We propose a new convex loss for Support Vector Machines, both for the binary classification and for the regression models. Therefore, we show the mathematical derivation of the dual problems and we experiment with them on several small datasets. The minimal dimension of those datasets is due to the difficult scalability of the SVM method to bigger instances. This preliminary study should prove that using pattern correlations inside the loss function could enhance the generalisation performances. Our method consistently achieved comparable or superior performance, with improvements of up to 2.0% in F1 scores for classification tasks and 1.0% reduction in Mean Squared Error (MSE) for regression tasks across various datasets, compared to standard losses. Coherently, results show that generalisation measures are never worse than the standard losses and several times they are better. In our opinion, it should be considered a careful study of this loss, coupled with shallow and deep neural networks. In fact, we present some novel results obtained with those architectures.

LLM unlearning is a technique to remove the impacts of undesirable knowledge from the model without retraining from scratch, which is indispensable towards trustworthy AI. Existing unlearning methods face significant limitations: conventional tuning-based unlearning is computationally heavy and prone to catastrophic forgetting. In contrast, in-contextualized unlearning is lightweight for precise unlearning but vulnerable to prompt removal or reverse engineering attacks. In response, we propose Distilled Unlearning from an Efficient Teacher (DUET), a novel distillation-based unlearning method that combines the merits of these two lines of work. It learns a student model to imitate the behavior of a prompt-steered teacher that effectively refuses undesirable knowledge generation while preserving general domain knowledge. Extensive evaluations on existing benchmarks with our enriched evaluation protocols demonstrate that DUET achieves higher performance in both forgetting and utility preservation, while being orders of magnitude more data-efficient than state-of-the-art unlearning methods.

Neural networks are growing more capable on their own, but we do not understand their neural mechanisms. Understanding these mechanisms' decision-making processes, or mechanistic interpretability, enables (1) accountability and control in high-stakes domains, (2) the study of digital brains and the emergence of cognition, and (3) discovery of new knowledge when AI systems outperform humans. This paper traces how attention head intervention emerged as a key method for causal interpretability of transformers. The evolution from visualization to intervention represents a paradigm shift from observing correlations to causally validating mechanistic hypotheses through direct intervention. Head intervention studies revealed robust empirical findings while also highlighting limitations that complicate interpretation. Recent work demonstrates that mechanistic understanding now enables targeted control of model behaviour, successfully suppressing toxic outputs and manipulating semantic content through selective attention head intervention, validating the practical utility of interpretability research for AI safety.

Autonomous driving requires generating safe and reliable trajectories from complex multimodal inputs. Traditional modular pipelines separate perception, prediction, and planning, while recent end-to-end (E2E) systems learn them jointly. Vision-language models (VLMs) further enrich this paradigm by introducing cross-modal priors and commonsense reasoning, yet current VLM-based planners face three key challenges: (i) a mismatch between discrete text reasoning and continuous control, (ii) high latency from autoregressive chain-of-thought decoding, and (iii) inefficient or non-causal planners that limit real-time deployment. We propose ColaVLA, a unified vision-language-action framework that transfers reasoning from text to a unified latent space and couples it with a hierarchical, parallel trajectory decoder. The Cognitive Latent Reasoner compresses scene understanding into compact, decision-oriented meta-action embeddings through ego-adaptive selection and only two VLM forward passes. The Hierarchical Parallel Planner then generates multi-scale, causality-consistent trajectories in a single forward pass. Together, these components preserve the generalization and interpretability of VLMs while enabling efficient, accurate and safe trajectory generation. Experiments on the nuScenes benchmark show that ColaVLA achieves state-of-the-art performance in both open-loop and closed-loop settings with favorable efficiency and robustness.

Large Language Models (LLMs) are prone to memorizing training data, which poses serious privacy risks. Two of the most prominent concerns are training data extraction and Membership Inference Attacks (MIAs). Prior research has shown that these threats are interconnected: adversaries can extract training data from an LLM by querying the model to generate a large volume of text and subsequently applying MIAs to verify whether a particular data point was included in the training set. In this study, we integrate multiple MIA techniques into the data extraction pipeline to systematically benchmark their effectiveness. We then compare their performance in this integrated setting against results from conventional MIA benchmarks, allowing us to evaluate their practical utility in real-world extraction scenarios.

