Understanding how neural systems efficiently process information through distributed representations is a fundamental challenge at the interface of neuroscience and machine learning. Recent approaches analyze the statistical and geometrical attributes of neural representations as population-level mechanistic descriptors of task implementation. In particular, manifold capacity has emerged as a promising framework linking population geometry to the separability of neural manifolds. However, this metric has been limited to linear readouts. Here, we propose a theoretical framework that overcomes this limitation by leveraging contextual input information. We derive an exact formula for the context-dependent capacity that depends on manifold geometry and context correlations, and validate it on synthetic and real data. Our framework's increased expressivity captures representation untanglement in deep networks at early stages of the layer hierarchy, previously inaccessible to analysis. As context-dependent nonlinearity is ubiquitous in neural systems, our data-driven and theoretically grounded approach promises to elucidate context-dependent computation across scales, datasets, and models.

Ship design is a complex design process that may take a team of naval architects many years to complete. Improving the ship design process can lead to significant cost savings, while still delivering high-quality designs to customers. A new technology for ship hull design is diffusion models, a type of generative artificial intelligence. Prior work with diffusion models for ship hull design created high-quality ship hulls with reduced drag and larger displaced volumes. However, the work could not generate hulls that meet specific design constraints. This paper proposes a conditional diffusion model that generates hull designs given specific constraints, such as the desired principal dimensions of the hull. In addition, this diffusion model leverages the gradients from a total resistance regression model to create low-resistance designs. Five design test cases compared the diffusion model to a design optimization algorithm to create hull designs with low resistance. In all five test cases, the diffusion model was shown to create diverse designs with a total resistance less than the optimized hull, having resistance reductions over 25%. The diffusion model also generated these designs without retraining. This work can significantly reduce the design cycle time of ships by creating high-quality hulls that meet user requirements with a data-driven approach.

Prediction-powered inference (PPI) is a method that improves statistical estimates based on limited human-labeled data. Specifically, PPI methods provide tighter confidence intervals by combining small amounts of human-labeled data with larger amounts of data labeled by a reasonably accurate, but potentially biased, automatic system. We propose a framework for PPI based on Bayesian inference that allows researchers to develop new task-appropriate PPI methods easily. Exploiting the ease with which we can design new metrics, we propose improved PPI methods for several importantcases, such as autoraters that give discrete responses (e.g., prompted LLM ``judges'') and autoraters with scores that have a non-linear relationship to human scores.

This study develops FusionTransNet, a framework designed for Origin-Destination (OD) flow predictions within smart and multimodal urban transportation systems. Urban transportation complexity arises from the spatiotemporal interactions among various traffic modes. Motivated by analyzing multimodal data from Shenzhen, a framework that can dissect complicated spatiotemporal interactions between these modes, from the microscopic local level to the macroscopic city-wide perspective, is essential. The framework contains three core components: the Intra-modal Learning Module, the Inter-modal Learning Module, and the Prediction Decoder. The Intra-modal Learning Module is designed to analyze spatial dependencies within individual transportation modes, facilitating a granular understanding of single-mode spatiotemporal dynamics. The Inter-modal Learning Module extends this analysis, integrating data across different modes to uncover cross-modal interdependencies, by breaking down the interactions at both local and global scales. Finally, the Prediction Decoder synthesizes insights from the preceding modules to generate accurate OD flow predictions, translating complex multimodal interactions into forecasts. Empirical evaluations conducted in metropolitan contexts, including Shenzhen and New York, demonstrate FusionTransNet's superior predictive accuracy compared to existing state-of-the-art methods. The implication of this study extends beyond urban transportation, as the method for transferring information across different spatiotemporal graphs at both local and global scales can be instrumental in other spatial systems, such as supply chain logistics and epidemics spreading.

Importance sampling (IS) represents a fundamental technique for a large surge of off-policy reinforcement learning approaches. Policy gradient (PG) methods, in particular, significantly benefit from IS, enabling the effective reuse of previously collected samples, thus increasing sample efficiency. However, classically, IS is employed in RL as a passive tool for re-weighting historical samples. However, the statistical community employs IS as an active tool combined with the use of behavioral distributions that allow the reduction of the estimate variance even below the sample mean one. In this paper, we focus on this second setting by addressing the behavioral policy optimization (BPO) problem. We look for the best behavioral policy from which to collect samples to reduce the policy gradient variance as much as possible. We provide an iterative algorithm that alternates between the cross-entropy estimation of the minimum-variance behavioral policy and the actual policy optimization, leveraging on defensive IS. We theoretically analyze such an algorithm, showing that it enjoys a convergence rate of order $O(\epsilon^{-4})$ to a stationary point, but depending on a more convenient variance term w.r.t. standard PG methods. We then provide a practical version that is numerically validated, showing the advantages in the policy gradient estimation variance and on the learning speed.

LiDAR odometry is the task of estimating the ego-motion of the sensor from sequential laser scans. This problem has been addressed by the community for more than two decades, and many effective solutions are available nowadays. Most of these systems implicitly rely on assumptions about the operating environment, the sensor used, and motion pattern. When these assumptions are violated, several well-known systems tend to perform poorly. This paper presents a LiDAR odometry system that can overcome these limitations and operate well under different operating conditions while achieving performance comparable with domain-specific methods. Our algorithm follows the well-known ICP paradigm that leverages a PCA-based kd-tree implementation that is used to extract structural information about the clouds being registered and to compute the minimization metric for the alignment. The drift is bound by managing the local map based on the estimated uncertainty of the tracked pose. To benefit the community, we release an open-source C++ anytime real-time implementation.

