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Large Language Models (LLMs) enhanced with external contexts, such as through retrieval-augmented generation (RAG), often face challenges in handling imperfect evidence. They tend to over-rely on external knowledge, making them vulnerable to misleading and unhelpful contexts. To address this, we propose the concept of context-robust LLMs, which can effectively balance internal knowledge with external context, similar to human cognitive processes. Specifically, context-robust LLMs should rely on external context only when lacking internal knowledge, identify contradictions between internal and external knowledge, and disregard unhelpful contexts. To achieve this goal, we introduce Grft, a lightweight and plug-and-play gated representation fine-tuning approach. Grft consists of two key components: a gating mechanism to detect and filter problematic inputs, and low-rank representation adapters to adjust hidden representations. By training a lightweight intervention function with only 0.0004\% of model size on fewer than 200 examples, Grft can effectively adapt LLMs towards context-robust behaviors.

Retrieval-Augmented Generation (RAG) systems have shown promise in enhancing the performance of Large Language Models (LLMs). However, these systems face challenges in effectively integrating external knowledge with the LLM's internal knowledge, often leading to issues with misleading or unhelpful information. This work aims to provide a systematic study on knowledge checking in RAG systems. We conduct a comprehensive analysis of LLM representation behaviors and demonstrate the significance of using representations in knowledge checking. Motivated by the findings, we further develop representation-based classifiers for knowledge filtering. We show substantial improvements in RAG performance, even when dealing with noisy knowledge databases. Our study provides new insights into leveraging LLM representations for enhancing the reliability and effectiveness of RAG systems.

Query Autocomplete (QAC) is a critical feature in modern search engines, facilitating user interaction by predicting search queries based on input prefixes. Despite its widespread adoption, the absence of large-scale, realistic datasets has hindered advancements in QAC system development. This paper addresses this gap by introducing AmazonQAC, a new QAC dataset sourced from Amazon Search logs, comprising 395M samples. The dataset includes actual sequences of user-typed prefixes leading to final search terms, as well as session IDs and timestamps that support modeling the context-dependent aspects of QAC. We assess Prefix Trees, semantic retrieval, and Large Language Models (LLMs) with and without finetuning. We find that finetuned LLMs perform best, particularly when incorporating contextual information. However, even our best system achieves only half of what we calculate is theoretically possible on our test data, which implies QAC is a challenging problem that is far from solved with existing systems. This contribution aims to stimulate further research on QAC systems to better serve user needs in diverse environments. We open-source this data on Hugging Face at https://huggingface.co/datasets/amazon/AmazonQAC., Comment: EMNLP 2024

Retrieval-augmented generation (RAG) enhances the outputs of language models by integrating relevant information retrieved from external knowledge sources. However, when the retrieval process involves private data, RAG systems may face severe privacy risks, potentially leading to the leakage of sensitive information. To address this issue, we propose using synthetic data as a privacy-preserving alternative for the retrieval data. We propose SAGE, a novel two-stage synthetic data generation paradigm. In the stage-1, we employ an attribute-based extraction and generation approach to preserve key contextual information from the original data. In the stage-2, we further enhance the privacy properties of the synthetic data through an agent-based iterative refinement process. Extensive experiments demonstrate that using our synthetic data as the retrieval context achieves comparable performance to using the original data while substantially reducing privacy risks. Our work takes the first step towards investigating the possibility of generating high-utility and privacy-preserving synthetic data for RAG, opening up new opportunities for the safe application of RAG systems in various domains.

Gradient Descent Ascent (GDA) methods for min-max optimization problems typically produce oscillatory behavior that can lead to instability, e.g., in bilinear settings. To address this problem, we introduce a dissipation term into the GDA updates to dampen these oscillations. The proposed Dissipative GDA (DGDA) method can be seen as performing standard GDA on a state-augmented and regularized saddle function that does not strictly introduce additional convexity/concavity. We theoretically show the linear convergence of DGDA in the bilinear and strongly convex-strongly concave settings and assess its performance by comparing DGDA with other methods such as GDA, Extra-Gradient (EG), and Optimistic GDA. Our findings demonstrate that DGDA surpasses these methods, achieving superior convergence rates. We support our claims with two numerical examples that showcase DGDA's effectiveness in solving saddle point problems.

