We present an in-context learning agent for formal theorem-proving in environments like Lean and Coq. Current state-of-the-art models for the problem are finetuned on environment-specific proof data. By contrast, our approach, called COPRA, repeatedly asks a high-capacity, general-purpose large language model (GPT-4) to propose tactic applications from within a stateful backtracking search. Proposed tactics are executed in the underlying proof environment. Feedback from the execution is used to build the prompt for the next model query, along with selected information from the search history and lemmas retrieved from an external database. We evaluate our implementation of COPRA on the miniF2F benchmark for Lean and a set of Coq tasks from the CompCert project. On these benchmarks, COPRA significantly outperforms few-shot invocations of GPT-4. It also compares favorably against finetuning-based approaches, outperforming REPROVER, a state-of-the-art finetuned approach for Lean, in terms of the pass@1 metric. Our code and data are available at //github.com/trishullab/copra.
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We study differentially private (DP) algorithms for recovering clusters in well-clustered graphs, which are graphs whose vertex set can be partitioned into a small number of sets, each inducing a subgraph of high inner conductance and small outer conductance. Such graphs have widespread application as a benchmark in the theoretical analysis of spectral clustering. We provide an efficient ($\epsilon$,$\delta$)-DP algorithm tailored specifically for such graphs. Our algorithm draws inspiration from the recent work of Chen et al., who developed DP algorithms for recovery of stochastic block models in cases where the graph comprises exactly two nearly-balanced clusters. Our algorithm works for well-clustered graphs with $k$ nearly-balanced clusters, and the misclassification ratio almost matches the one of the best-known non-private algorithms. We conduct experimental evaluations on datasets with known ground truth clusters to substantiate the prowess of our algorithm. We also show that any (pure) $\epsilon$-DP algorithm would result in substantial error.
Retrieval-augmented generation models augment knowledge encoded in a language model by providing additional relevant external knowledge (context) during generation. Although it has been shown that the quantity and quality of context impact the performance of retrieval-augmented generation models during inference, limited research explores how these characteristics affect model training. This paper explores how context quantity and quality during model training affect the performance of Fusion-in-Decoder (FiD), the state-of-the-art retrieval-augmented generation model, in extractive open-domain question answering tasks. Experimental results suggest that FiD models overfit to context quality during training and show suboptimal performance when evaluated on different context quality. Through the experimental results, we also reveal FiD models trained with different context quality have different cross-attention distribution patterns. Specifically, as context quality during training increases, FiD models tend to attend more uniformly to each passage in context. Finally, based on these observations, we propose a method to mitigate overfitting to specific context quality by introducing bias to the cross-attention distribution, which we demonstrate to be effective in improving the performance of FiD models on different context quality.
Few-shot knowledge graph completion (FKGC) aims to query the unseen facts of a relation given its few-shot reference entity pairs. The side effect of noises due to the uncertainty of entities and triples may limit the few-shot learning, but existing FKGC works neglect such uncertainty, which leads them more susceptible to limited reference samples with noises. In this paper, we propose a novel uncertainty-aware few-shot KG completion framework (UFKGC) to model uncertainty for a better understanding of the limited data by learning representations under Gaussian distribution. Uncertainty representation is first designed for estimating the uncertainty scope of the entity pairs after transferring feature representations into a Gaussian distribution. Further, to better integrate the neighbors with uncertainty characteristics for entity features, we design an uncertainty-aware relational graph neural network (UR-GNN) to conduct convolution operations between the Gaussian distributions. Then, multiple random samplings are conducted for reference triples within the Gaussian distribution to generate smooth reference representations during the optimization. The final completion score for each query instance is measured by the designed uncertainty optimization to make our approach more robust to the noises in few-shot scenarios. Experimental results show that our approach achieves excellent performance on two benchmark datasets compared to its competitors.
Pretrained language models (PLMs) have shown remarkable few-shot learning capabilities when provided with properly formatted examples. However, selecting the "best" examples remains an open challenge. We propose a complexity-based prompt selection approach for sequence tagging tasks. This approach avoids the training of a dedicated model for selection of examples, and instead uses certain metrics to align the syntactico-semantic complexity of test sentences and examples. We use both sentence- and word-level metrics to match the complexity of examples to the (test) sentence being considered. Our results demonstrate that our approach extracts greater performance from PLMs: it achieves state-of-the-art performance on few-shot NER, achieving a 5% absolute improvement in F1 score on the CoNLL2003 dataset for GPT-4. We also see large gains of upto 28.85 points (F1/Acc.) in smaller models like GPT-j-6B.
When analysing Differentially Private (DP) machine learning pipelines, the potential privacy cost of data-dependent pre-processing is frequently overlooked in privacy accounting. In this work, we propose a general framework to evaluate the additional privacy cost incurred by non-private data-dependent pre-processing algorithms. Our framework establishes upper bounds on the overall privacy guarantees by utilising two new technical notions: a variant of DP termed Smooth DP and the bounded sensitivity of the pre-processing algorithms. In addition to the generic framework, we provide explicit overall privacy guarantees for multiple data-dependent pre-processing algorithms, such as data imputation, quantization, deduplication and PCA, when used in combination with several DP algorithms. Notably, this framework is also simple to implement, allowing direct integration into existing DP pipelines.
