Decoder-only language models have the ability to dynamically switch between various computational tasks based on input prompts. Despite many successful applications of prompting, there is very limited understanding of the internal mechanism behind such flexibility. In this work, we investigate how different prompting methods affect the geometry of representations in these models. Employing a framework grounded in statistical physics, we reveal that various prompting techniques, while achieving similar performance, operate through distinct representational mechanisms for task adaptation. Our analysis highlights the critical role of input distribution samples and label semantics in few-shot in-context learning. We also demonstrate evidence of synergistic and interfering interactions between different tasks on the representational level. Our work contributes to the theoretical understanding of large language models and lays the groundwork for developing more effective, representation-aware prompting strategies.

Human Activity Recognition (HAR) using ambient sensors has great potential for practical applications, particularly in elder care and independent living. However, deploying HAR systems in real-world settings remains challenging due to the high cost of labeled data, the need for pre-segmented sensor streams, and the lack of flexibility in activity granularity. To address these limitations, we introduce DISCOVER, a method designed to discover fine-grained human sub-activities from unlabeled sensor data without relying on pre-segmentation. DISCOVER combines unsupervised feature extraction and clustering with a user-friendly visualization tool to streamline the labeling process. DISCOVER enables domain experts to efficiently annotate only a minimal set of representative cluster centroids, reducing the annotation workload to a small number of samples (0.05% of our dataset). We demonstrate DISCOVER's effectiveness through a re-annotation exercise on widely used HAR datasets, showing that it uncovers finer-grained activities and produces more nuanced annotations than traditional coarse labels. DISCOVER represents a step toward practical, deployable HAR systems that adapt to diverse real environments.

A BSTRACT Recent advancements in protein design have leveraged diffusion models to generate structural scaffolds, followed by a process known as protein inverse folding, which involves sequence inference on these scaffolds. However, these methodologies face significant challenges when applied to hyper-variable structures such as antibody Complementarity-Determining Regions (CDRs), where sequence inference frequently results in non-functional sequences due to hallucinations. Distinguished from prevailing protein inverse folding approaches, this paper introduces IgSeek, a novel structure-retrieval framework that infers CDR sequences by retrieving similar structures from a natural antibody database. Specifically, IgSeek employs a simple yet effective multi-channel equivariant graph neural network to generate high-quality geometric representations of CDR backbone structures. Subsequently, it aligns sequences of structurally similar CDRs and utilizes structurally conserved sequence motifs to enhance inference accuracy. Our experiments demonstrate that IgSeek not only proves to be highly efficient in structural retrieval but also outperforms state-of-the-art approaches in sequence recovery for both antibodies and T -Cell Receptors, offering a new retrieval-based perspective for therapeutic protein design. 1 M AIN Antibodies, known for their high specificity and affinity, have emerged as pivotal therapeutic agents in the treatment of complex diseases, including cancer Adams & Weiner (2005), autoimmune disorders Feldmann & Maini (2003), and infectious diseases Abraham (2020). In 2023, the global best-selling drug was Keytruda, a cancer treatment antibody, with sales reaching $25 billion, surpassing Humira, another antibody used for treating rheumatoid arthritis, which had dominated the market for the past decade (Dunleavy, 2024). Traditionally, the discovery of antibodies has predominantly relied on immunizing animals with antigens V an Wauwe et al. (1980) or employing various display techniques such as phage MacCallum et al. (1996) and yeast displays Chao et al. (2006). However, these approaches face significant challenges when dealing with structurally intricate proteins, which are difficult to express in a soluble and functional form. Additionally, even when numerous candidate antibodies are generated through these techniques, they may not necessarily bind to the desired domain or exhibit therapeutic efficacy.

Minimizing the inclusive Kullback-Leibler (KL) divergence with stochastic gradient descent (SGD) is challenging since its gradient is defined as an integral over the posterior. Recently, multiple methods have been proposed to run SGD with biased gradient estimates obtained from a Markov chain. This paper provides the first non-asymptotic convergence analysis of these methods by establishing their mixing rate and gradient variance. To do this, we demonstrate that these methods-which we collectively refer to as Markov chain score ascent (MCSA) methods-can be cast as special cases of the Markov chain gradient descent framework. Furthermore, by leveraging this new understanding, we develop a novel MCSA scheme, parallel MCSA (pMCSA), that achieves a tighter bound on the gradient variance. We demonstrate that this improved theoretical result translates to superior empirical performance.

