We consider finite-dimensional Bayesian linear inverse problems with Gaussian priors and additive Gaussian noise models. The goal of this note is to present a simple derivation of the well-known fact that solving the Bayesian D-optimal experimental design problem, i.e., maximizing the expected information gain, is equivalent to minimizing the log-determinant of posterior covariance operator. We focus on finite-dimensional inverse problems. However, the presentation is kept generic to facilitate extensions to infinite-dimensional inverse problems.
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We consider the problem of accurate sparse fine-tuning of large language models (LLMs), that is, fine-tuning pretrained LLMs on specialized tasks, while inducing sparsity in their weights. On the accuracy side, we observe that standard loss-based fine-tuning may fail to recover accuracy, especially at high sparsities. To address this, we perform a detailed study of distillation-type losses, determining an L2-based distillation approach we term SquareHead which enables accurate recovery even at higher sparsities, across all model types. On the practical efficiency side, we show that sparse LLMs can be executed with speedups by taking advantage of sparsity, for both CPU and GPU runtimes. While the standard approach is to leverage sparsity for computational reduction, we observe that in the case of memory-bound LLMs sparsity can also be leveraged for reducing memory bandwidth. We exhibit end-to-end results showing speedups due to sparsity, while recovering accuracy, on T5 (language translation), Whisper (speech translation), and open GPT-type (MPT for text generation). For MPT text generation, we show for the first time that sparse fine-tuning can reach 75% sparsity without accuracy drops, provide notable end-to-end speedups for both CPU and GPU inference, and highlight that sparsity is also compatible with quantization approaches. Models and software for reproducing our results are provided in Section 6.
Large Language Models (LLMs) have already become quite proficient at solving simpler programming tasks like those in HumanEval or MBPP benchmarks. However, solving more complex and competitive programming tasks is still quite challenging for these models - possibly due to their tendency to generate solutions as monolithic code blocks instead of decomposing them into logical sub-tasks and sub-modules. On the other hand, experienced programmers instinctively write modularized code with abstraction for solving complex tasks, often reusing previously developed modules. To address this gap, we propose CodeChain, a novel framework for inference that elicits modularized code generation through a chain of self-revisions, each being guided by some representative sub-modules generated in previous iterations. Concretely, CodeChain first instructs the LLM to generate modularized codes through chain-of-thought prompting. Then it applies a chain of self-revisions by iterating the two steps: 1) extracting and clustering the generated sub-modules and selecting the cluster representatives as the more generic and re-usable implementations, and 2) augmenting the original chain-of-thought prompt with these selected module-implementations and instructing the LLM to re-generate new modularized solutions. We find that by naturally encouraging the LLM to reuse the previously developed and verified sub-modules, CodeChain can significantly boost both modularity as well as correctness of the generated solutions, achieving relative pass@1 improvements of 35% on APPS and 76% on CodeContests. It is shown to be effective on both OpenAI LLMs as well as open-sourced LLMs like WizardCoder. We also conduct comprehensive ablation studies with different methods of prompting, number of clusters, model sizes, program qualities, etc., to provide useful insights that underpin CodeChain's success.
Spectral independence is a recently-developed framework for obtaining sharp bounds on the convergence time of the classical Glauber dynamics. This new framework has yielded optimal $O(n \log n)$ sampling algorithms on bounded-degree graphs for a large class of problems throughout the so-called uniqueness regime, including, for example, the problems of sampling independent sets, matchings, and Ising-model configurations. Our main contribution is to relax the bounded-degree assumption that has so far been important in establishing and applying spectral independence. Previous methods for avoiding degree bounds rely on using $L^p$-norms to analyse contraction on graphs with bounded connective constant (Sinclair, Srivastava, Yin; FOCS'13). The non-linearity of $L^p$-norms is an obstacle to applying these results to bound spectral independence. Our solution is to capture the $L^p$-analysis recursively by amortising over the subtrees of the recurrence used to analyse contraction. Our method generalises previous analyses that applied only to bounded-degree graphs. As a main application of our techniques, we consider the random graph $G(n,d/n)$, where the previously known algorithms run in time $n^{O(\log d)}$ or applied only to large $d$. We refine these algorithmic bounds significantly, and develop fast $n^{1+o(1)}$ algorithms based on Glauber dynamics that apply to all $d$, throughout the uniqueness regime.
Discrepancies in decision-making between Autonomous Driving Systems (ADS) and human drivers underscore the need for intuitive human gaze predictors to bridge this gap, thereby improving user trust and experience. Existing gaze datasets, despite their value, suffer from noise that hampers effective training. Furthermore, current gaze prediction models exhibit inconsistency across diverse scenarios and demand substantial computational resources, restricting their on-board deployment in autonomous vehicles. We propose a novel adaptive cleansing technique for purging noise from existing gaze datasets, coupled with a robust, lightweight convolutional self-attention gaze prediction model. Our approach not only significantly enhances model generalizability and performance by up to 12.13% but also ensures a remarkable reduction in model complexity by up to 98.2% compared to the state-of-the art, making in-vehicle deployment feasible to augment ADS decision visualization and performance.
