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The Taylor spectrum of pairs of isometries
Get PDFIn the paper we fully describe Taylor spectrum of pairs of isometries given by diagrams. In most cases both isometries in such pairs have non-trivial shift part and its Taylor spectrum is a proper subset (of Lebesgue measure in ) of the closed bidisc.24 page
Adaptive Sphericity Tests for High Dimensional Data
Get PDFIn this paper, we investigate sphericity testing in high-dimensional settings, where existing methods primarily rely on sum-type test procedures that often underperform under sparse alternatives. To address this limitation, we propose two max-type test procedures utilizing the sample covariance matrix and the sample spatial-sign covariance matrix, respectively. Furthermore, we introduce two Cauchy combination test procedures that integrate both sum-type and max-type tests, demonstrating their superiority across a wide range of sparsity levels in the alternative hypothesis. Our simulation studies corroborate these findings, highlighting the enhanced performance of our proposed methodologies in high-dimensional sphericity test
Reinforcement Learning Gradients as Vitamin for Online Finetuning Decision Transformers
Get PDFDecision Transformers have recently emerged as a new and compelling paradigm for offline Reinforcement Learning (RL), completing a trajectory in an autoregressive way. While improvements have been made to overcome initial shortcomings, online finetuning of decision transformers has been surprisingly under-explored. The widely adopted state-of-the-art Online Decision Transformer (ODT) still struggles when pretrained with low-reward offline data. In this paper, we theoretically analyze the online-finetuning of the decision transformer, showing that the commonly used Return-To-Go (RTG) that\u27s far from the expected return hampers the online fine-tuning process. This problem, however, is well-addressed by the value function and advantage of standard RL algorithms. As suggested by our analysis, in our experiments, we hence find that simply adding TD3 gradients to the finetuning process of ODT effectively improves the online finetuning performance of ODT, especially if ODT is pretrained with low-reward offline data. These findings provide new directions to further improve decision transformers.Accepted as NeurIPS 2024 spotlight. 33 pages, 26 figure
Extended electrochemical monitoring of biomolecular binding using commercially available, reusable electrodes in microliter volumes
Get PDFElectrochemical biosensors ( E-AB or E-DNA type sensors) that utilize square-wave voltammetry originated in academic labs with a few standard experimental configurations for the electrochemical cell and data analysis. We report here on adaptations of these approaches that are friendly to novice scientists such as those in undergraduate laboratories. These approaches utilize commercially available components, low volumes, work over extended periods and enable facile analysis using a custom excel sheet
Persistent hubs in CMJ branching processes with independent increments and preferential attachment trees
Get PDFA sequence of trees contains a \emph{persistent hub}, or displays \emph{degree centrality}, if there is a fixed node of maximal degree for all sufficiently large . We derive sufficient criteria for the emergence of a persistent hub in genealogical trees associated with Crump-Mode-Jagers branching processes with independent waiting times between births of individuals, and sufficient criteria for the non-emergence of a persistent hub. We also derive criteria for uniqueness of these persistent hubs. As an application, we improve results in the literature concerning the emergence of unique persistent hubs in generalised preferential attachment trees, in particular, allowing for cases where there may not be a \emph{Malthusian parameter} associated with the process. The approach we use is mostly self-contained, and does not rely on prior results about Crump-Mode-Jagers branching processes.27 pages, 2 figure
A Structural Text-Based Scaling Model for Analyzing Political Discourse
Get PDFScaling political actors based on their individual characteristics and behavior helps profiling and grouping them as well as understanding changes in the political landscape. In this paper we introduce the Structural Text-Based Scaling (STBS) model to infer ideological positions of speakers for latent topics from text data. We expand the usual Poisson factorization specification for topic modeling of text data and use flexible shrinkage priors to induce sparsity and enhance interpretability. We also incorporate speaker-specific covariates to assess their association with ideological positions. Applying STBS to U.S. Senate speeches from Congress session 114, we identify immigration and gun violence as the most polarizing topics between the two major parties in Congress. Additionally, we find that, in discussions about abortion, the gender of the speaker significantly influences their position, with female speakers focusing more on women\u27s health. We also see that a speaker\u27s region of origin influences their ideological position more than their religious affiliation.22 pages including 2.5 pages of references, 7 figures 20 additional pages of appendix (supplement), 5 figures, 2 table