Audio-visual representation learning aims to develop systems with human-like perception by utilizing correlation between auditory and visual information. However, current models often focus on a limited set of tasks, and generalization abilities of learned representations are unclear. To this end, we propose the AV-SUPERB benchmark that enables general-purpose evaluation of unimodal audio/visual and bimodal fusion representations on 7 datasets covering 5 audio-visual tasks in speech and audio processing. We evaluate 5 recent self-supervised models and show that none of these models generalize to all tasks, emphasizing the need for future study on improving universal model performance. In addition, we show that representations may be improved with intermediate-task fine-tuning and audio event classification with AudioSet serves as a strong intermediate task. We release our benchmark with evaluation code and a model submission platform to encourage further research in audio-visual learning.
Recent contrastive representation learning methods rely on estimating mutual information (MI) between multiple views of an underlying context. E.g., we can derive multiple views of a given image by applying data augmentation, or we can split a sequence into views comprising the past and future of some step in the sequence. Contrastive lower bounds on MI are easy to optimize, but have a strong underestimation bias when estimating large amounts of MI. We propose decomposing the full MI estimation problem into a sum of smaller estimation problems by splitting one of the views into progressively more informed subviews and by applying the chain rule on MI between the decomposed views. This expression contains a sum of unconditional and conditional MI terms, each measuring modest chunks of the total MI, which facilitates approximation via contrastive bounds. To maximize the sum, we formulate a contrastive lower bound on the conditional MI which can be approximated efficiently. We refer to our general approach as Decomposed Estimation of Mutual Information (DEMI). We show that DEMI can capture a larger amount of MI than standard non-decomposed contrastive bounds in a synthetic setting, and learns better representations in a vision domain and for dialogue generation.
Federated Learning (FL) is a decentralized machine-learning paradigm, in which a global server iteratively averages the model parameters of local users without accessing their data. User heterogeneity has imposed significant challenges to FL, which can incur drifted global models that are slow to converge. Knowledge Distillation has recently emerged to tackle this issue, by refining the server model using aggregated knowledge from heterogeneous users, other than directly averaging their model parameters. This approach, however, depends on a proxy dataset, making it impractical unless such a prerequisite is satisfied. Moreover, the ensemble knowledge is not fully utilized to guide local model learning, which may in turn affect the quality of the aggregated model. Inspired by the prior art, we propose a data-free knowledge distillation} approach to address heterogeneous FL, where the server learns a lightweight generator to ensemble user information in a data-free manner, which is then broadcasted to users, regulating local training using the learned knowledge as an inductive bias. Empirical studies powered by theoretical implications show that, our approach facilitates FL with better generalization performance using fewer communication rounds, compared with the state-of-the-art.
Unsupervised domain adaptation (UDA) methods for person re-identification (re-ID) aim at transferring re-ID knowledge from labeled source data to unlabeled target data. Although achieving great success, most of them only use limited data from a single-source domain for model pre-training, making the rich labeled data insufficiently exploited. To make full use of the valuable labeled data, we introduce the multi-source concept into UDA person re-ID field, where multiple source datasets are used during training. However, because of domain gaps, simply combining different datasets only brings limited improvement. In this paper, we try to address this problem from two perspectives, \ie{} domain-specific view and domain-fusion view. Two constructive modules are proposed, and they are compatible with each other. First, a rectification domain-specific batch normalization (RDSBN) module is explored to simultaneously reduce domain-specific characteristics and increase the distinctiveness of person features. Second, a graph convolutional network (GCN) based multi-domain information fusion (MDIF) module is developed, which minimizes domain distances by fusing features of different domains. The proposed method outperforms state-of-the-art UDA person re-ID methods by a large margin, and even achieves comparable performance to the supervised approaches without any post-processing techniques.
In semi-supervised domain adaptation, a few labeled samples per class in the target domain guide features of the remaining target samples to aggregate around them. However, the trained model cannot produce a highly discriminative feature representation for the target domain because the training data is dominated by labeled samples from the source domain. This could lead to disconnection between the labeled and unlabeled target samples as well as misalignment between unlabeled target samples and the source domain. In this paper, we propose a novel approach called Cross-domain Adaptive Clustering to address this problem. To achieve both inter-domain and intra-domain adaptation, we first introduce an adversarial adaptive clustering loss to group features of unlabeled target data into clusters and perform cluster-wise feature alignment across the source and target domains. We further apply pseudo labeling to unlabeled samples in the target domain and retain pseudo-labels with high confidence. Pseudo labeling expands the number of ``labeled" samples in each class in the target domain, and thus produces a more robust and powerful cluster core for each class to facilitate adversarial learning. Extensive experiments on benchmark datasets, including DomainNet, Office-Home and Office, demonstrate that our proposed approach achieves the state-of-the-art performance in semi-supervised domain adaptation.
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