Long video understanding is essential for human-like intelligence, enabling coherent perception and reasoning over extended temporal contexts. While the emerging thinking-with-frames paradigm, which alternates between global temporal reasoning and local frame examination, has advanced the reasoning capabilities of video multi-modal large language models (MLLMs), it suffers from a significant efficiency bottleneck due to the progressively growing and redundant multi-modal context. To address this, we propose SpecTemp, a reinforcement learning-based Speculative Temporal reasoning framework that decouples temporal perception from reasoning via a cooperative dual-model design. In SpecTemp, a lightweight draft MLLM rapidly explores and proposes salient frames from densely sampled temporal regions, while a powerful target MLLM focuses on temporal reasoning and verifies the draft's proposals, iteratively refining its attention until convergence. This design mirrors the collaborative pathways of the human brain, balancing efficiency with accuracy. To support training, we construct the SpecTemp-80K dataset, featuring synchronized dual-level annotations for coarse evidence spans and fine-grained frame-level evidence. Experiments across multiple video understanding benchmarks demonstrate that SpecTemp not only maintains competitive accuracy but also significantly accelerates inference compared with existing thinking-with-frames methods.

Flow matching models effectively represent complex distributions, yet estimating expectations of functions of their outputs remains challenging under limited sampling budgets. Independent sampling often yields high-variance estimates, especially when rare but high-impact outcomes dominate the expectation. We propose a non-IID sampling framework that jointly draws multiple samples to cover diverse, salient regions of a flow matching model's generative distribution. To balance diversity and quality, we introduce a score-based regularization for the diversity mechanism (SR), which uses the score function, i.e., the gradient of the log probability, to ensure samples are pushed apart within high-density regions of the data manifold, mitigating off-manifold drift. To enable unbiased estimation when desired, we further develop an approach for importance weighting of non-IID flow samples by learning a residual velocity field that reproduces the marginal distribution of the non-IID samples and by evolving importance weights along trajectories. Empirically, our method produces diverse, high-quality samples and accurate estimates of both importance weights and expectations, advancing the reliable characterization of flow matching model outputs. Our code will be publicly available on GitHub.

Machine unlearning algorithms aim to remove the impact of selected training data from a model without the computational expenses of retraining from scratch. Two such algorithms are ``Descent-to-Delete" (D2D) and ``Rewind-to-Delete" (R2D), full-batch gradient descent algorithms that are easy to implement and satisfy provable unlearning guarantees. In particular, the stochastic version of D2D is widely implemented as the ``finetuning" unlearning baseline, despite lacking theoretical backing on nonconvex functions. In this work, we prove $(\varepsilon, δ)$ certified unlearning guarantees for stochastic R2D and D2D for strongly convex, convex, and nonconvex loss functions, by analyzing unlearning through the lens of disturbed or biased gradient systems, which may be contracting, semi-contracting, or expansive respectively. Our argument relies on optimally coupling the random behavior of the unlearning and retraining trajectories, resulting in a sensitivity bound that holds in expectation that yields $(\varepsilon, δ)$ unlearning. We determine that D2D can yield tighter guarantees for strongly convex functions, but R2D is more appropriate for convex and nonconvex functions. Finally, we compare the algorithms empirically, demonstrating the strengths and weaknesses of each approach.

We introduce an Analyze-Revise-Finetune (ARF) pipeline that enables smaller open-source language models (LLMs) to surpass substantially larger proprietary models in customer service summarization tasks. The pipeline first analyzes and categorizes common errors in summaries produced by a teacher model (GPT-3.5), then performs a targeted revision using a compact editor model (Llama 3.1 70B) to generate high-quality, refined training data. Fine-tuning smaller student models (e.g., Llama 3.1 8B, QWen3 4B) on this refined data resulted in superior summarization performance compared to GPT-3.5. The ARF pipeline improves cost efficiency and data privacy while maintaining competitive accuracy, illustrating a generalizable framework for enhancing open-source LLMs across diverse downstream applications.

We perform in-depth evaluations of in-context learning (ICL) on state-of-the-art transformer, state-space, and hybrid large language models over two categories of knowledge-based ICL tasks. Using a combination of behavioral probing and intervention-based methods, we have discovered that, while LLMs of different architectures can behave similarly in task performance, their internals could remain different. We discover that function vectors (FVs) responsible for ICL are primarily located in the self-attention and Mamba layers, and speculate that Mamba2 uses a different mechanism from FVs to perform ICL. FVs are more important for ICL involving parametric knowledge retrieval, but not for contextual knowledge understanding. Our work contributes to a more nuanced understanding across architectures and task types. Methodologically, our approach also highlights the importance of combining both behavioural and mechanistic analyses to investigate LLM capabilities.