Illuminating Networks: Enhancing Visible Light Communication with Physical-Layer Network Coding (PNC-VLC Scheme)
Get PDFWireless communications using light waves are called visible light communication. A technique called Physical-layer Network coding allows several users to communicate simultaneously over the same channel in a distributed space-time Coding scheme. Herein, we report a new PNC-VLC one-to-many scheme using physical-layer network coding in VLC system for enhancing throughput by boosting data transmission at relay nodes. We develop an integrated PNC-VLC framework including physical-layer signal processing algorithms and medium access control approaches. Our proposed technique is then modelled mathematically and compared with some of the VLC and PNC-VLC schemes under various channel conditions and scenarios. Our investigation revealed that our proposed technique performed better than traditional PNC schemes in achieving better Bit Error Rate performance in different channe
InfoRM: Mitigating Reward Hacking in RLHF via Information-Theoretic Reward Modeling
Get PDFDespite the success of reinforcement learning from human feedback (RLHF) in aligning language models with human values, reward hacking, also termed reward overoptimization, remains a critical challenge. This issue primarily arises from reward misgeneralization, where reward models (RMs) compute reward using spurious features that are irrelevant to human preferences. In this work, we tackle this problem from an information-theoretic perspective and propose a framework for reward modeling, namely InfoRM, by introducing a variational information bottleneck objective to filter out irrelevant information. Notably, we further identify a correlation between overoptimization and outliers in the IB latent space of InfoRM, establishing it as a promising tool for detecting reward overoptimization. Inspired by this finding, we propose the Cluster Separation Index (CSI), which quantifies deviations in the IB latent space, as an indicator of reward overoptimization to facilitate the development of online mitigation strategies. Extensive experiments on a wide range of settings and RM scales (70M, 440M, 1.4B, and 7B) demonstrate the effectiveness of InfoRM. Further analyses reveal that InfoRM\u27s overoptimization detection mechanism is not only effective but also robust across a broad range of datasets, signifying a notable advancement in the field of RLHF. The code will be released upon acceptance.The paper has been accepted by NeurIPS 202
Unified Mechanism-Specific Amplification by Subsampling and Group Privacy Amplification
Get PDFAmplification by subsampling is one of the main primitives in machine learning with differential privacy (DP): Training a model on random batches instead of complete datasets results in stronger privacy. This is traditionally formalized via mechanism-agnostic subsampling guarantees that express the privacy parameters of a subsampled mechanism as a function of the original mechanism\u27s privacy parameters. We propose the first general framework for deriving mechanism-specific guarantees, which leverage additional information beyond these parameters to more tightly characterize the subsampled mechanism\u27s privacy. Such guarantees are of particular importance for privacy accounting, i.e., tracking privacy over multiple iterations. Overall, our framework based on conditional optimal transport lets us derive existing and novel guarantees for approximate DP, accounting with Rényi DP, and accounting with dominating pairs in a unified, principled manner. As an application, we analyze how subsampling affects the privacy of groups of multiple users. Our tight mechanism-specific bounds outperform tight mechanism-agnostic bounds and classic group privacy results.Accepted at NeurIPS 202
Weak lensing of strong lensing: beyond the tidal regime
Get PDFThe analysis of strong lensing images usually involves an external convergence and shear, which are meant to model the effect of perturbations along the line of sight, on top of the main lens. Such a description of line-of-sight perturbations supposes that the corresponding gravitational fields can be treated in the tidal regime. Going one step further introduces additional effects, known as flexion, which have been hitherto neglected in strong lensing. In this work, we build a minimal model for the line-of-sight flexion, which adds four new complex parameters to the lens model. Contrary to convergence and shear, the line-of-sight flexion cannot be projected onto the main lens plane. For a CDM cosmology, we predict the typical line-of-sight flexion to be on the order of on galactic scales. Neglecting its effect in lens modelling is found to bias the recovery of other parameters; in particular, the line-of-sight shear can be biased up to . Accounting for the line-of-sight flexion in our minimal framework restores accuracy, at the the cost of degrading precision. With current imaging capabilities, the line-of-sight flexion is unlikely to be measurable on individual strong lensing images; it must therefore be considered a nuisance parameter rather than an observable in its own right.21 + 5 pages, 12 figures. v2: added a citation. v3: minor adjustment