Current computational approaches for analysing or generating code-mixed sentences do not explicitly model "naturalness" or "acceptability" of code-mixed sentences, but rely on training corpora to reflect distribution of acceptable code-mixed sentences. Modelling human judgement for the acceptability of code-mixed text can help in distinguishing natural code-mixed text and enable quality-controlled generation of code-mixed text. To this end, we construct Cline - a dataset containing human acceptability judgements for English-Hindi (en-hi) code-mixed text. Cline is the largest of its kind with 16,642 sentences, consisting of samples sourced from two sources: synthetically generated code-mixed text and samples collected from online social media. Our analysis establishes that popular code-mixing metrics such as CMI, Number of Switch Points, Burstines, which are used to filter/curate/compare code-mixed corpora have low correlation with human acceptability judgements, underlining the necessity of our dataset. Experiments using Cline demonstrate that simple Multilayer Perceptron (MLP) models trained solely on code-mixing metrics are outperformed by fine-tuned pre-trained Multilingual Large Language Models (MLLMs). Specifically, XLM-Roberta and Bernice outperform IndicBERT across different configurations in challenging data settings. Comparison with ChatGPT's zero and fewshot capabilities shows that MLLMs fine-tuned on larger data outperform ChatGPT, providing scope for improvement in code-mixed tasks. Zero-shot transfer from English-Hindi to English-Telugu acceptability judgments using our model checkpoints proves superior to random baselines, enabling application to other code-mixed language pairs and providing further avenues of research. We publicly release our human-annotated dataset, trained checkpoints, code-mix corpus, and code for data generation and model training.

Malicious software is a pernicious global problem. A novel multi-task learning framework is proposed in this paper for malware image classification for accurate and fast malware detection. We generate bitmap (BMP) and (PNG) images from malware features, which we feed to a deep learning classifier. Our state-of-the-art multi-task learning approach has been tested on a new dataset, for which we have collected approximately 100,000 benign and malicious PE, APK, Mach-o, and ELF examples. Experiments with seven tasks tested with 4 activation functions, ReLU, LeakyReLU, PReLU, and ELU separately demonstrate that PReLU gives the highest accuracy of more than 99.87% on all tasks. Our model can effectively detect a variety of obfuscation methods like packing, encryption, and instruction overlapping, strengthing the beneficial claims of our model, in addition to achieving the state-of-art methods in terms of accuracy.

In this study, we utilized statistical analysis and machine learning methods to examine whether rehabilitation exercises can improve patients post-stroke functional abilities, as well as forecast the improvement in functional abilities. Our dataset is patients' rehabilitation exercises and demographic information recorded in the unstructured electronic health records (EHRs) data and free-text rehabilitation procedure notes. We collected data for 265 stroke patients from the University of Pittsburgh Medical Center. We employed a pre-existing natural language processing (NLP) algorithm to extract data on rehabilitation exercises and developed a rule-based NLP algorithm to extract Activity Measure for Post-Acute Care (AM-PAC) scores, covering basic mobility (BM) and applied cognitive (AC) domains, from procedure notes. Changes in AM-PAC scores were classified based on the minimal clinically important difference (MCID), and significance was assessed using Friedman and Wilcoxon tests. To identify impactful exercises, we used Chi-square tests, Fisher's exact tests, and logistic regression for odds ratios. Additionally, we developed five machine learning models-logistic regression (LR), Adaboost (ADB), support vector machine (SVM), gradient boosting (GB), and random forest (RF)-to predict outcomes in functional ability. Statistical analyses revealed significant associations between functional improvements and specific exercises. The RF model achieved the best performance in predicting functional outcomes. In this study, we identified three rehabilitation exercises that significantly contributed to patient post-stroke functional ability improvement in the first two months. Additionally, the successful application of a machine learning model to predict patient-specific functional outcomes underscores the potential for precision rehabilitation.

While effective in practice, iterative methods for solving large systems of linear equations can be significantly affected by problem-dependent condition number quantities. This makes characterizing their time complexity challenging, particularly when we wish to make comparisons between deterministic and stochastic methods, that may or may not rely on preconditioning and/or fast matrix multiplication. In this work, we consider a fine-grained notion of complexity for iterative linear solvers which we call the spectral tail condition number, $\kappa_\ell$, defined as the ratio between the $\ell$th largest and the smallest singular value of the matrix representing the system. Concretely, we prove the following main algorithmic result: Given an $n\times n$ matrix $A$ and a vector $b$, we can find $\tilde{x}$ such that $\|A\tilde{x}-b\|\leq\epsilon\|b\|$ in time $\tilde{O}(\kappa_\ell\cdot n^2\log 1/\epsilon)$ for any $\ell = O(n^{\frac1{\omega-1}})=O(n^{0.729})$, where $\omega \approx 2.372$ is the current fast matrix multiplication exponent. This guarantee is achieved by Sketch-and-Project with Nesterov's acceleration. Some of the implications of our result, and of the use of $\kappa_\ell$, include direct improvement over a fine-grained analysis of the Conjugate Gradient method, suggesting a stronger separation between deterministic and stochastic iterative solvers; and relating the complexity of iterative solvers to the ongoing algorithmic advances in fast matrix multiplication, since the bound on $\ell$ improves with $\omega$. Our main technical contributions are new sharp characterizations for the first and second moments of the random projection matrix that commonly arises in sketching algorithms, building on a combination of techniques from combinatorial sampling via determinantal point processes and Gaussian universality results from random matrix theory.