Despite the widespread adoption of Large Language Models (LLMs), their strongest capabilities remain largely confined to a small number of high-resource languages for which there is abundant training data. Recently, continual pre-training (CPT) has emerged as a means to fine-tune these models to low-resource regional dialects. In this paper, we study the use of CPT for dialect learning under tight data and compute budgets. Using low-rank adaptation (LoRA) and compute-efficient continual pre-training, we adapt three LLMs to the Québec French dialect using a very small dataset and benchmark them on the COLE suite. Our experiments demonstrate an improvement on the minority dialect benchmarks with minimal regression on the prestige language benchmarks with around 1% of model parameters updated. Analysis of the results demonstrate that gains are highly contingent on corpus composition. These findings indicate that CPT with parameter-efficient fine-tuning (PEFT) can narrow the dialect gap by providing cost-effective and sustainable language resource creation, expanding high-quality LLM access to minority linguistic communities. To support reproducibility and broaden access, we release the first Québec French LLMs on Hugging Face.

Motivated by the geometric advantages of quaternions in representing rotations and postures, we propose a quaternion-valued supervised learning Hopfield-structured neural network (QSHNN) with a fully connected structure inspired by the classic Hopfield neural network (HNN). Starting from a continuous-time dynamical model of HNNs, we extend the formulation to the quaternionic domain and establish the existence and uniqueness of fixed points with asymptotic stability. For the learning rules, we introduce a periodic projection strategy that modifies standard gradient descent by periodically projecting each 4*4 block of the weight matrix onto the closest quaternionic structure in the least-squares sense. This approach preserves both convergence and quaternionic consistency throughout training. Benefiting from this rigorous mathematical foundation, the experimental model implementation achieves high accuracy, fast convergence, and strong reliability across randomly generated target sets. Moreover, the evolution trajectories of the QSHNN exhibit well-bounded curvature, i.e., sufficient smoothness, which is crucial for applications such as control systems or path planning modules in robotic arms, where joint postures are parameterized by quaternion neurons. Beyond these application scenarios, the proposed model offers a practical implementation framework and a general mathematical methodology for designing neural networks under hypercomplex or non-commutative algebraic structures.

Existing semi-supervised video anomaly detection (VAD) methods often struggle with detecting complex anomalies involving object interactions and generally lack explainability. To overcome these limitations, we propose a novel VAD framework leveraging Multimodal Large Language Models (MLLMs). Unlike previous MLLM-based approaches that make direct anomaly judgments at the frame level, our method focuses on extracting and interpreting object activity and interactions over time. By querying an MLLM with visual inputs of object pairs at different moments, we generate textual descriptions of the activity and interactions from nominal videos. These textual descriptions serve as a high-level representation of the activity and interactions of objects in a video. They are used to detect anomalies during test time by comparing them to textual descriptions found in nominal training videos. Our approach inherently provides explainability and can be combined with many traditional VAD methods to further enhance their interpretability. Extensive experiments on benchmark datasets demonstrate that our method not only detects complex interaction-based anomalies effectively but also achieves state-of-the-art performance on datasets without interaction anomalies.

In this paper, we propose a rotation-constrained compensation method to address the errors introduced by structured pruning of large language models (LLMs). LLMs are trained on massive datasets and accumulate rich semantic knowledge in their representation space. In contrast, pruning is typically carried out with only a small amount of calibration data, which makes output mismatches unavoidable. Although direct least-squares fitting can reduce such errors, it tends to overfit to the limited calibration set, destructively modifying pretrained weights. To overcome this difficulty, we update the pruned parameters under a rotation constraint. This constrained update preserves the geometry of output representations (i.e., norms and inner products) and simultaneously re-aligns the pruned subspace with the original outputs. Furthermore, in rotation-constrained compensation, removing components that strongly contribute to the principal directions of the output makes error recovery difficult. Since input dimensions with large variance strongly affect these principal directions, we design a variance-aware importance score that ensures such dimensions are preferentially kept in the pruned model. By combining this scoring rule with rotation-constrained updates, the proposed method effectively compensates errors while retaining the components likely to be more important in a geometry-preserving manner. In the experiments, we apply the proposed method to Llama-7B and Llama-2-13B, and evaluate it on WikiText2 and multiple language understanding benchmarks. The results demonstrate consistently better perplexity and task accuracy compared with existing baselines.

