We establish closed-form enumeration formulas for chromatic feature vectors of 2-trees under the bichromatic triangle constraint. These efficiently computable structural features derive from constrained graph colorings where each triangle uses exactly two colors, forbidding monochromatic and rainbow triangles, a constraint arising in distributed systems where components avoid complete concentration or isolation. For theta graphs Theta_n, we prove r_k(Theta_n) = S(n-2, k-1) for k >= 3 (Stirling numbers of the second kind) and r_2(Theta_n) = 2^(n-2) + 1, computable in O(n) time. For fan graphs Phi_n, we establish r_2(Phi_n) = F_{n+1} (Fibonacci numbers) and derive explicit formulas r_k(Phi_n) = sum_{t=k-1}^{n-1} a_{n-1,t} * S(t, k-1) with efficiently computable binomial coefficients, achieving O(n^2) computation per component. Unlike classical chromatic polynomials, which assign identical features to all n-vertex 2-trees, bichromatic constraints provide informative structural features. While not complete graph invariants, these features capture meaningful structural properties through connections to Fibonacci polynomials, Bell numbers, and independent set enumeration. Applications include Byzantine fault tolerance in hierarchical networks, VM allocation in cloud computing, and secret-sharing protocols in distributed cryptography.

Many optimization tasks involve streaming data with unknown concept drifts, posing a significant challenge as Streaming Data-Driven Optimization (SDDO). Existing methods, while leveraging surrogate model approximation and historical knowledge transfer, are often under restrictive assumptions such as fixed drift intervals and fully environmental observability, limiting their adaptability to diverse dynamic environments. We propose TRACE, a TRAnsferable C}oncept-drift Estimator that effectively detects distributional changes in streaming data with varying time scales. TRACE leverages a principled tokenization strategy to extract statistical features from data streams and models drift patterns using attention-based sequence learning, enabling accurate detection on unseen datasets and highlighting the transferability of learned drift patterns. Further, we showcase TRACE's plug-and-play nature by integrating it into a streaming optimizer, facilitating adaptive optimization under unknown drifts. Comprehensive experimental results on diverse benchmarks demonstrate the superior generalization, robustness, and effectiveness of our approach in SDDO scenarios.

Among the various types of cyberattacks, identifying zero-day attacks is problematic because they are unknown to security systems as their pattern and characteristics do not match known blacklisted attacks. There are many Machine Learning (ML) models designed to analyze and detect network attacks, especially using supervised models. However, these models are designed to classify samples (normal and attacks) based on the patterns they learn during the training phase, so they perform inefficiently on unseen attacks. This research addresses this issue by evaluating five different supervised models to assess their performance and execution time in predicting zero-day attacks and find out which model performs accurately and quickly. The goal is to improve the performance of these supervised models by not only proposing a framework that applies grid search, dimensionality reduction and oversampling methods to overcome the imbalance problem, but also comparing the effectiveness of oversampling on ml model metrics, in particular the accuracy. To emulate attack detection in real life, this research applies a highly imbalanced data set and only exposes the classifiers to zero-day attacks during the testing phase, so the models are not trained to flag the zero-day attacks. Our results show that Random Forest (RF) performs best under both oversampling and non-oversampling conditions, this increased effectiveness comes at the cost of longer processing times. Therefore, we selected XG Boost (XGB) as the top model due to its fast and highly accurate performance in detecting zero-day attacks.

We propose new methodologies for both unlearning random set of samples and class unlearning and show that they outperform existing methods. The main driver of our unlearning methods is the similarity of predictions to a retrained model on both the forget and remain samples. We introduce Adversarial Machine UNlearning (AMUN), which surpasses prior state-of-the-art methods for image classification based on SOTA MIA scores. AMUN lowers the model's confidence on forget samples by fine-tuning on their corresponding adversarial examples. Through theoretical analysis, we identify factors governing AMUN's performance, including smoothness. To facilitate training of smooth models with a controlled Lipschitz constant, we propose FastClip, a scalable method that performs layer-wise spectral-norm clipping of affine layers. In a separate study, we show that increased smoothness naturally improves adversarial example transfer, thereby supporting the second factor above. Following the same principles for class unlearning, we show that existing methods fail in replicating a retrained model's behavior by introducing a nearest-neighbor membership inference attack (MIA-NN) that uses the probabilities assigned to neighboring classes to detect unlearned samples and demonstrate the vulnerability of such methods. We then propose a fine-tuning objective that mitigates this leakage by approximating, for forget-class inputs, the distribution over remaining classes that a model retrained from scratch would produce. To construct this approximation, we estimate inter-class similarity and tilt the target model's distribution accordingly. The resulting Tilted ReWeighting(TRW) distribution serves as the desired target during fine-tuning. Across multiple benchmarks, TRW matches or surpasses existing unlearning methods on prior metrics.

