Robustness Assessment of Mathematical Reasoning in the Presence of Missing and Contradictory Conditions

Large language models (LLMs) have demonstrated impressive performance on reasoning tasks, which can be further improved through few-shot prompting techniques. However, the current evaluation primarily focuses on carefully constructed benchmarks and neglects the consideration of real-world reasoning problems that present missing and contradictory conditions, known as ill-defined problems. Our observations suggest that existing few-shot prompting techniques are ineffective in such scenarios, often providing overconfident answers or hallucination. To further study this problem, we develop a benchmark called Problems with Missing and Contradictory conditions (PMC) and introduce two novel metrics to evaluate the performance of few-shot prompting methods in these scenarios. Our analysis using the PMC benchmark reveals a trade-off dilemma between the performance of mathematical reasoning for well-defined problems and the ability to recognize ill-defined problems. To address the challenges posed by PMC, we propose a novel few-shot prompting method called SMT-LIB Prompting (SLP), which utilizes the SMT-LIB language to model the problems instead of solving them directly. Subsequently, a double-check solving strategy checks the satisfiability and uniqueness of the solution and provides final feedback. Extensive experiments demonstrate the superiority of our SLP approach compared to existing few-shot prompting methods when dealing with problems with missing and contradictory conditions. We will open-source our benchmark and code to facilitate future research.

LawGPT: A Chinese Legal Knowledge-Enhanced Large Language Model

Large language models (LLMs), including both proprietary and open-source models, have showcased remarkable capabilities in addressing a wide range of downstream tasks. Nonetheless, when it comes to practical Chinese legal tasks, these models fail to meet the actual requirements. Proprietary models do not ensure data privacy for sensitive legal cases, while open-source models demonstrate unsatisfactory performance due to their lack of legal knowledge. To address this problem, we introduce LawGPT, the first open-source model specifically designed for Chinese legal applications. LawGPT comprises two key components: legal-oriented pre-training and legal supervised fine-tuning. Specifically, we employ large-scale Chinese legal documents for legal-oriented pre-training to incorporate legal domain knowledge. To further improve the model's performance on downstream legal tasks, we create a knowledge-driven instruction dataset for legal supervised fine-tuning. Our experimental results demonstrate that LawGPT outperforms the open-source LLaMA 7B model. Our code and resources are publicly available at https://github.com/pengxiao-song/LaWGPT and have received 5.7K stars on GitHub.

DeCoOp: Robust Prompt Tuning with Out-of-Distribution Detection

Vision-language models (VLMs), such as CLIP, have demonstrated impressive zero-shot capabilities for various downstream tasks. Their performance can be further enhanced through few-shot prompt tuning methods. However, current studies evaluate the performance of learned prompts separately on base and new classes. This evaluation lacks practicality for real-world applications since downstream tasks cannot determine whether the data belongs to base or new classes in advance. In this paper, we explore a problem setting called Open-world Prompt Tuning (OPT), which involves tuning prompts on base classes and evaluating on a combination of base and new classes. By introducing Decomposed Prompt Tuning framework (DePT), we theoretically demonstrate that OPT can be solved by incorporating out-of-distribution detection into prompt tuning, thereby enhancing the base-to-new discriminability. Based on DePT, we present a novel prompt tuning approach, namely, Decomposed Context Optimization (DeCoOp), which introduces new-class detectors and sub-classifiers to further enhance the base-class and new-class discriminability. Experimental results on 11 benchmark datasets validate the effectiveness of DePT and demonstrate that DeCoOp outperforms current state-of-the-art methods, providing a significant 2% average accuracy improvement.

