The large volume and complexity of medical imaging datasets are bottlenecks for storage, transmission, and processing. To tackle these challenges, the application of low-rank matrix approximation (LRMA) and its derivative, local LRMA (LLRMA) has demonstrated potential. A detailed analysis of the literature identifies LRMA and LLRMA methods applied to various imaging modalities, and the challenges and limitations associated with existing LRMA and LLRMA methods are addressed. We note a significant shift towards a preference for LLRMA in the medical imaging field since 2015, demonstrating its potential and effectiveness in capturing complex structures in medical data compared to LRMA. Acknowledging the limitations of shallow similarity methods used with LLRMA, we suggest advanced semantic image segmentation for similarity measure, explaining in detail how it can be used to measure similar patches and its feasibility. We note that LRMA and LLRMA are mainly applied to unstructured medical data, and we propose extending their application to different medical data types, including structured and semi-structured. This paper also discusses how LRMA and LLRMA can be applied to regular data with missing entries and the impact of inaccuracies in predicting missing values and their effects. We discuss the impact of patch size and propose the use of random search (RS) to determine the optimal patch size. To enhance feasibility, a hybrid approach using Bayesian optimization and RS is proposed, which could improve the application of LRMA and LLRMA in medical imaging.

Empirical studies have identified a range of learnability biases and limitations of transformers, such as a persistent difficulty in learning to compute simple formal languages such as PARITY, and a bias towards low-degree functions. However, theoretical understanding remains limited, with existing expressiveness theory either overpredicting or underpredicting realistic learning abilities. We prove that, under the transformer architecture, the loss landscape is constrained by the input-space sensitivity: Transformers whose output is sensitive to many parts of the input string inhabit isolated points in parameter space, leading to a low-sensitivity bias in generalization. We show theoretically and empirically that this theory unifies a broad array of empirical observations about the learning abilities and biases of transformers, such as their generalization bias towards low sensitivity and low degree, and difficulty in length generalization for PARITY. This shows that understanding transformers' inductive biases requires studying not just their in-principle expressivity, but also their loss landscape.

We present an algorithm for skill discovery from expert demonstrations. The algorithm first utilizes Large Language Models (LLMs) to propose an initial segmentation of the trajectories. Following that, a hierarchical variational inference framework incorporates the LLM-generated segmentation information to discover reusable skills by merging trajectory segments. To further control the trade-off between compression and reusability, we introduce a novel auxiliary objective based on the Minimum Description Length principle that helps guide this skill discovery process. Our results demonstrate that agents equipped with our method are able to discover skills that help accelerate learning and outperform baseline skill learning approaches on new long-horizon tasks in BabyAI, a grid world navigation environment, as well as ALFRED, a household simulation environment.

The reliance of language model training on massive amounts of computation and vast datasets scraped from potentially low-quality, copyrighted, or sensitive data has come into question practically, legally, and ethically. Federated learning provides a plausible alternative by enabling previously untapped data to be voluntarily gathered from collaborating organizations. However, when scaled globally, federated learning requires collaboration across heterogeneous legal, security, and privacy regimes while accounting for the inherent locality of language data; this further exacerbates the established challenge of federated statistical heterogeneity. We propose a Worldwide Federated Language Model Training~(WorldLM) system based on federations of federations, where each federation has the autonomy to account for factors such as its industry, operating jurisdiction, or competitive environment. WorldLM enables such autonomy in the presence of statistical heterogeneity via partial model localization by allowing sub-federations to attentively aggregate key layers from their constituents. Furthermore, it can adaptively share information across federations via residual layer embeddings. Evaluations of language modeling on naturally heterogeneous datasets show that WorldLM outperforms standard federations by up to $1.91\times$, approaches the personalized performance of fully local models, and maintains these advantages under privacy-enhancing techniques.

Neural collapse ($\mathcal{NC}$) is a phenomenon observed in classification tasks where top-layer representations collapse into their class means, which become equinorm, equiangular and aligned with the classifiers. These behaviors -- associated with generalization and robustness -- would manifest under specific conditions: models are trained towards zero loss, with noise-free labels belonging to balanced classes, which do not outnumber the model's hidden dimension. Recent studies have explored $\mathcal{NC}$ in the absence of one or more of these conditions to extend and capitalize on the associated benefits of ideal geometries. Language modeling presents a curious frontier, as \textit{training by token prediction} constitutes a classification task where none of the conditions exist: the vocabulary is imbalanced and exceeds the embedding dimension; different tokens might correspond to similar contextual embeddings; and large language models (LLMs) in particular are typically only trained for a few epochs. This paper empirically investigates the impact of scaling the architectures and training of causal language models (CLMs) on their progression towards $\mathcal{NC}$. We find that $\mathcal{NC}$ properties that develop with scaling are linked to generalization. Moreover, there is evidence of some relationship between $\mathcal{NC}$ and generalization independent of scale. Our work therefore underscores the generality of $\mathcal{NC}$ as it extends to the novel and more challenging setting of language modeling. Downstream, we seek to inspire further research on the phenomenon to deepen our understanding of LLMs -- and neural networks at large -- and improve existing architectures based on $\mathcal{NC}$-related properties.