Stochastic variational inference (SVI) uses stochastic optimization to scale up Bayesian computation to massive data. We present an alternative perspective on SVI as approximate parallel coordinate ascent. SVI trades-off bias and variance to step close to the unknown true coordinate optimum given by batch variational Bayes (VB). We define a model to automate this process.

In this paper, we consider sparse networks consisting of a finite number of nonoverlapping communities, i.e. disjoint clusters, so that there is higher density within clusters than across clusters. Both the intra-and inter-cluster edge densities vanish when the size of the graph grows large, making the cluster reconstruction problem nosier and hence difficult to solve. We are interested in scenarios where the network size is very large, so that the adjacency matrix of the graph is hard to manipulate and store. The data stream model in which columns of the adjacency matrix are revealed sequentially constitutes a natural framework in this setting. For this model, we develop two novel clustering algorithms that extract the clusters asymptotically accurately. The first algorithm is offline, as it needs to store and keep the assignments of nodes to clusters, and requires a memory that scales linearly with the network size. The second algorithm is online, as it may classify a node when the corresponding column is revealed and then discard this information. This algorithm requires a memory growing sub-linearly with the network size. To construct these efficient streaming memory-limited clustering algorithms, we first address the problem of clustering with partial information, where only a small proportion of the columns of the adjacency matrix is observed and develop, for this setting, a new spectral algorithm which is of independent interest.

This paper presents a parallel feature selection method for classification that scales up to very high dimensions and large data sizes. Our original method is inspired by group testing theory, under which the feature selection procedure consists of a collection of randomized tests to be performed in parallel. Each test corresponds to a subset of features, for which a scoring function may be applied to measure the relevance of the features in a classification task. We develop a general theory providing sufficient conditions under which true features are guaranteed to be correctly identified. Superior performance of our method is demonstrated on a challenging relation extraction task from a very large data set that have both redundant features and sample size in the order of millions. We present comprehensive comparisons with state-of-the-art feature selection methods on a range of data sets, for which our method exhibits competitive performance in terms of running time and accuracy. Moreover, it also yields substantial speedup when used as a pre-processing step for most other existing methods.

The accurate estimation of covariance matrices is essential for many signal processing and machine learning algorithms. In high dimensional settings the sample covariance is known to perform poorly, hence regularization strategies such as analytic shrinkage of Ledoit/Wolf are applied.

In many problem settings, parameter vectors are not merely sparse, but dependent in such a way that non-zero coefficients tend to cluster together. We refer to this form of dependency as "region sparsity". Classical sparse regression methods, such as the lasso and automatic relevance determination (ARD), model parameters as independent a priori, and therefore do not exploit such dependencies. Here we introduce a hierarchical model for smooth, region-sparse weight vectors and tensors in a linear regression setting. Our approach represents a hierarchical extension of the relevance determination framework, where we add a transformed Gaussian process to model the dependencies between the prior variances of regression weights. We combine this with a structured model of the prior variances of Fourier coefficients, which eliminates unnecessary high frequencies. The resulting prior encourages weights to be region-sparse in two different bases simultaneously. We develop efficient approximate inference methods and show substantial improvements over comparable methods (e.g., group lasso and smooth RVM) for both simulated and real datasets from brain imaging.

State of the art statistical estimators for high-dimensional problems take the form of regularized, and hence non-smooth, convex programs. A key facet of these statistical estimation problems is that these are typically not strongly convex under a high-dimensional sampling regime when the Hessian matrix becomes rankdeficient. Under vanilla convexity however, proximal optimization methods attain only a sublinear rate. In this paper, we investigate a novel variant of strong convexity, which we call Constant Nullspace Strong Convexity (CNSC), where we require that the objective function be strongly convex only over a constant subspace. As we show, the CNSC condition is naturally satisfied by high-dimensional statistical estimators. We then analyze the behavior of proximal methods under this CNSC condition: we show global linear convergence of Proximal Gradient and local quadratic convergence of Proximal Newton Method, when the regularization function comprising the statistical estimator is decomposable. We corroborate our theory via numerical experiments, and show a qualitative difference in the convergence rates of the proximal algorithms when the loss function does satisfy the CNSC condition.