Sharpness-aware minimization (SAM) was proposed to reduce sharpness of minima and has been shown to enhance generalization performance in various settings. In this work we show that perturbing only the affine normalization parameters (typically comprising 0.1% of the total parameters) in the adversarial step of SAM can outperform perturbing all of the parameters.This finding generalizes to different SAM variants and both ResNet (Batch Normalization) and Vision Transformer (Layer Normalization) architectures. We consider alternative sparse perturbation approaches and find that these do not achieve similar performance enhancement at such extreme sparsity levels, showing that this behaviour is unique to the normalization layers. Although our findings reaffirm the effectiveness of SAM in improving generalization performance, they cast doubt on whether this is solely caused by reduced sharpness.
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Deep equilibrium (DEQ) models have emerged as a promising class of implicit layer models, which abandon traditional depth by solving for the fixed points of a single nonlinear layer. Despite their success, the stability of the fixed points for these models remains poorly understood. By considering DEQ models as nonlinear dynamic systems, we propose a robust DEQ model named LyaDEQ with guaranteed provable stability via Lyapunov theory. The crux of our method is ensuring the Lyapunov stability of the DEQ model's fixed points, which enables the proposed model to resist minor initial perturbations. To avoid poor adversarial defense due to Lyapunov-stable fixed points being located near each other, we orthogonalize the layers after the Lyapunov stability module to separate different fixed points. We evaluate LyaDEQ models under well-known adversarial attacks, and experimental results demonstrate significant improvement in robustness. Furthermore, we show that the LyaDEQ model can be combined with other defense methods, such as adversarial training, to achieve even better adversarial robustness.
Feature bagging is a well-established ensembling method which aims to reduce prediction variance by combining predictions of many estimators trained on subsets or projections of features. Here, we develop a theory of feature-bagging in noisy least-squares ridge ensembles and simplify the resulting learning curves in the special case of equicorrelated data. Using analytical learning curves, we demonstrate that subsampling shifts the double-descent peak of a linear predictor. This leads us to introduce heterogeneous feature ensembling, with estimators built on varying numbers of feature dimensions, as a computationally efficient method to mitigate double-descent. Then, we compare the performance of a feature-subsampling ensemble to a single linear predictor, describing a trade-off between noise amplification due to subsampling and noise reduction due to ensembling. Our qualitative insights carry over to linear classifiers applied to image classification tasks with realistic datasets constructed using a state-of-the-art deep learning feature map.
The emergence of pretrained models has significantly impacted Natural Language Processing (NLP) and Computer Vision to relational datasets. Traditionally, these models are assessed through fine-tuned downstream tasks. However, this raises the question of how to evaluate these models more efficiently and more effectively. In this study, we explore a novel approach where we leverage the meta features associated with each entity as a source of worldly knowledge and employ entity representations from the models. We propose using the consistency between these representations and the meta features as a metric for evaluating pretrained models. Our method's effectiveness is demonstrated across various domains, including models with relational datasets, large language models and image models.
Replay-based methods have proved their effectiveness on online continual learning by rehearsing past samples from an auxiliary memory. With many efforts made on improving training schemes based on the memory, however, the information carried by each sample in the memory remains under-investigated. Under circumstances with restricted storage space, the informativeness of the memory becomes critical for effective replay. Although some works design specific strategies to select representative samples, by only employing a small number of original images, the storage space is still not well utilized. To this end, we propose to Summarize the knowledge from the Stream Data (SSD) into more informative samples by distilling the training characteristics of real images. Through maintaining the consistency of training gradients and relationship to the past tasks, the summarized samples are more representative for the stream data compared to the original images. Extensive experiments are conducted on multiple online continual learning benchmarks to support that the proposed SSD method significantly enhances the replay effects. We demonstrate that with limited extra computational overhead, SSD provides more than 3% accuracy boost for sequential CIFAR-100 under extremely restricted memory buffer. Code in //github.com/vimar-gu/SSD.
Recent improvements in adder optimization could be achieved by optimizing the AND-trees occurring within the constructed circuits. The overlap of such trees and its potential for pure size optimization has not been taken into account though. Motivated by this, we examine the fundamental problem of minimizing the size of a circuit for multiple AND-functions on intersecting variable sets. Our formulation generalizes the overlapping \AND-trees within adder optimization but is in NP, in contrast to general Boolean circuit optimization which is in $\Sigma_2^p$ (and thus suspected not to be in NP). While restructuring the AND- or XOR-trees simultaneously, we optimize the total number of gates needed for all functions to be computed. We show that this problem is APX-hard already for functions of few variables and present efficient approximation algorithms for the case in which the Boolean functions depend on at most 3 or 4 variables each, achieving guarantees of $\frac 43$ and $1.9$, respectively. To conclude, we give a polynomial approximation algorithm with guarantee $\frac 23k$ for AND-functions of up to $k$ variables. To achieve these results, the key technique is to determine how much overlap among the variable sets makes tree construction cheap and how little makes the optimum solution large.