Currently, there is a noticeable lack of AI in the medical field to support doctors in treating heterogenous brain tumors such as Glioblastoma Multiforme (GBM), the deadliest human cancer in the world with a five-year survival rate of just 5.1%. This project develops an AI system offering the only end-to-end solution by aiding doctors with both diagnosis and treatment planning. In the diagnosis phase, a sequential decision-making framework consisting of 4 classification models (Convolutional Neural Networks and Support Vector Machine) are used. Each model progressively classifies the patient's brain into increasingly specific categories, with the final step being named diagnosis. For treatment planning, an RL system consisting of 3 generative models is used. First, the resection model (diffusion model) analyzes the diagnosed GBM MRI and predicts a possible resection outcome. Second, the radiotherapy model (Spatio-Temporal Vision Transformer) generates an MRI of the brain's progression after a user-defined number of weeks. Third, the chemotherapy model (Diffusion Model) produces the post-treatment MRI. A survival rate calculator (Convolutional Neural Network) then checks if the generated post treatment MRI has a survival rate within 15% of the user defined target. If not, a feedback loop using proximal policy optimization iterates over this system until an optimal resection location is identified. When compared to existing solutions, this project found 3 key findings: (1) Using a sequential decision-making framework consisting of 4 small diagnostic models reduced computing costs by 22.28x, (2) Transformers regression capabilities decreased tumor progression inference time by 113 hours, and (3) Applying Augmentations resembling Real-life situations improved overall DICE scores by 2.9%. These results project to increase survival rates by 0.9%, potentially saving approximately 2,250 lives.

Across standard test functions and ablations with/without line search, OGR variants match or outperform BFGS in final objective and step efficiency, with particular gains in nonconvex landscapes where saddle handling matters. Exact Hessians (via AD) are used only as an oracle baseline to evaluate estimation quality, not to form steps. II. Online Gradient Regression (OGR) Online Gradient Regression (OGR) is a second-order optimization framework that accelerates stochastic gradient descent (SGD) by online least-squares regression of noisy gradients to infer local curvature and the distance to a stationary point [3]. The central assumption is that, in a small neighborhood, the objective F (θ) is well-approximated by a quadratic model, so the gradient varies approximately linearly with the parameters. OGR maintains exponentially weighted statistics of recent (θ t, g t) pairs and updates a local model each iteration at negligible extra cost compared to computing the gradient itself [2], [3]. A. Direct multivariate approach In given time T, based on recent gradients g t R d and positions θ t R d for t < T, we would like to locally approximate behavior with 2nd order polynomial using parametrization: f (θ) = h + 1 2 (θ p) T H(θ p) f = H(θ p) for Hessian H R d d and p R d position of saddle or extremum. For local behavior we will work on averages with weights w t further decreasing exponentially, defining averages: v null t

We present a novel approach to EEG decoding for non-invasive brain-machine interfaces (BMIs), with a focus on motor-behavior classification. While conventional con-volutional architectures such as EEGNet and DeepConvNet are effective in capturing local spatial patterns, they are markedly less suited for modeling long-range temporal dependencies and nonlinear dynamics [1, 2]. To address this limitation, we integrate an Echo State Network (ESN), a prominent paradigm in reservoir computing into the decoding pipeline [3, 4, 5]. ESNs construct a high-dimensional, sparsely connected recurrent reservoir that excels at tracking temporal dynamics, thereby complementing the spatial representational power of CNNs. Evaluated on a skateboard-trick EEG dataset preprocessed via the PREP pipeline and implemented in MNE-Python, our ESNNet achieves 83.2% within-subject and 51.3% LOSO accuracies, surpassing widely used CNN-based baselines [6, 7].

