach to low-light image enhancement based on decomposed physics-informed priors. Existing methods that directly map low-light to normal-light images in the sRGB color space suffer from inconsistent color predictions and high sensitivity to spectral power distribution (SPD) variations, resulting in unstable performance under diverse lighting conditions. To address these challenges, we introduce a Physics-informed Color-aware Transform (PiCat), a learning-based framework that converts low-light images from the sRGB color space into deep illumination-invariant descriptors via our proposed Color-aware Transform (CAT). This transformation enables robust handling of complex lighting and SPD variations. Complementing this, we propose the Content-Noise Decomposition Network (CNDN), which refines the descriptor distributions to better align with well-lit conditions by mitigating noise and other distortions, thereby effectively restoring content representations to low-light images. The CAT and the CNDN collectively act as a physical prior, guiding the transformation process from low-light to normal-light domains. Our proposed PiCat framework demonstrates superior performance compared to state-of-the-art methods across five benchmark datasets.

Neural networks often have identifiable computational structures - components of the network which perform an interpretable algorithm or task - but the mechanisms by which these emerge and the best methods for detecting these structures are not well understood. In this paper we investigate the emergence of computational structure in a transformer-like model trained to simulate the physics of a particle system, where the transformer's attention mechanism is used to transfer information between particles. We show that (a) structures emerge in the attention heads of the transformer which learn to detect particle collisions, (b) the emergence of these structures is associated to degenerate geometry in the loss landscape, and (c) the dynamics of this emergence follows a power law. This suggests that these components are governed by a degenerate "effective potential". These results have implications for the convergence time of computational structure within neural networks and suggest that the emergence of computational structure can be detected by studying the dynamics of network components.

The low-quality structure in raw depth maps is prevalent in real-world RGB-D datasets, which makes real-world depth recovery a critical task in recent years. However, the lack of paired raw-ground truth (raw-GT) data in the real world poses challenges for generalized depth recovery. Existing methods insufficiently consider the diversity of structure misalignment in raw depth maps, which leads to poor generalization in real-world depth recovery. Notably, random structure misalignments are not limited to raw depth data but also affect GT depth in real-world datasets. In the proposed method, we tackle the generalization problem from both input and output perspectives. For input, we enrich the diversity of structure misalignment in raw depth maps by designing a new raw depth generation pipeline, which helps the network avoid overfitting to a specific condition. Furthermore, a structure uncertainty module is designed to explicitly identify the misaligned structure for input raw depth maps to better generalize in unseen scenarios. Notably the well-trained depth foundation model (DFM) can help the structure uncertainty module estimate the structure uncertainty better. For output, a robust feature alignment module is designed to precisely align with the accurate structure of RGB images avoiding the interference of inaccurate GT depth. Extensive experiments on multiple datasets demonstrate the proposed method achieves competitive accuracy and generalization capabilities across various challenging raw depth maps.

Although Arabic is spoken by over 400 million people, advanced Arabic writing assistance tools remain limited. To address this gap, we present ARWI, a new writing assistant that helps learners improve essay writing in Modern Standard Arabic. ARWI is the first publicly available Arabic writing assistant to include a prompt database for different proficiency levels, an Arabic text editor, state-of-the-art grammatical error detection and correction, and automated essay scoring aligned with the Common European Framework of Reference standards for language attainment. Moreover, ARWI can be used to gather a growing auto-annotated corpus, facilitating further research on Arabic grammar correction and essay scoring, as well as profiling patterns of errors made by native speakers and non-native learners. A preliminary user study shows that ARWI provides actionable feedback, helping learners identify grammatical gaps, assess language proficiency, and guide improvement.