Statistical Learning
In-context Learning and Gradient Descent Revisited
Deutch, Gilad, Magar, Nadav, Natan, Tomer Bar, Dar, Guy
In-context learning (ICL) has shown impressive results in few-shot learning tasks, yet its underlying mechanism is still not fully understood. Recent works suggest that ICL can be thought of as a gradient descent (GD) based optimization process. While promising, these results mainly focus on simplified settings of ICL and provide only a preliminary evaluation of the similarities between the two methods. In this work, we revisit the comparison between ICL and GD-based finetuning and study what properties of ICL an equivalent process must follow. We highlight a major difference in the flow of information between ICL and standard finetuning. Namely, ICL can only rely on information from lower layers at every point, while finetuning depends on loss gradients from deeper layers. We refer to this discrepancy as Layer Causality and show that a layer causal variant of the finetuning process aligns with ICL on par with vanilla finetuning and is even better in most cases across relevant metrics. To the best of our knowledge, this is the first work to discuss this discrepancy explicitly and suggest a solution that tackles this problem with minimal changes.
Improving Entropy-Based Test-Time Adaptation from a Clustering View
Lin, Guoliang, Lai, Hanjiang, Pan, Yan, Yin, Jian
Domain shift is a common problem in the realistic world, where training data and test data follow different data distributions. To deal with this problem, fully test-time adaptation (TTA) leverages the unlabeled data encountered during test time to adapt the model. In particular, Entropy-Based TTA (EBTTA) methods, which minimize the prediction's entropy on test samples, have shown great success. In this paper, we introduce a new perspective on the EBTTA, which interprets these methods from a view of clustering. It is an iterative algorithm: 1) in the assignment step, the forward process of the EBTTA models is the assignment of labels for these test samples, and 2) in the updating step, the backward process is the update of the model via the assigned samples. Based on the interpretation, we can gain a deeper understanding of EBTTA, where we show that the entropy loss would further increase the largest probability. Accordingly, we offer an alternative explanation for why existing EBTTA methods are sensitive to initial assignments, outliers, and batch size. This observation can guide us to put forward the improvement of EBTTA. We propose robust label assignment, weight adjustment, and gradient accumulation to alleviate the above problems. Experimental results demonstrate that our method can achieve consistent improvements on various datasets. Code is provided in the supplementary material.
GQFedWAvg: Optimization-Based Quantized Federated Learning in General Edge Computing Systems
Li, Yangchen, Cui, Ying, Lau, Vincent
The optimal implementation of federated learning (FL) in practical edge computing systems has been an outstanding problem. In this paper, we propose an optimization-based quantized FL algorithm, which can appropriately fit a general edge computing system with uniform or nonuniform computing and communication resources at the workers. Specifically, we first present a new random quantization scheme and analyze its properties. Then, we propose a general quantized FL algorithm, namely GQFedWAvg. Specifically, GQFedWAvg applies the proposed quantization scheme to quantize wisely chosen model update-related vectors and adopts a generalized mini-batch stochastic gradient descent (SGD) method with the weighted average local model updates in global model aggregation. Besides, GQFedWAvg has several adjustable algorithm parameters to flexibly adapt to the computing and communication resources at the server and workers. We also analyze the convergence of GQFedWAvg. Next, we optimize the algorithm parameters of GQFedWAvg to minimize the convergence error under the time and energy constraints. We successfully tackle the challenging non-convex problem using general inner approximation (GIA) and multiple delicate tricks. Finally, we interpret GQFedWAvg's function principle and show its considerable gains over existing FL algorithms using numerical results.