Rapid expansion of social media platforms such as X (formerly Twitter), Facebook, and Reddit has enabled large-scale analysis of public perceptions on diverse topics, including social issues, politics, natural disasters, and consumer sentiment. Topic modeling is a widely used approach for uncovering latent themes in text data, typically framed as an unsupervised classification task. However, traditional models, originally designed for longer and more formal documents, struggle with short social media posts due to limited co-occurrence statistics, fragmented semantics, inconsistent spelling, and informal language. To address these challenges, we propose a new method, TopiCLEAR: Topic extraction by CLustering Embeddings with Adaptive dimensional Reduction. Specifically, each text is embedded using Sentence-BERT (SBERT) and provisionally clustered using Gaussian Mixture Models (GMM). The clusters are then refined iteratively using a supervised projection based on linear discriminant analysis, followed by GMM-based clustering until convergence. Notably, our method operates directly on raw text, eliminating the need for preprocessing steps such as stop word removal. We evaluate our approach on four diverse datasets, 20News, AgNewsTitle, Reddit, and TweetTopic, each containing human-labeled topic information. Compared with seven baseline methods, including a recent SBERT-based method and a zero-shot generative AI method, our approach achieves the highest similarity to human-annotated topics, with significant improvements for both social media posts and online news articles. Additionally, qualitative analysis shows that our method produces more interpretable topics, highlighting its potential for applications in social media data and web content analytics.

Instruction tuning is one of the key steps required for adapting large language models (LLMs) to a broad spectrum of downstream applications. However, this procedure is difficult because real-world datasets are rarely homogeneous; they consist of a mixture of diverse information, causing gradient interference, where conflicting gradients pull the model in opposing directions, degrading performance. A common strategy to mitigate this issue is to group data based on semantic or embedding similarity. However, this fails to capture how data influences model parameters during learning. While recent works have attempted to cluster gradients directly, they randomly project gradients into lower dimensions to manage memory, which leads to accuracy loss. Moreover, these methods rely on expert ensembles which necessitates multiple inference passes and expensive on-the-fly gradient computations during inference. To address these limitations, we propose GradientSpace, a framework that clusters samples directly in full-dimensional gradient space. We introduce an online SVD-based algorithm that operates on LoRA gradients to identify latent skills without the infeasible cost of storing all sample gradients. Each cluster is used to train a specialized LoRA expert along with a lightweight router trained to select the best expert during inference. We show that routing to a single, appropriate expert outperforms expert ensembles used in prior work, while significantly reducing inference latency. Our experiments across mathematical reasoning, code generation, finance, and creative writing tasks demonstrate that GradientSpace leads to coherent expert specialization and consistent accuracy gains over state-of-the-art clustering methods and finetuning techniques.

Time series classification faces a fundamental trade-off between accuracy and computational efficiency. While comprehensive ensembles like HIVE-COTE 2.0 achieve state-of-the-art accuracy, their 340-hour training time on the UCR benchmark renders them impractical for large-scale datasets. We investigate whether targeted combinations of two efficient algorithms from complementary paradigms can capture ensemble benefits while maintaining computational feasibility. Combining Hydra (competing convolutional kernels) and Quant (hierarchical interval quantiles) across six ensemble configurations, we evaluate performance on 10 large-scale MONSTER datasets (7,898 to 1,168,774 training instances). Our strongest configuration improves mean accuracy from 0.829 to 0.836, succeeding on 7 of 10 datasets. However, prediction-combination ensembles capture only 11% of theoretical oracle potential, revealing a substantial meta-learning optimization gap. Feature-concatenation approaches exceeded oracle bounds by learning novel decision boundaries, while prediction-level complementarity shows moderate correlation with ensemble gains. The central finding: the challenge has shifted from ensuring algorithms are different to learning how to combine them effectively. Current meta-learning strategies struggle to exploit the complementarity that oracle analysis confirms exists. Improved combination strategies could potentially double or triple ensemble gains across diverse time series classification applications.