A core challenge in scientific machine learning, and scientific computing more generally, is modeling continuous phenomena which (in practice) are represented discretely. Machine-learned operators (MLOs) have been introduced as a means to achieve this modeling goal, as this class of architecture can perform inference at arbitrary resolution. In this work, we evaluate whether this architectural innovation is sufficient to perform "zero-shot super-resolution," namely to enable a model to serve inference on higher-resolution data than that on which it was originally trained. We comprehensively evaluate both zero-shot sub-resolution and super-resolution (i.e., multi-resolution) inference in MLOs. We decouple multi-resolution inference into two key behaviors: 1) extrapolation to varying frequency information; and 2) interpolating across varying resolutions. We empirically demonstrate that MLOs fail to do both of these tasks in a zero-shot manner. Consequently, we find MLOs are not able to perform accurate inference at resolutions different from those on which they were trained, and instead they are brittle and susceptible to aliasing. To address these failure modes, we propose a simple, computationally-efficient, and data-driven multi-resolution training protocol that overcomes aliasing and that provides robust multi-resolution generalization.

Automated interpretability aims to translate large language model (LLM) features into human understandable descriptions. However, natural language feature descriptions can be vague, inconsistent, and require manual relabeling. In response, we introduce semantic regexes, structured language descriptions of LLM features. By combining primitives that capture linguistic and semantic patterns with modifiers for contextualization, composition, and quantification, semantic regexes produce precise and expressive feature descriptions. Across quantitative benchmarks and qualitative analyses, semantic regexes match the accuracy of natural language while yielding more concise and consistent feature descriptions. Their inherent structure affords new types of analyses, including quantifying feature complexity across layers, scaling automated interpretability from insights into individual features to model-wide patterns. Finally, in user studies, we find that semantic regexes help people build accurate mental models of LLM features.

Mixtures of linear dynamical systems (MoLDS) provide a path to model time-series data that exhibit diverse temporal dynamics across trajectories. However, its application remains challenging in complex and noisy settings, limiting its effectiveness for neural data analysis. Tensor-based moment methods can provide global identifiability guarantees for MoLDS, but their performance degrades under noise and complexity. Commonly used expectation-maximization (EM) methods offer flexibility in fitting latent models but are highly sensitive to initialization and prone to poor local minima. Here, we propose a tensor-based method that provides identifiability guarantees for learning MoLDS, which is followed by EM updates to combine the strengths of both approaches. The novelty in our approach lies in the construction of moment tensors using the input-output data to recover globally consistent estimates of mixture weights and system parameters. These estimates can then be refined through a Kalman EM algorithm, with closed-form updates for all LDS parameters. We validate our framework on synthetic benchmarks and real-world datasets. On synthetic data, the proposed Tensor-EM method achieves more reliable recovery and improved robustness compared to either pure tensor or randomly initialized EM methods. We then analyze neural recordings from the primate somatosensory cortex while a non-human primate performs reaches in different directions. Our method successfully models and clusters different conditions as separate subsystems, consistent with supervised single-LDS fits for each condition. Finally, we apply this approach to another neural dataset where monkeys perform a sequential reaching task. These results demonstrate that MoLDS provides an effective framework for modeling complex neural data, and that Tensor-EM is a reliable approach to MoLDS learning for these applications.

We study optimizing a destination-to-chutes task mapping to improve throughput in Robotic Sorting Systems (RSS), where a team of robots sort packages on a sortation floor by transporting them from induct workstations to eject chutes based on their shipping destinations (e.g. Los Angeles or Pittsburgh). The destination-to-chutes task mapping is used to determine which chutes a robot can drop its package. Finding a high-quality task mapping is challenging because of the complexity of a real-world RSS. First, optimizing task mapping is interdependent with robot target assignment and path planning. Second, chutes will be CLOSED for a period of time once they receive sufficient packages to allow for downstream processing. Third, task mapping quality directly impacts the downstream processing, as scattered chutes for the same destination increase package handling time. In this paper, we first formally define task mappings and the problem of Task Mapping Optimization (TMO). We then present a simulator of RSS to evaluate task mappings. We then present a simple TMO method based on the Evolutionary Algorithm and Mixed Integer Linear Programming, demonstrating the advantage of our optimized task mappings over the greedily generated ones in various RSS setups with different map sizes, numbers of chutes, and destinations. Finally, we use Quality Diversity algorithms to analyze the throughput of a diverse set of task mappings. Our code is available online at https://github.com/lunjohnzhang/tmo_public.