This paper presents a new approach for training two-stage object detection ensemble models, more specifically, Faster R-CNN models to estimate uncertainty. We propose training one Region Proposal Network(RPN)~\cite{//doi.org/10.48550/arxiv.1506.01497} and multiple Fast R-CNN prediction heads is all you need to build a robust deep ensemble network for estimating uncertainty in object detection. We present this approach and provide experiments to show that this approach is much faster than the naive method of fully training all $n$ models in an ensemble. We also estimate the uncertainty by measuring this ensemble model's Expected Calibration Error (ECE). We then further compare the performance of this model with that of Gaussian YOLOv3, a variant of YOLOv3 that models uncertainty using predicted bounding box coordinates. The source code is released at \url{//github.com/Akola-Mbey-Denis/EfficientEnsemble}
We consider the problem of model selection in a high-dimensional sparse linear regression model under the differential privacy framework. In particular, we consider the problem of differentially private best subset selection and study its utility guarantee. We adopt the well-known exponential mechanism for selecting the best model, and under a certain margin condition, we establish its strong model recovery property. However, the exponential search space of the exponential mechanism poses a serious computational bottleneck. To overcome this challenge, we propose a Metropolis-Hastings algorithm for the sampling step and establish its polynomial mixing time to its stationary distribution in the problem parameters $n,p$, and $s$. Furthermore, we also establish approximate differential privacy for the final estimates of the Metropolis-Hastings random walk using its mixing property. Finally, we also perform some illustrative simulations that echo the theoretical findings of our main results.
We propose a Monte Carlo method to efficiently find, count, and sample abstract triangulations of a given manifold M. The method is based on a biased random walk through all possible triangulations of M (in the Pachner graph), constructed by combining (bi-stellar) moves with suitable chosen accept/reject probabilities (Metropolis-Hastings). Asymptotically, the method guarantees that samples of triangulations are drawn at random from a chosen probability. This enables us not only to sample (rare) triangulations of particular interest but also to estimate the (extremely small) probability of obtaining them when isomorphism types of triangulations are sampled uniformly at random. We implement our general method for surface triangulations and 1-vertex triangulations of 3-manifolds. To showcase its usefulness, we present a number of experiments: (a) we recover asymptotic growth rates for the number of isomorphism types of simplicial triangulations of the 2-dimensional sphere; (b) we experimentally observe that the growth rate for the number of isomorphism types of 1-vertex triangulations of the 3-dimensional sphere appears to be singly exponential in the number of their tetrahedra; and (c) we present experimental evidence that a randomly chosen isomorphism type of 1-vertex n-tetrahedra 3-sphere triangulation, for n tending to infinity, almost surely shows a fixed edge-degree distribution which decays exponentially for large degrees, but shows non-monotonic behaviour for small degrees.
Remotely sensed data are dominated by mixed Land Use and Land Cover (LULC) types. Spectral unmixing is a technique to extract information from mixed pixels into their constituent LULC types and corresponding abundance fractions. Traditionally, solving this task has relied on either classical methods that require prior knowledge of endmembers or machine learning methods that avoid explicit endmembers calculation, also known as blind spectral unmixing (BSU). Most BSU studies based on Deep Learning (DL) focus on one time-step hyperspectral data, yet its acquisition remains quite costly compared with multispectral data. To our knowledge, here we provide the first study on BSU of LULC classes using multispectral time series data with DL models. We further boost the performance of a Long-Short Term Memory (LSTM)-based model by incorporating geographic plus topographic (geo-topographic) and climatic ancillary information. Our experiments show that combining spectral-temporal input data together with geo-topographic and climatic information substantially improves the abundance estimation of LULC classes in mixed pixels. To carry out this study, we built a new labeled dataset of the region of Andalusia (Spain) with monthly multispectral time series of pixels for the year 2013 from MODIS at 460m resolution, for two hierarchical levels of LULC classes, named Andalusia MultiSpectral MultiTemporal Unmixing (Andalusia-MSMTU). This dataset provides, at the pixel level, a multispectral time series plus ancillary information annotated with the abundance of each LULC class inside each pixel. The dataset and code are available to the public.
Human-in-the-loop aims to train an accurate prediction model with minimum cost by integrating human knowledge and experience. Humans can provide training data for machine learning applications and directly accomplish some tasks that are hard for computers in the pipeline with the help of machine-based approaches. In this paper, we survey existing works on human-in-the-loop from a data perspective and classify them into three categories with a progressive relationship: (1) the work of improving model performance from data processing, (2) the work of improving model performance through interventional model training, and (3) the design of the system independent human-in-the-loop. Using the above categorization, we summarize major approaches in the field, along with their technical strengths/ weaknesses, we have simple classification and discussion in natural language processing, computer vision, and others. Besides, we provide some open challenges and opportunities. This survey intends to provide a high-level summarization for human-in-the-loop and motivates interested readers to consider approaches for designing effective human-in-the-loop solutions.
Within the rapidly developing Internet of Things (IoT), numerous and diverse physical devices, Edge devices, Cloud infrastructure, and their quality of service requirements (QoS), need to be represented within a unified specification in order to enable rapid IoT application development, monitoring, and dynamic reconfiguration. But heterogeneities among different configuration knowledge representation models pose limitations for acquisition, discovery and curation of configuration knowledge for coordinated IoT applications. This paper proposes a unified data model to represent IoT resource configuration knowledge artifacts. It also proposes IoT-CANE (Context-Aware recommendatioN systEm) to facilitate incremental knowledge acquisition and declarative context driven knowledge recommendation.
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