On Momentum-Based Gradient Methods for Bilevel Optimization with Nonconvex Lower-Level
Bilevel optimization is a popular two-level hierarchical optimization, which has been widely applied to many machine learning tasks such as hyperparameter learning, meta learning and continual learning. Although many bilevel optimization methods recently have been developed, the bilevel methods are not well studied when the lower-level problem is nonconvex. To fill this gap, in the paper, we study a class of nonconvex bilevel optimization problems, where both upper-level and lower-level problems are nonconvex, and the lower-level problem satisfies Polyak-{\L}ojasiewicz (PL) condition. We propose an efficient momentum-based gradient bilevel method (MGBiO) to solve these deterministic problems. Meanwhile, we propose a class of efficient momentum-based stochastic gradient bilevel methods (MSGBiO and VR-MSGBiO) to solve these stochastic problems. Moreover, we provide a useful convergence analysis framework for our methods. Specifically, under some mild conditions, we prove that our MGBiO method has a sample (or gradient) complexity of $O(\epsilon^{-2})$ for finding an $\epsilon$-stationary solution of the deterministic bilevel problems (i.e., $\|\nabla F(x)\|\leq \epsilon$), which improves the existing best results by a factor of $O(\epsilon^{-1})$. Meanwhile, we prove that our MSGBiO and VR-MSGBiO methods have sample complexities of $\tilde{O}(\epsilon^{-4})$ and $\tilde{O}(\epsilon^{-3})$, respectively, in finding an $\epsilon$-stationary solution of the stochastic bilevel problems (i.e., $\mathbb{E}\|\nabla F(x)\|\leq \epsilon$), which improves the existing best results by a factor of $\tilde{O}(\epsilon^{-3})$. Extensive experimental results on bilevel PL game and hyper-representation learning demonstrate the efficiency of our algorithms. This paper commemorates the mathematician Boris Polyak (1935 -2023).
Data Selection for Language Models via Importance Resampling
Xie, Sang Michael, Santurkar, Shibani, Ma, Tengyu, Liang, Percy
Selecting a suitable pretraining dataset is crucial for both general-domain (e.g., GPT-3) and domain-specific (e.g., Codex) language models (LMs). We formalize this problem as selecting a subset of a large raw unlabeled dataset to match a desired target distribution given unlabeled target samples. Due to the scale and dimensionality of the raw text data, existing methods use simple heuristics or require human experts to manually curate data. Instead, we extend the classic importance resampling approach used in low-dimensions for LM data selection. We propose Data Selection with Importance Resampling (DSIR), an efficient and scalable framework that estimates importance weights in a reduced feature space for tractability and selects data with importance resampling according to these weights. We instantiate the DSIR framework with hashed n-gram features for efficiency, enabling the selection of 100M documents from the full Pile dataset in 4.5 hours. To measure whether hashed n-gram features preserve the aspects of the data that are relevant to the target, we define KL reduction, a data metric that measures the proximity between the selected pretraining data and the target on some feature space. Across 8 data selection methods (including expert selection), KL reduction on hashed n-gram features highly correlates with average downstream accuracy (r=0.82). When selecting data for continued pretraining on a specific domain, DSIR performs comparably to expert curation across 8 target distributions. When pretraining general-domain models (target is Wikipedia and books), DSIR improves over random selection and heuristic filtering baselines by 2-2.5% on the GLUE benchmark. Code is available at https://github.com/p-lambda/dsir.
Predicting Influenza A Viral Host Using PSSM and Word Embeddings
The rapid mutation of the influenza virus threatens public health. Reassortment among viruses with different hosts can lead to a fatal pandemic. However, it is difficult to detect the original host of the virus during or after an outbreak as influenza viruses can circulate between different species. Therefore, early and rapid detection of the viral host would help reduce the further spread of the virus. We use various machine learning models with features derived from the position-specific scoring matrix (PSSM) and features learned from word embedding and word encoding to infer the origin host of viruses. The results show that the performance of the PSSM-based model reaches the MCC around 95%, and the F1 around 96%. The MCC obtained using the model with word embedding is around 96%, and the F1 is around 97%.