Large language models (LLMs) have demonstrated notable potential in medical applications, yet they face substantial challenges in handling complex real-world clinical diagnoses using conventional prompting methods. Current prompt engineering and multi-agent approaches typically optimize isolated inferences, neglecting the accumulation of reusable clinical experience. To address this, this study proposes a novel Multi-Agent Clinical Diagnosis (MACD) framework, which allows LLMs to self-learn clinical knowledge via a multi-agent pipeline that summarizes, refines, and applies diagnostic insights. It mirrors how physicians develop expertise through experience, enabling more focused and accurate diagnosis on key disease-specific cues. We further extend it to a MACD-human collaborative workflow, where multiple LLM-based diagnostician agents engage in iterative consultations, supported by an evaluator agent and human oversight for cases where agreement is not reached. Evaluated on 4,390 real-world patient cases across seven diseases using diverse open-source LLMs (Llama-3.1 8B/70B, DeepSeek-R1-Distill-Llama 70B), MACD significantly improves primary diagnostic accuracy, outperforming established clinical guidelines with gains up to 22.3% (MACD). In direct comparison with physician-only diagnosis under the same evaluation protocol, MACD achieves comparable or superior performance, with improvements up to 16%. Furthermore, the MACD-human workflow yields an 18.6% improvement over physician-only diagnosis, demonstrating the synergistic potential of human-AI collaboration. Notably, the self-learned clinical knowledge exhibits strong cross-model stability, transferability across LLMs, and capacity for model-specific personalization.This work thus presents a scalable self-learning paradigm that bridges the gap between the intrinsic knowledge of LLMs.

Multimodal models, such as the Contrastive Language-Image Pre-training (CLIP) model, have demonstrated remarkable success in aligning visual and linguistic representations. However, these models exhibit limitations when applied to specialised visual domains, such as diagrams, which encode structured, symbolic information distinct from that of natural imagery. In this paper, we introduce a novel training paradigm explicitly designed to enhance the comprehension of diagrammatic images within vision-language models. Our approach uses ``hard'' samples for our proposed contrastive learning that incorporates two specialised loss functions that leverage the inherent structural properties of diagrams. By integrating these objectives into model training, our method enables models to develop a more structured and semantically coherent understanding of diagrammatic content. We empirically validate our approach on a benchmark dataset of flowcharts, as a representative class of diagrammatic imagery, demonstrating substantial improvements over standard CLIP and conventional hard negative CLIP learning paradigms for both image-text matching and visual question answering tasks. Our findings underscore the significance of tailored training strategies for specialised tasks and contribute to advancing diagrammatic understanding within the broader landscape of vision-language integration.

Despite its significance, Arabic, a linguistically rich and morphologically complex language, faces the challenge of being under-resourced. The scarcity of large annotated datasets hampers the development of accurate tools for subjectivity analysis in Arabic. Recent advances in deep learning and Transformers have proven highly effective for text classification in English and French. This paper proposes a new approach for subjectivity assessment in Arabic textual data. To address the dearth of specialized annotated datasets, we developed a comprehensive dataset, AraDhati+, by leveraging existing Arabic datasets and collections (ASTD, LABR, HARD, and SANAD). Subsequently, we fine-tuned state-of-the-art Arabic language models (XLM-RoBERTa, AraBERT, and ArabianGPT) on AraDhati+ for effective subjectivity classification. Furthermore, we experimented with an ensemble decision approach to harness the strengths of individual models. Our approach achieves a remarkable accuracy of 97.79\,\% for Arabic subjectivity classification. Results demonstrate the effectiveness of the proposed approach in addressing the challenges posed by limited resources in Arabic language processing.