Motion planning and control are two core components of the robotic systems autonomy stack. The standard approach to combine these methodologies comprises an offline/open-loop stage, planning, that designs a feasible and safe trajectory to follow, and an online/closed-loop stage, tracking, that corrects for unmodeled dynamics and disturbances. Such an approach generally introduces conservativeness into the planning stage, which becomes difficult to overcome as the model complexity increases and real-time decisions need to be made in a changing environment. This work addresses these challenges for the class of differentially flat nonlinear systems by integrating planning and control into a cohesive closed-loop task. Precisely, we develop an optimization-based framework that aims to steer a differentially flat system to a trajectory implicitly defined via a constrained time-varying optimization problem. To that end, we generalize the notion of feedback linearization, which makes non-linear systems behave as linear systems, and develop controllers that effectively transform a differentially flat system into an optimization algorithm that seeks to find the optimal solution of a (possibly time-varying) optimization problem. Under sufficient regularity assumptions, we prove global asymptotic convergence for the optimization dynamics to the minimizer of the time-varying optimization problem. We illustrate the effectiveness of our method with two numerical examples: a multi-robot tracking problem and a robot obstacle avoidance problem.

In constrained reinforcement learning (C-RL), an agent seeks to learn from the environment a policy that maximizes the expected cumulative reward while satisfying minimum requirements in secondary cumulative reward constraints. Several algorithms rooted in sampled-based primal-dual methods have been recently proposed to solve this problem in policy space. However, such methods are based on stochastic gradient descent ascent algorithms whose trajectories are connected to the optimal policy only after a mixing output stage that depends on the algorithm's history. As a result, there is a mismatch between the behavioral policy and the optimal one. In this work, we propose a novel algorithm for constrained RL that does not suffer from these limitations. Leveraging recent results on regularized saddle-flow dynamics, we develop a novel stochastic gradient descent-ascent algorithm whose trajectories converge to the optimal policy almost surely.

We investigate the problem of finding inner ap-proximations of positive semidefinite (PSD) cones. We developa novel decomposition framework of the PSD cone by meansof conical combinations of smaller dimensional sub-cones. Weshow that many inner approximation techniques could besummarized within this framework, including the set of (scaled)diagonally dominant matrices, Factor-widthkmatrices, andChordal Sparse matrices. Furthermore, we provide a moreflexible family of inner approximations of the PSD cone, wherewe aim to arrange the sub-cones so that they are maximallyseparated from each other. In doing so, these approximationstend to occupy large fractions of the volume of the PSD cone.The proposed approach is connected to a classical packingproblem in Riemannian Geometry. Precisely, we show thatthe problem of finding maximally distant sub-cones in anambient PSD cone is equivalent to the problem of packingsub-spaces in a Grassmannian Manifold. We further leverageexisting computational method for constructing packings inGrassmannian manifolds to build tighter approximations ofthe PSD cone. Numerical experiments show how the proposedframework can balance between accuracy and computationalcomplexity, to efficiently solve positive-semidefinite programs.

We develop an optimization-based framework for joint real-time trajectory planning and feedback control of feedback-linearizable systems. To achieve this goal, we define a target trajectory as the optimal solution of a time-varying optimization problem. In general, however, such trajectory may not be feasible due to , e.g., nonholonomic constraints. To solve this problem, we design a control law that generates feasible trajectories that asymptotically converge to the target trajectory. More precisely, for systems that are (dynamic) full-state linearizable, the proposed control law implicitly transforms the nonlinear system into an optimization algorithm of sufficiently high order. We prove global exponential convergence to the target trajectory for both the optimization algorithm and the original system. We illustrate the effectiveness of our proposed method on multi-target or multi-agent tracking problems with constraints.

Graph mining is one of the most important categories of graph algorithms. However, exploring the subgraphs of an input graph produces a huge amount of intermediate data. The 'think like a vertex' programming paradigm, pioneered by Pregel, cannot readily formulate mining problems, which is designed to produce graph computation problems like PageRank. Existing mining systems like Arabesque and RStream need large amounts of computing and memory resources. In this paper, we present Kaleido, an efficient single machine, out-of-core graph mining system which treats disks as an extension of memory. Kaleido treats intermediate data in graph mining tasks as a tensor and adopts a succinct data structure for the intermediate data. Kaleido utilizes the eigenvalue of the adjacency matrix of a subgraph to efficiently solve the subgraph isomorphism problems with an acceptable constraint that the vertex number of a subgraph is less than 9. Kaleido implements half-memory-half-disk storage for storing large intermediate data, which treats the disk as an extension of the memory. Comparing with two state-of-the-art mining systems, Arabesque and RStream, Kaleido outperforms them by a GeoMean 12.3$\times$ and 40.0$\times$ respectively., Comment: 13 pages