Scaling Law Analysis in Federated Learning: How to Select the Optimal Model Size?

The recent success of large language models (LLMs) has sparked a growing interest in training large-scale models. As the model size continues to scale, concerns are growing about the depletion of high-quality, well-curated training data. This has led practitioners to explore training approaches like Federated Learning (FL), which can leverage the abundant data on edge devices while maintaining privacy. However, the decentralization of training datasets in FL introduces challenges to scaling large models, a topic that remains under-explored. This paper fills this gap and provides qualitative insights on generalizing the previous model scaling experience to federated learning scenarios. Specifically, we derive a PAC-Bayes (Probably Approximately Correct Bayesian) upper bound for the generalization error of models trained with stochastic algorithms in federated settings and quantify the impact of distributed training data on the optimal model size by finding the analytic solution of model size that minimizes this bound. Our theoretical results demonstrate that the optimal model size has a negative power law relationship with the number of clients if the total training compute is unchanged. Besides, we also find that switching to FL with the same training compute will inevitably reduce the upper bound of generalization performance that the model can achieve through training, and that estimating the optimal model size in federated scenarios should depend on the average training compute across clients. Furthermore, we also empirically validate the correctness of our results with extensive training runs on different models, network settings, and datasets.

A Provably-Correct and Robust Convex Model for Smooth Separable NMF

Nonnegative matrix factorization (NMF) is a linear dimensionality reduction technique for nonnegative data, with applications such as hyperspectral unmixing and topic modeling. NMF is a difficult problem in general (NP-hard), and its solutions are typically not unique. To address these two issues, additional constraints or assumptions are often used. In particular, separability assumes that the basis vectors in the NMF are equal to some columns of the input matrix. In that case, the problem is referred to as separable NMF (SNMF) and can be solved in polynomial-time with robustness guarantees, while identifying a unique solution. However, in real-world scenarios, due to noise or variability, multiple data points may lie near the basis vectors, which SNMF does not leverage. In this work, we rely on the smooth separability assumption, which assumes that each basis vector is close to multiple data points. We explore the properties of the corresponding problem, referred to as smooth SNMF (SSNMF), and examine how it relates to SNMF and orthogonal NMF. We then propose a convex model for SSNMF and show that it provably recovers the sought-after factors, even in the presence of noise. We finally adapt an existing fast gradient method to solve this convex model for SSNMF, and show that it compares favorably with state-of-the-art methods on both synthetic and hyperspectral datasets.

Robustness of Minimum-Volume Nonnegative Matrix Factorization under an Expanded Sufficiently Scattered Condition

Minimum-volume nonnegative matrix factorization (min-vol NMF) has been used successfully in many applications, such as hyperspectral imaging, chemical kinetics, spectroscopy, topic modeling, and audio source separation. However, its robustness to noise has been a long-standing open problem. In this paper, we prove that min-vol NMF identifies the groundtruth factors in the presence of noise under a condition referred to as the expanded sufficiently scattered condition which requires the data points to be sufficiently well scattered in the latent simplex generated by the basis vectors.

Efficient Topic Extraction via Graph-Based Labeling: A Lightweight Alternative to Deep Models

Extracting topics from text has become an essential task, especially with the rapid growth of unstructured textual data. Most existing works rely on highly computational methods to address this challenge. In this paper, we argue that probabilistic and statistical approaches, such as topic modeling (TM), can offer effective alternatives that require fewer computational resources. TM is a statistical method that automatically discovers topics in large collections of unlabeled text; however, it produces topics as distributions of representative words, which often lack clear interpretability. Our objective is to perform topic labeling by assigning meaningful labels to these sets of words. To achieve this without relying on computationally expensive models, we propose a graph-based approach that not only enriches topic words with semantically related terms but also explores the relationships among them. By analyzing these connections within the graph, we derive suitable labels that accurately capture each topic's meaning. We present a comparative study between our proposed method and several benchmarks, including ChatGPT-3.5, across two different datasets. Our method achieved consistently better results than traditional benchmarks in terms of BERTScore and cosine similarity and produced results comparable to ChatGPT-3.5, while remaining computationally efficient. Finally, we discuss future directions for topic labeling and highlight potential research avenues for enhancing interpretability and automation.

Whose Narrative is it Anyway? A KV Cache Manipulation Attack

The Key Value(KV) cache is an important component for efficient inference in autoregressive Large Language Models (LLMs), but its role as a representation of the model's internal state makes it a potential target for integrity attacks. This paper introduces "History Swapping," a novel block-level attack that manipulates the KV cache to steer model generation without altering the user-facing prompt. The attack involves overwriting a contiguous segment of the active generation's cache with a precomputed cache from a different topic. We empirically evaluate this method across 324 configurations on the Qwen 3 family of models, analyzing the impact of timing, magnitude, and layer depth of the cache overwrite. Our findings reveal that only full-layer overwrites can successfully hijack the conversation's topic, leading to three distinct behaviors: immediate and persistent topic shift, partial recovery, or a delayed hijack. Furthermore, we observe that high-level structural plans are encoded early in the generation process and local discourse structure is maintained by the final layers of the model. This work demonstrates that the KV cache is a significant vector for security analysis, as it encodes not just context but also topic trajectory and structural planning, making it a powerful interface for manipulating model behavior.