In this work, we present a simple yet theoretically motivated improvement to Supervised Fine-Tuning (SFT) for the Large Language Model (LLM), addressing its limited generalization compared to reinforcement learning (RL). Through mathematical analysis, we reveal that standard SFT gradients implicitly encode a problematic reward structure that may severely restrict the generalization capabilities of model compared to RL. To rectify this, we propose Dynamic Fine-Tuning (\model), stabilizing gradient updates for each token by dynamically rescaling the objective function with the probability of this token. With just a single-line change, the method outperforms standard SFT on multiple difficult benchmarks and base models, from math reasoning to code generation and multi-modal tasks, demonstrating improved generalization. Additionally, \model~achieves competitive results in offline RL settings, providing an effective yet streamlined alternative. By bridging theoretical insights with practical solutions, this work advances the state of SFT. The source code will be available at https://github.com/yongliang-wu/DFT.

Vision-Language Models (VLMs) like CLIP have demonstrated remarkable generalization in zero- and few-shot settings, but adapting them efficiently to decentralized, heterogeneous data remains a challenge. While prompt tuning has emerged as a popular parameter-efficient approach in personalized federated learning, existing methods often sacrifice generalization in favor of personalization, struggling particularly on unseen classes or domains. In this work, we propose pFedMMA, the first personalized federated learning framework that leverages multi-modal adapters for vision-language tasks. Each adapter contains modality-specific up- and down-projection layers alongside a globally shared projection that aligns cross-modal features. Our optimization strategy allows clients to locally adapt to personalized data distributions while collaboratively training the shared projection to improve global generalization. This design is also communication-efficient, as only the shared component is exchanged during communication rounds. Through extensive experiments across eleven datasets, including domain- and label-shift scenarios, we show that pFedMMA achieves state-of-the-art trade-offs between personalization and generalization, outperforming recent federated prompt tuning methods.

We propose a concept-based adversarial attack framework that extends beyond single-image perturbations by adopting a probabilistic perspective. Rather than modifying a single image, our method operates on an entire concept - represented by a distribution - to generate diverse adversarial examples. Preserving the concept is essential, as it ensures that the resulting adversarial images remain identifiable as instances of the original underlying category or identity. By sampling from this concept-based adversarial distribution, we generate images that maintain the original concept but vary in pose, viewpoint, or background, thereby misleading the classifier. Mathematically, this framework remains consistent with traditional adversarial attacks in a principled manner. Our theoretical and empirical results demonstrate that concept-based adversarial attacks yield more diverse adversarial examples and effectively preserve the underlying concept, while achieving higher attack efficiency.

Large Language Models (LLMs) are expected to provide helpful and harmless responses, yet they often exhibit sycophancy--conforming to user beliefs regardless of factual accuracy or ethical soundness. Prior research on sycophancy has primarily focused on single-turn factual correctness, overlooking the dynamics of real-world interactions. In this work, we introduce SYCON Bench, a novel benchmark for evaluating sycophantic behavior in multi-turn, free-form conversational settings. Our benchmark measures how quickly a model conforms to the user (Turn of Flip) and how frequently it shifts its stance under sustained user pressure (Number of Flip). Applying SYCON Bench to 17 LLMs across three real-world scenarios, we find that sycophancy remains a prevalent failure mode. Our analysis shows that alignment tuning amplifies sycophantic behavior, whereas model scaling and reasoning optimization strengthen the model's ability to resist undesirable user views. Reasoning models generally outperform instruction-tuned models but often fail when they over-index on logical exposition instead of directly addressing the user's underlying beliefs. Finally, we evaluate four additional prompting strategies and demonstrate that adopting a third-person perspective reduces sycophancy by up to 63.8% in debate scenario. We release our code and data at https://github.com/JiseungHong/SYCON-Bench.

The relationship between inverse reinforcement learning (IRL) and inverse optimization (IO) for Markov decision processes (MDPs) has been relatively underexplored in the literature, despite addressing the same problem. In this work, we revisit the relationship between the IO framework for MDPs, IRL, and apprenticeship learning (AL). We incorporate prior beliefs on the structure of the cost function into the IRL and AL problems, and demonstrate that the convex-analytic view of the AL formalism emerges as a relaxation of our framework. Notably, the AL formalism is a special case in our framework when the regularization term is absent. Focusing on the suboptimal expert setting, we formulate the AL problem as a regularized min-max problem. The regularizer plays a key role in addressing the ill-posedness of IRL by guiding the search for plausible cost functions. To solve the resulting regularized-convex-concave-min-max problem, we use stochastic mirror descent (SMD) and establish convergence bounds for the proposed method. Numerical experiments highlight the critical role of regularization in learning cost vectors and apprentice policies.

