23 research outputs found
Building a Better Bijection between Classes of Compositions
A bijective proof is given for the following theorem: The number of compositions of n into parts congruent to a (mod b) equals the number of compositions of n + b - a into parts congruent to b (mod a) that are greater than or equal to b. The bijection is then shown to preserve palindromicity
Neural Image Compression: Generalization, Robustness, and Spectral Biases
Recent advances in neural image compression (NIC) have produced models that
are starting to outperform classic codecs. While this has led to growing
excitement about using NIC in real-world applications, the successful adoption
of any machine learning system in the wild requires it to generalize (and be
robust) to unseen distribution shifts at deployment. Unfortunately, current
research lacks comprehensive datasets and informative tools to evaluate and
understand NIC performance in real-world settings. To bridge this crucial gap,
first, this paper presents a comprehensive benchmark suite to evaluate the
out-of-distribution (OOD) performance of image compression methods.
Specifically, we provide CLIC-C and Kodak-C by introducing 15 corruptions to
the popular CLIC and Kodak benchmarks. Next, we propose spectrally-inspired
inspection tools to gain deeper insight into errors introduced by image
compression methods as well as their OOD performance. We then carry out a
detailed performance comparison of several classic codecs and NIC variants,
revealing intriguing findings that challenge our current understanding of the
strengths and limitations of NIC. Finally, we corroborate our empirical
findings with theoretical analysis, providing an in-depth view of the OOD
performance of NIC and its dependence on the spectral properties of the data.
Our benchmarks, spectral inspection tools, and findings provide a crucial
bridge to the real-world adoption of NIC. We hope that our work will propel
future efforts in designing robust and generalizable NIC methods. Code and data
will be made available at https://github.com/klieberman/ood_nic.Comment: NeurIPS 202
"Understanding Robustness Lottery": A Geometric Visual Comparative Analysis of Neural Network Pruning Approaches
Deep learning approaches have provided state-of-the-art performance in many
applications by relying on large and overparameterized neural networks.
However, such networks have been shown to be very brittle and are difficult to
deploy on resource-limited platforms. Model pruning, i.e., reducing the size of
the network, is a widely adopted strategy that can lead to a more robust and
compact model. Many heuristics exist for model pruning, but empirical studies
show that some heuristics improve performance whereas others can make models
more brittle or have other side effects. This work aims to shed light on how
different pruning methods alter the network's internal feature representation
and the corresponding impact on model performance. To facilitate a
comprehensive comparison and characterization of the high-dimensional model
feature space, we introduce a visual geometric analysis of feature
representations. We decomposed and evaluated a set of critical geometric
concepts from the common adopted classification loss, and used them to design a
visualization system to compare and highlight the impact of pruning on model
performance and feature representation. The proposed tool provides an
environment for in-depth comparison of pruning methods and a comprehensive
understanding of how model response to common data corruption. By leveraging
the proposed visualization, machine learning researchers can reveal the
similarities between pruning methods and redundant in robustness evaluation
benchmarks, obtain geometric insights about the differences between pruned
models that achieve superior robustness performance, and identify samples that
are robust or fragile to model pruning and common data corruption to model
pruning and data corruption but also obtain insights and explanations on how
some pruned models achieve superior robustness performance
Restricted Compositions
An in depth study on many families of restricted compositions. General results are presented for proving infinite families of congruences and enumerating sequences defined by rational generating functions
A Bijection between Two Classes of Restricted Compositions
Two proofs, one using generating functions, the other bijective, are given for the following theorem: The number of compositions of n into parts congruent to 1 (mod k) equals the number of compositions of n + k − 1 into parts greater than k − 1. This bijection is then proven to hold for palindromic compositions. A more general theorem is presented in conclusion
Construction of a Full Row-Rank Matrix System for Multiple Scanning Directions in Computed Tomography
A full row-rank system matrix generated by scans along two directions in discrete tomography was recently studied. In this paper, we generalize the result to multiple directions. Let Ax = h be a reduced binary linear system generated by scans along three directions. Using geometry, it is shown in this paper that the linearly dependent rows of the system matrix A can be explicitly identified and a full row-rank matrix can be obtained after the removal of those rows. The results could be extended to any number of multiple directions. Therefore, certain software packages requiring a full row-rank system matrix can be adopted to reconstruct an image. Meanwhile, the cost of computation is reduced by using a full row-rank matrix
Zeroth-Order SciML: Non-intrusive Integration of Scientific Software with Deep Learning
Using deep learning (DL) to accelerate and/or improve scientific workflows
can yield discoveries that are otherwise impossible. Unfortunately, DL models
have yielded limited success in complex scientific domains due to large data
requirements. In this work, we propose to overcome this issue by integrating
the abundance of scientific knowledge sources (SKS) with the DL training
process. Existing knowledge integration approaches are limited to using
differentiable knowledge source to be compatible with first-order DL training
paradigm. In contrast, our proposed approach treats knowledge source as a
black-box in turn allowing to integrate virtually any knowledge source. To
enable an end-to-end training of SKS-coupled-DL, we propose to use zeroth-order
optimization (ZOO) based gradient-free training schemes, which is
non-intrusive, i.e., does not require making any changes to the SKS. We
evaluate the performance of our ZOO training scheme on two real-world material
science applications. We show that proposed scheme is able to effectively
integrate scientific knowledge with DL training and is able to outperform
purely data-driven model for data-limited scientific applications. We also
discuss some limitations of the proposed method and mention potentially
worthwhile future directions