Dual-Variable Force Characterisation method for Human-Robot Interaction in Wearable Robotics

Understanding the physical interaction with wearable robots is essential to ensure safety and comfort. However, this interaction is complex in two key aspects: (1) the motion involved, and (2) the non-linear behaviour of soft tissues. Multiple approaches have been undertaken to better understand this interaction and to improve the quantitative metrics of physical interfaces or cuffs. As these two topics are closely interrelated, finite modelling and soft tissue characterisation offer valuable insights into pressure distribution and shear stress induced by the cuff. Nevertheless, current characterisation methods typically rely on a single fitting variable along one degree of freedom, which limits their applicability, given that interactions with wearable robots often involve multiple degrees of freedom. To address this limitation, this work introduces a dual-variable characterisation method, involving normal and tangential forces, aimed at identifying reliable material parameters and evaluating the impact of single-variable fitting on force and torque responses. This method demonstrates the importance of incorporating two variables into the characterisation process by analysing the normalized mean square error (NMSE) across different scenarios and material models, providing a foundation for simulation at the closest possible level, with a focus on the cuff and the human limb involved in the physical interaction between the user and the wearable robot.

TimeFlow: Towards Stochastic-Aware and Efficient Time Series Generation via Flow Matching Modeling

Generating high-quality time series data has emerged as a critical research topic due to its broad utility in supporting downstream time series mining tasks. A major challenge lies in modeling the intrinsic stochasticity of temporal dynamics, as real-world sequences often exhibit random fluctuations and localized variations. While diffusion models have achieved remarkable success, their generation process is computationally inefficient, often requiring hundreds to thousands of expensive function evaluations per sample. Flow matching has emerged as a more efficient paradigm, yet its conventional ordinary differential equation (ODE)-based formulation fails to explicitly capture stochasticity, thereby limiting the fidelity of generated sequences. By contrast, stochastic differential equation (SDE) are naturally suited for modeling randomness and uncertainty. Motivated by these insights, we propose TimeFlow, a novel SDE-based flow matching framework that integrates a encoder-only architecture. Specifically, we design a component-wise decomposed velocity field to capture the multi-faceted structure of time series and augment the vanilla flow-matching optimization with an additional stochastic term to enhance representational expressiveness. TimeFlow is flexible and general, supporting both unconditional and conditional generation tasks within a unified framework. Extensive experiments across diverse datasets demonstrate that our model consistently outperforms strong baselines in generation quality, diversity, and efficiency.

MemoriesDB: A Temporal-Semantic-Relational Database for Long-Term Agent Memory / Modeling Experience as a Graph of Temporal-Semantic Surfaces

We introduce MemoriesDB, a unified data architecture designed to avoid decoherence across time, meaning, and relation in long-term computational memory. Each memory is a time-semantic-relational entity-a structure that simultaneously encodes when an event occurred, what it means, and how it connects to other events. Built initially atop PostgreSQL with pgvector extensions, MemoriesDB combines the properties of a time-series datastore, a vector database, and a graph system within a single append-only schema. Each memory is represented as a vertex uniquely labeled by its microsecond timestamp and accompanied by low- and high-dimensional normalized embeddings that capture semantic context. Directed edges between memories form labeled relations with per-edge metadata, enabling multiple contextual links between the same vertices. Together these constructs form a time-indexed stack of temporal-semantic surfaces, where edges project as directional arrows in a 1+1-dimensional similarity field, tracing the evolution of meaning through time while maintaining cross-temporal coherence. This formulation supports efficient time-bounded retrieval, hybrid semantic search, and lightweight structural reasoning in a single query path. A working prototype demonstrates scalable recall and contextual reinforcement using standard relational infrastructure, and we discuss extensions toward a columnar backend, distributed clustering, and emergent topic modeling.

Latent space analysis and generalization to out-of-distribution data

Understanding the relationships between data points in the latent decision space derived by the deep learning system is critical to evaluating and interpreting the performance of the system on real world data. Detecting \textit{out-of-distribution} (OOD) data for deep learning systems continues to be an active research topic. We investigate the connection between latent space OOD detection and classification accuracy of the model. Using open source simulated and measured Synthetic Aperture RADAR (SAR) datasets, we empirically demonstrate that the OOD detection cannot be used as a proxy measure for model performance. We hope to inspire additional research into the geometric properties of the latent space that may yield future insights into deep learning robustness and generalizability.

AA-Omniscience: Evaluating Cross-Domain Knowledge Reliability in Large Language Models

Existing language model evaluations primarily measure general capabilities, yet reliable use of these models across a range of domains demands factual accuracy and recognition of knowledge gaps. We introduce AA-Omniscience, a benchmark designed to measure both factual recall and knowledge calibration across 6,000 questions. Questions are derived from authoritative academic and industry sources, and cover 42 economically relevant topics within six different domains. The evaluation measures a model's Omniscience Index, a bounded metric (-100 to 100) measuring factual recall that jointly penalizes hallucinations and rewards abstention when uncertain, with 0 equating to a model that answers questions correctly as much as it does incorrectly. Among evaluated models, Claude 4.1 Opus attains the highest score (4.8), making it one of only three models to score above zero. These results reveal persistent factuality and calibration weaknesses across frontier models. Performance also varies by domain, with the models from three different research labs leading across the six domains. This performance variability suggests models should be chosen according to the demands of the use case rather than general performance for tasks where knowledge is important.