Non-iterative SLAM for Warehouse Robots Using Ground Textures
Xu, Kuan, Yang, Zheng, Xie, Lihua, Wang, Chen
We present a novel visual SLAM method for the warehouse robot with a single downward-facing camera using ground textures. Traditional methods resort to feature matching or point registration for pose optimization, which easily suffers from repetitive features and poor texture quality. In this paper, we present a robust kernel cross-correlator for robust image-level registration. Compared with the existing methods that often use iterative solutions, our method, named non-iterative visual SLAM (NI-SLAM), has a closed-form solution with a complexity of $O(n\log n)$. This allows it to run very efficiently, yet still provide better accuracy and robustness than the state-of-the-art methods. In the experiments, we demonstrate that it achieves 78% improvement over the state-of-the-art systems for indoor and outdoor localization. We have successfully tested it on warehouse robots equipped with a single downward camera, showcasing its product-ready superiority in a real operating area.
CoPaSul Manual -- Contour-based parametric and superpositional intonation stylization
The purposes of the CoPaSul toolkit are (1) automatic prosodic annotation and (2) prosodic feature extraction from syllable to utterance level. CoPaSul stands for contour-based, parametric, superpositional intonation stylization. In this framework intonation is represented as a superposition of global and local contours that are described parametrically in terms of polynomial coefficients. On the global level (usually associated but not necessarily restricted to intonation phrases) the stylization serves to represent register in terms of time-varying F0 level and range. On the local level (e.g. accent groups), local contour shapes are described. From this parameterization several features related to prosodic boundaries and prominence can be derived. Furthermore, by coefficient clustering prosodic contour classes can be obtained in a bottom-up way. Next to the stylization-based feature extraction also standard F0 and energy measures (e.g. mean and variance) as well as rhythmic aspects can be calculated. At the current state automatic annotation comprises: segmentation into interpausal chunks, syllable nucleus extraction, and unsupervised localization of prosodic phrase boundaries and prominent syllables. F0 and partly also energy feature sets can be derived for: standard measurements (as median and IQR), register in terms of F0 level and range, prosodic boundaries, local contour shapes, bottom-up derived contour classes, Gestalt of accent groups in terms of their deviation from higher level prosodic units, as well as for rhythmic aspects quantifying the relation between F0 and energy contours and prosodic event rates.
Exponentially Convergent Algorithms for Supervised Matrix Factorization
Lee, Joowon, Lyu, Hanbaek, Yao, Weixin
Supervised matrix factorization (SMF) is a classical machine learning method that simultaneously seeks feature extraction and classification tasks, which are not necessarily a priori aligned objectives. Our goal is to use SMF to learn low-rank latent factors that offer interpretable, data-reconstructive, and class-discriminative features, addressing challenges posed by high-dimensional data. Training SMF model involves solving a nonconvex and possibly constrained optimization with at least three blocks of parameters. Known algorithms are either heuristic or provide weak convergence guarantees for special cases. In this paper, we provide a novel framework that 'lifts' SMF as a low-rank matrix estimation problem in a combined factor space and propose an efficient algorithm that provably converges exponentially fast to a global minimizer of the objective with arbitrary initialization under mild assumptions. Our framework applies to a wide range of SMF-type problems for multi-class classification with auxiliary features. To showcase an application, we demonstrate that our algorithm successfully identified well-known cancer-associated gene groups for various cancers.
Biarchetype analysis: simultaneous learning of observations and features based on extremes
Alcacer, Aleix, Epifanio, Irene, Gual-Arnau, Ximo
Cluster analysis (CLA) is one of the most widely used tools in exploratory data analysis. The idea of clustering is to make groups of observations in such a way that each group contains similar observations that are different to those of the rest of the groups. If the data consist of well-separated clusters, appropriate clustering techniques can obtain, on the one hand, the representative of each cluster (the mean or centroid of the cluster for the popular k-means technique), and, on the other hand, the assignations of each observation to one cluster, or a degree of belonging to each cluster for fuzzy clustering techniques. However, CLA is also used as a segmentation technique in the absence of well-separated (clearly differentiated) clusters in data. Many times, data follow a fan-spread pattern, i.e. features vary continuously across observations. The centroids are located in the middle of the data cloud since data points have to be covered in such a way that the distance between them and the assigned centroid is minimized (see [Wu et al., 2016] about the relationship between CLA and set partitioning). In those cases, where data can be viewed as a superposition of various populations, it is of particular interest to use Archetype Analysis (AA) for segmenting [Keller et al., 2019].