In the realm of spoken language understanding (SLU), numerous natural language understanding (NLU) methodologies have been adapted by supplying large language models (LLMs) with transcribed speech instead of conventional written text. In real-world scenarios, prior to input into an LLM, an automated speech recognition (ASR) system generates an output transcript hypothesis, where inherent errors can degrade subsequent SLU tasks. Here we introduce a method that utilizes the ASR system's lattice output instead of relying solely on the top hypothesis, aiming to encapsulate speech ambiguities and enhance SLU outcomes. Our in-context learning experiments, covering spoken question answering and intent classification, underline the LLM's resilience to noisy speech transcripts with the help of word confusion networks from lattices, bridging the SLU performance gap between using the top ASR hypothesis and an oracle upper bound. Additionally, we delve into the LLM's robustness to varying ASR performance conditions and scrutinize the aspects of in-context learning which prove the most influential.
We develop a distributed Block Chebyshev-Davidson algorithm to solve large-scale leading eigenvalue problems for spectral analysis in spectral clustering. First, the efficiency of the Chebyshev-Davidson algorithm relies on the prior knowledge of the eigenvalue spectrum, which could be expensive to estimate. This issue can be lessened by the analytic spectrum estimation of the Laplacian or normalized Laplacian matrices in spectral clustering, making the proposed algorithm very efficient for spectral clustering. Second, to make the proposed algorithm capable of analyzing big data, a distributed and parallel version has been developed with attractive scalability. The speedup by parallel computing is approximately equivalent to $\sqrt{p}$, where $p$ denotes the number of processes. {Numerical results will be provided to demonstrate its efficiency in spectral clustering and scalability advantage over existing eigensolvers used for spectral clustering in parallel computing environments.}
sEMG pattern recognition algorithms have been explored extensively in decoding movement intent, yet are known to be vulnerable to changing recording conditions, exhibiting significant drops in performance across subjects, and even across sessions. Multi-channel surface EMG, also referred to as high-density sEMG (HD-sEMG) systems, have been used to improve performance with the information collected through the use of additional electrodes. However, a lack of robustness is ever present due to limited datasets and the difficulties in addressing sources of variability, such as electrode placement. In this study, we propose training on a collection of input channel subsets and augmenting our training distribution with data from different electrode locations, simultaneously targeting electrode shift and reducing input dimensionality. Our method increases robustness against electrode shift and results in significantly higher intersession performance across subjects and classification algorithms.
Recently, a considerable literature has grown up around the theme of Graph Convolutional Network (GCN). How to effectively leverage the rich structural information in complex graphs, such as knowledge graphs with heterogeneous types of entities and relations, is a primary open challenge in the field. Most GCN methods are either restricted to graphs with a homogeneous type of edges (e.g., citation links only), or focusing on representation learning for nodes only instead of jointly propagating and updating the embeddings of both nodes and edges for target-driven objectives. This paper addresses these limitations by proposing a novel framework, namely the Knowledge Embedding based Graph Convolutional Network (KE-GCN), which combines the power of GCNs in graph-based belief propagation and the strengths of advanced knowledge embedding (a.k.a. knowledge graph embedding) methods, and goes beyond. Our theoretical analysis shows that KE-GCN offers an elegant unification of several well-known GCN methods as specific cases, with a new perspective of graph convolution. Experimental results on benchmark datasets show the advantageous performance of KE-GCN over strong baseline methods in the tasks of knowledge graph alignment and entity classification.
Multi-relation Question Answering is a challenging task, due to the requirement of elaborated analysis on questions and reasoning over multiple fact triples in knowledge base. In this paper, we present a novel model called Interpretable Reasoning Network that employs an interpretable, hop-by-hop reasoning process for question answering. The model dynamically decides which part of an input question should be analyzed at each hop; predicts a relation that corresponds to the current parsed results; utilizes the predicted relation to update the question representation and the state of the reasoning process; and then drives the next-hop reasoning. Experiments show that our model yields state-of-the-art results on two datasets. More interestingly, the model can offer traceable and observable intermediate predictions for reasoning analysis and failure diagnosis, thereby allowing manual manipulation in predicting the final answer.
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