Modern machine learning increasingly leverages the insight that high-dimensional data often lie near low-dimensional, non-linear manifolds, an idea known as the manifold hypothesis. By explicitly modeling the geometric structure of data through learning Riemannian geometry algorithms can achieve improved performance and interpretability in tasks like clustering, dimensionality reduction, and interpolation. In particular, learned pullback geometry has recently undergone transformative developments that now make it scalable to learn and scalable to evaluate, which further opens the door for principled non-linear data analysis and interpretable machine learning. However, there are still steps to be taken when considering real-world multi-modal data. This work focuses on addressing distortions and modeling errors that can arise in the multi-modal setting and proposes to alleviate both challenges through isometrizing the learned Riemannian structure and balancing regularity and expressivity of the diffeomorphism parametrization. We showcase the effectiveness of the synergy of the proposed approaches in several numerical experiments with both synthetic and real data.

Sentiment analysis is a crucial task in natural language processing (NLP) that enables the extraction of meaningful insights from textual data, particularly from dynamic platforms like Twitter and IMDB. This study explores a hybrid framework combining transformer-based models, specifically BERT, GPT-2, RoBERTa, XLNet, and DistilBERT, to improve sentiment classification accuracy and robustness. The framework addresses challenges such as noisy data, contextual ambiguity, and generalization across diverse datasets by leveraging the unique strengths of these models. BERT captures bidirectional context, GPT-2 enhances generative capabilities, RoBERTa optimizes contextual understanding with larger corpora and dynamic masking, XLNet models dependency through permutation-based learning, and DistilBERT offers efficiency with reduced computational overhead while maintaining high accuracy. We demonstrate text cleaning, tokenization, and feature extraction using Term Frequency Inverse Document Frequency (TF-IDF) and Bag of Words (BoW), ensure high-quality input data for the models. The hybrid approach was evaluated on benchmark datasets Sentiment140 and IMDB, achieving superior accuracy rates of 94\% and 95\%, respectively, outperforming standalone models. The results validate the effectiveness of combining multiple transformer models in ensemble-like setups to address the limitations of individual architectures. This research highlights its applicability to real-world tasks such as social media monitoring, customer sentiment analysis, and public opinion tracking which offers a pathway for future advancements in hybrid NLP frameworks.

Traditional neural network regression models provide only point estimates, failing to capture predictive uncertainty. Probabilistic neural networks (PNNs) address this limitation by producing output distributions, enabling the construction of prediction intervals. However, the common assumption of Gaussian output distributions often results in overly wide intervals, particularly in the presence of outliers or deviations from normality. To enhance the adaptability of PNNs, we propose t-Distributed Neural Networks (TDistNNs), which generate t-distributed outputs, parameterized by location, scale, and degrees of freedom. The degrees of freedom parameter allows TDistNNs to model heavy-tailed predictive distributions, improving robustness to non-Gaussian data and enabling more adaptive uncertainty quantification. We incorporate a likelihood based on the t-distribution into neural network training and derive efficient gradient computations for seamless integration into deep learning frameworks. Empirical evaluations on synthetic and real-world data demonstrate that TDistNNs improve the balance between coverage and interval width. Notably, for identical architectures, TDistNNs consistently produce narrower prediction intervals than Gaussian-based PNNs while maintaining proper coverage. This work contributes a flexible framework for uncertainty estimation in neural networks tasked with regression, particularly suited to settings involving complex output distributions.

Multi-illuminant color constancy methods aim to eliminate local color casts within an image through pixel-wise illuminant estimation. Existing methods mainly employ deep learning to establish a direct mapping between an image and its illumination map, which neglects the impact of image scales. To alleviate this problem, we represent an illuminant map as the linear combination of components estimated from multi-scale images. Furthermore, we propose a tri-branch convolution networks to estimate multi-grained illuminant distribution maps from multi-scale images. These multi-grained illuminant maps are merged adaptively with an attentional illuminant fusion module. Through comprehensive experimental analysis and evaluation, the results demonstrate the effectiveness of our method, and it has achieved state-of-the-art performance.