A novel approach is given to overcome the computational challenges of the full-matrix Adaptive Gradient algorithm (Full AdaGrad) in stochastic optimization. By developing a recursive method that estimates the inverse of the square root of the covariance of the gradient, alongside a streaming variant for parameter updates, the study offers efficient and practical algorithms for large-scale applications. This innovative strategy significantly reduces the complexity and resource demands typically associated with full-matrix methods, enabling more effective optimization processes. Moreover, the convergence rates of the proposed estimators and their asymptotic efficiency are given. Their effectiveness is demonstrated through numerical studies.
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A Riemannian geometric framework for Markov chain Monte Carlo (MCMC) is developed where using the Fisher-Rao metric on the manifold of probability density functions (pdfs) informed proposal densities for Metropolis-Hastings (MH) algorithms are constructed. We exploit the square-root representation of pdfs under which the Fisher-Rao metric boils down to the standard $L^2$ metric on the positive orthant of the unit hypersphere. The square-root representation allows us to easily compute the geodesic distance between densities, resulting in a straightforward implementation of the proposed geometric MCMC methodology. Unlike the random walk MH that blindly proposes a candidate state using no information about the target, the geometric MH algorithms effectively move an uninformed base density (e.g., a random walk proposal density) towards different global/local approximations of the target density. We compare the proposed geometric MH algorithm with other MCMC algorithms for various Markov chain orderings, namely the covariance, efficiency, Peskun, and spectral gap orderings. The superior performance of the geometric algorithms over other MH algorithms like the random walk Metropolis, independent MH and variants of Metropolis adjusted Langevin algorithms is demonstrated in the context of various multimodal, nonlinear and high dimensional examples. In particular, we use extensive simulation and real data applications to compare these algorithms for analyzing mixture models, logistic regression models and ultra-high dimensional Bayesian variable selection models. A publicly available R package accompanies the article.
We present a large-scale study of linguistic bias exhibited by ChatGPT covering ten dialects of English (Standard American English, Standard British English, and eight widely spoken non-"standard" varieties from around the world). We prompted GPT-3.5 Turbo and GPT-4 with text by native speakers of each variety and analyzed the responses via detailed linguistic feature annotation and native speaker evaluation. We find that the models default to "standard" varieties of English; based on evaluation by native speakers, we also find that model responses to non-"standard" varieties consistently exhibit a range of issues: lack of comprehension (10% worse compared to "standard" varieties), stereotyping (16% worse), demeaning content (22% worse), and condescending responses (12% worse). We also find that if these models are asked to imitate the writing style of prompts in non-"standard" varieties, they produce text that exhibits lower comprehension of the input and is especially prone to stereotyping. GPT-4 improves on GPT-3.5 in terms of comprehension, warmth, and friendliness, but it also results in a marked increase in stereotyping (+17%). The results suggest that GPT-3.5 Turbo and GPT-4 exhibit linguistic discrimination in ways that can exacerbate harms for speakers of non-"standard" varieties.
While in-context Learning (ICL) has proven to be an effective technique to improve the performance of Large Language Models (LLMs) in a variety of complex tasks, notably in translating natural language questions into Structured Query Language (NL2SQL), the question of how to select the most beneficial demonstration examples remains an open research problem. While prior works often adapted off-the-shelf encoders to retrieve examples dynamically, an inherent discrepancy exists in the representational capacities between the external retrievers and the LLMs. Further, optimizing the selection of examples is a non-trivial task, since there are no straightforward methods to assess the relative benefits of examples without performing pairwise inference. To address these shortcomings, we propose DeTriever, a novel demonstration retrieval framework that learns a weighted combination of LLM hidden states, where rich semantic information is encoded. To train the model, we propose a proxy score that estimates the relative benefits of examples based on the similarities between output queries. Experiments on two popular NL2SQL benchmarks demonstrate that our method significantly outperforms the state-of-the-art baselines on one-shot NL2SQL tasks.
The LBR-Stack is a collection of packages that simplify the usage and extend the capabilities of KUKA's Fast Robot Interface (FRI). It is designed for mission critical hard real-time applications. Supported are the KUKA LBR Med 7/14 and KUKA LBR IIWA 7/14 robots in the Gazebo simulation and for communication with real hardware.