Langevin Dynamics is a Stochastic Differential Equation (SDE) central to sampling and generative modeling and is implemented via time discretization. Langevin Monte Carlo (LMC), based on the Euler-Maruyama discretization, is the simplest and most studied algorithm. LMC can suffer from slow convergence - requiring a large number of steps of small step-size to obtain good quality samples. This becomes stark in the case of diffusion models where a large number of steps gives the best samples, but the quality degrades rapidly with smaller number of steps. Randomized Midpoint Method has been recently proposed as a better discretization of Langevin dynamics for sampling from strongly log-concave distributions. However, important applications such as diffusion models involve non-log concave densities and contain time varying drift. We propose its variant, the Poisson Midpoint Method, which approximates a small step-size LMC with large step-sizes. We prove that this can obtain a quadratic speed up of LMC under very weak assumptions. We apply our method to diffusion models for image generation and show that it maintains the quality of DDPM with 1000 neural network calls with just 50-80 neural network calls and outperforms ODE based methods with similar compute.

Synthetic data generation holds considerable promise, offering avenues to enhance privacy, fairness, and data accessibility. Despite the availability of various methods for generating synthetic tabular data, challenges persist, particularly in specialized applications such as survival analysis. One significant obstacle in survival data generation is censoring, which manifests as not knowing the precise timing of observed (target) events for certain instances. Existing methods face difficulties in accurately reproducing the real distribution of event times for both observed (uncensored) events and censored events, i.e., the generated event-time distributions do not accurately match the underlying distributions of the real data. So motivated, we propose a simple paradigm to produce synthetic survival data by generating covariates conditioned on event times (and censoring indicators), thus allowing one to reuse existing conditional generative models for tabular data without significant computational overhead, and without making assumptions about the (usually unknown) generation mechanism underlying censoring. We evaluate this method via extensive experiments on real-world datasets. Our methodology outperforms multiple competitive baselines at generating survival data, while improving the performance of downstream survival models trained on it and tested on real data.

The training dynamics of linear networks are well studied in two distinct setups: the lazy regime and balanced/active regime, depending on the initialization and width of the network. We provide a surprisingly simple unyfing formula for the evolution of the learned matrix that contains as special cases both lazy and balanced regimes but also a mixed regime in between the two. In the mixed regime, a part of the network is lazy while the other is balanced. More precisely the network is lazy along singular values that are below a certain threshold and balanced along those that are above the same threshold. At initialization, all singular values are lazy, allowing for the network to align itself with the task, so that later in time, when some of the singular value cross the threshold and become active they will converge rapidly (convergence in the balanced regime is notoriously difficult in the absence of alignment). The mixed regime is the `best of both worlds': it converges from any random initialization (in contrast to balanced dynamics which require special initialization), and has a low rank bias (absent in the lazy dynamics). This allows us to prove an almost complete phase diagram of training behavior as a function of the variance at initialization and the width, for a MSE training task.

Federated learning client selection is crucial for determining participant clients while balancing model accuracy and communication efficiency. Existing methods have limitations in handling data heterogeneity, computational burdens, and independent client treatment. To address these challenges, we propose GPFL, which measures client value by comparing local and global descent directions. We also employ an Exploit-Explore mechanism to enhance performance. Experimental results on FEMINST and CIFAR-10 datasets demonstrate that GPFL outperforms baselines in Non-IID scenarios, achieving over 9\% improvement in FEMINST test accuracy. Moreover, GPFL exhibits shorter computation times through pre-selection and parameter reuse in federated learning.

Recent studies have indicated that Large Language Models (LLMs) harbor an inherent understanding of truthfulness, yet often fail to express fully and generate false statements. This gap between "knowing" and "telling" poses a challenge for ensuring the truthfulness of generated content. To address this, we introduce Adaptive Activation Steering (ACT), a tuning-free method that adaptively shift LLM's activations in "truthful" direction during inference. ACT addresses diverse categories of hallucinations by utilizing diverse steering vectors and adjusting the steering intensity adaptively. Applied as an add-on across various models, ACT significantly improves truthfulness in LLaMA ($\uparrow$ 142\%), LLaMA2 ($\uparrow$ 24\%), Alpaca ($\uparrow$ 36\%), Vicuna ($\uparrow$ 28\%), and LLaMA2-Chat ($\uparrow$ 19\%). Furthermore, we verify ACT's scalability across larger models (13B, 33B, 65B), underscoring the adaptability of ACT to large-scale language models.