Online Resource Allocation for Edge Intelligence with Colocated Model Retraining and Inference

With edge intelligence, AI models are increasingly pushed to the edge to serve ubiquitous users. However, due to the drift of model, data, and task, AI model deployed at the edge suffers from degraded accuracy in the inference serving phase. Model retraining handles such drifts by periodically retraining the model with newly arrived data. When colocating model retraining and model inference serving for the same model on resource-limited edge servers, a fundamental challenge arises in balancing the resource allocation for model retraining and inference, aiming to maximize long-term inference accuracy. This problem is particularly difficult due to the underlying mathematical formulation being time-coupled, non-convex, and NP-hard. To address these challenges, we introduce a lightweight and explainable online approximation algorithm, named ORRIC, designed to optimize resource allocation for adaptively balancing the accuracy of model training and inference. The competitive ratio of ORRIC outperforms that of the traditional Inference-Only paradigm, especially when data drift persists for a sufficiently lengthy time. This highlights the advantages and applicable scenarios of colocating model retraining and inference. Notably, ORRIC can be translated into several heuristic algorithms for different resource environments. Experiments conducted in real scenarios validate the effectiveness of ORRIC.

Opara: Exploiting Operator Parallelism for Expediting DNN Inference on GPUs

GPUs have become the defacto hardware devices to accelerate Deep Neural Network (DNN) inference in deep learning(DL) frameworks. However, the conventional sequential execution mode of DNN operators in mainstream DL frameworks cannot fully utilize GPU resources, due to the increasing complexity of DNN model structures and the progressively smaller computational sizes of DNN operators. Moreover, the inadequate operator launch order in parallelized execution scenarios can lead to GPU resource wastage and unexpected performance interference among operators. To address such performance issues above, we propose Opara, a resource- and interference-aware DNN Operator parallel scheduling framework to accelerate the execution of DNN inference on GPUs. Specifically, Opara first employs CUDA Streams and CUDA Graph to automatically parallelize the execution of multiple DNN operators. It further leverages the resource demands of DNN operators to judiciously adjust the operator launch order on GPUs by overlapping the execution of compute-intensive and memory-intensive operators, so as to expedite DNN inference. We implement and open source a prototype of Opara based on PyTorch in a non-intrusive manner. Extensive prototype experiments with representative DNN and Transformer-based models demonstrate that Opara outperforms the default sequential CUDA Graph in PyTorch and the state-of-the-art DNN operator parallelism systems by up to 1.68$\times$ and 1.29$\times$, respectively, yet with acceptable runtime overhead.

DYNAMITE: Dynamic Interplay of Mini-Batch Size and Aggregation Frequency for Federated Learning with Static and Streaming Dataset

Federated Learning (FL) is a distributed learning paradigm that can coordinate heterogeneous edge devices to perform model training without sharing private data. While prior works have focused on analyzing FL convergence with respect to hyperparameters like batch size and aggregation frequency, the joint effects of adjusting these parameters on model performance, training time, and resource consumption have been overlooked, especially when facing dynamic data streams and network characteristics. This paper introduces novel analytical models and optimization algorithms that leverage the interplay between batch size and aggregation frequency to navigate the trade-offs among convergence, cost, and completion time for dynamic FL training. We establish a new convergence bound for training error considering heterogeneous datasets across devices and derive closed-form solutions for co-optimized batch size and aggregation frequency that are consistent across all devices. Additionally, we design an efficient algorithm for assigning different batch configurations across devices, improving model accuracy and addressing the heterogeneity of both data and system characteristics. Further, we propose an adaptive control algorithm that dynamically estimates network states, efficiently samples appropriate data batches, and effectively adjusts batch sizes and aggregation frequency on the fly. Extensive experiments demonstrate the superiority of our offline optimal solutions and online adaptive algorithm.