Accurate recognition of rare and new words remains a pressing problem for contextualized Automatic Speech Recognition (ASR) systems. Most context-biasing methods involve modification of the ASR model or the beam-search decoding algorithm, complicating model reuse and slowing down inference. This work presents a new approach to fast context-biasing with CTC-based Word Spotter (CTC-WS) for CTC and Transducer (RNN-T) ASR models. The proposed method matches CTC log-probabilities against a compact context graph to detect potential context-biasing candidates. The valid candidates then replace their greedy recognition counterparts in corresponding frame intervals. A Hybrid Transducer-CTC model enables the CTC-WS application for the Transducer model. The results demonstrate a significant acceleration of the context-biasing recognition with a simultaneous improvement in F-score and WER compared to baseline methods. The proposed method is publicly available in the NVIDIA NeMo toolkit.
We provide a posteriori error estimates for a discontinuous Galerkin scheme for the parabolic-elliptic Keller-Segel system in 2 or 3 space dimensions. The estimates are conditional, in the sense that an a posteriori computable quantity needs to be small enough - which can be ensured by mesh refinement - and optimal in the sense that the error estimator decays with the same order as the error under mesh refinement. A specific feature of our error estimator is that it can be used to prove existence of a weak solution up to a certain time based on numerical results.
The literature shows the possible existence of a problem called collinearity in both Nelson-Siegel and Nelson-Siegel-Svensson models due to the relationship between the slope and curvature components. The presence of this problem and the estimation of both models by Ordinary Least Squares would lead to coefficients estimates that may be unstable among other consequences. However, these estimates are used to make monetary policy decisions. For this reason, it is important to try mitigating this collinearity problem. Consequently, some authors propose traditional procedures for the treatment of collinearity such as: non-linear optimisation, to fix the shape parameter or ridge regression. Nevertheless, all these processes have their disadvantages. Alternatively, a new method with good properties called raise regression is proposed in this paper. Finally, the methodologies are illustrated with an empirical comparison on Euribor Overnight Index Swap and Euribor Interest Rates Swap data between 2011 and 2021.
DistServe improves the performance of large language models (LLMs) serving by disaggregating the prefill and decoding computation. Existing LLM serving systems colocate the two phases and batch the computation of prefill and decoding across all users and requests. We find that this strategy not only leads to strong prefill-decoding interferences but also couples the resource allocation and parallelism plans for both phases. LLM applications often emphasize individual latency for each phase: time to first token (TTFT) for the prefill phase and time per output token (TPOT) of each request for the decoding phase. In the presence of stringent latency requirements, existing systems have to prioritize one latency over the other, or over-provision compute resources to meet both. DistServe assigns prefill and decoding computation to different GPUs, hence eliminating prefill-decoding interferences. Given the application's TTFT and TPOT requirements, DistServe co-optimizes the resource allocation and parallelism strategy tailored for each phase. DistServe also places the two phases according to the serving cluster's bandwidth to minimize the communication caused by disaggregation. As a result, DistServe significantly improves LLM serving performance in terms of the maximum rate that can be served within both TTFT and TPOT constraints on each GPU. Our evaluations show that on various popular LLMs, applications, and latency requirements, DistServe can serve 7.4x more requests or 12.6x tighter SLO, compared to state-of-the-art systems, while staying within latency constraints for > 90% of requests.
The rapid development of Large Language Models (LLMs) and Generative Pre-Trained Transformers(GPTs) in the field of Generative Artificial Intelligence (AI) can significantly impact task automation in themodern economy. We anticipate that the PRA field will inevitably be affected by this technology1. Thus, themain goal of this paper is to engage the risk assessment community into a discussion of benefits anddrawbacks of this technology for PRA. We make a preliminary analysis of possible application of LLM inProbabilistic Risk Assessment (PRA) modeling context referring to the ongoing experience in softwareengineering field. We explore potential application scenarios and the necessary conditions for controlledLLM usage in PRA modeling (whether static or dynamic). Additionally, we consider the potential impact ofthis technology on PRA modeling tools.
Realm Management Monitor (RMM) is an essential firmware component within the recent Arm Confidential Computing Architecture (Arm CCA). Previous work applies formal techniques to verify the specification and prototype reference implementation of RMM. However, relying solely on a single verification tool may lead to the oversight of certain bugs or vulnerabilities. This paper discusses the application of ESBMC, a state-of-the-art Satisfiability Modulo Theories (SMT)-based software model checker, to further enhance RRM verification. We demonstrate ESBMC's ability to precisely parse the source code and identify specification failures within a reasonable time frame. Moreover, we propose potential improvements for ESBMC to enhance its efficiency for industry engineers. This work contributes to exploring the capabilities of formal verification techniques in real-world scenarios and suggests avenues for further improvements to better meet industrial verification needs.
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