Parameter-Efficient Long-Tailed Recognition

The "pre-training and fine-tuning" paradigm in addressing long-tailed recognition tasks has sparked significant interest since the emergence of large vision-language models like the contrastive language-image pre-training (CLIP). While previous studies have shown promise in adapting pre-trained models for these tasks, they often undesirably require extensive training epochs or additional training data to maintain good performance. In this paper, we propose PEL, a fine-tuning method that can effectively adapt pre-trained models to long-tailed recognition tasks in fewer than 20 epochs without the need for extra data. We first empirically find that commonly used fine-tuning methods, such as full fine-tuning and classifier fine-tuning, suffer from overfitting, resulting in performance deterioration on tail classes. To mitigate this issue, PEL introduces a small number of task-specific parameters by adopting the design of any existing parameter-efficient fine-tuning method. Additionally, to expedite convergence, PEL presents a novel semantic-aware classifier initialization technique derived from the CLIP textual encoder without adding any computational overhead. Our experimental results on four long-tailed datasets demonstrate that PEL consistently outperforms previous state-of-the-art approaches. The source code is available at https://github.com/shijxcs/PEL.

BeeFlow: Behavior Tree-based Serverless Workflow Modeling and Scheduling for Resource-Constrained Edge Clusters

Serverless computing has gained popularity in edge computing due to its flexible features, including the pay-per-use pricing model, auto-scaling capabilities, and multi-tenancy support. Complex Serverless-based applications typically rely on Serverless workflows (also known as Serverless function orchestration) to express task execution logic, and numerous application- and system-level optimization techniques have been developed for Serverless workflow scheduling. However, there has been limited exploration of optimizing Serverless workflow scheduling in edge computing systems, particularly in high-density, resource-constrained environments such as system-on-chip clusters and single-board-computer clusters. In this work, we discover that existing Serverless workflow scheduling techniques typically assume models with limited expressiveness and cause significant resource contention. To address these issues, we propose modeling Serverless workflows using behavior trees, a novel and fundamentally different approach from existing directed-acyclic-graph- and state machine-based models. Behavior tree-based modeling allows for easy analysis without compromising workflow expressiveness. We further present observations derived from the inherent tree structure of behavior trees for contention-free function collections and awareness of exact and empirical concurrent function invocations. Based on these observations, we introduce BeeFlow, a behavior tree-based Serverless workflow system tailored for resource-constrained edge clusters. Experimental results demonstrate that BeeFlow achieves up to 3.2X speedup in a high-density, resource-constrained edge testbed and 2.5X speedup in a high-profile cloud testbed, compared with the state-of-the-art.

Solving Elliptic Optimal Control Problems using Physics Informed Neural Networks

In this work, we present and analyze a numerical solver for optimal control problems (without / with box constraint) for linear and semilinear second-order elliptic problems. The approach is based on a coupled system derived from the first-order optimality system of the optimal control problem, and applies physics informed neural networks (PINNs) to solve the coupled system. We present an error analysis of the numerical scheme, and provide $L^2(\Omega)$ error bounds on the state, control and adjoint state in terms of deep neural network parameters (e.g., depth, width, and parameter bounds) and the number of sampling points in the domain and on the boundary. The main tools in the analysis include offset Rademacher complexity and boundedness and Lipschitz continuity of neural network functions. We present several numerical examples to illustrate the approach and compare it with three existing approaches.

Serving Graph Neural Networks With Distributed Fog Servers For Smart IoT Services

Graph Neural Networks (GNNs) have gained growing interest in miscellaneous applications owing to their outstanding ability in extracting latent representation on graph structures. To render GNN-based service for IoT-driven smart applications, traditional model serving paradigms usually resort to the cloud by fully uploading geo-distributed input data to remote datacenters. However, our empirical measurements reveal the significant communication overhead of such cloud-based serving and highlight the profound potential in applying the emerging fog computing. To maximize the architectural benefits brought by fog computing, in this paper, we present Fograph, a novel distributed real-time GNN inference framework that leverages diverse and dynamic resources of multiple fog nodes in proximity to IoT data sources. By introducing heterogeneity-aware execution planning and GNN-specific compression techniques, Fograph tailors its design to well accommodate the unique characteristics of GNN serving in fog environments. Prototype-based evaluation and case study demonstrate that Fograph significantly outperforms the state-of-the-art cloud serving and fog deployment by up to 5.39x execution speedup and 6.84x throughput improvement.