Implementing a reward function that perfectly captures a complex task in the real world is impractical. As a result, it is often appropriate to think of the reward function as a proxy for the true objective rather than as its definition. We study this phenomenon through the lens of Goodhart's law, which predicts that increasing optimisation of an imperfect proxy beyond some critical point decreases performance on the true objective. First, we propose a way to quantify the magnitude of this effect and show empirically that optimising an imperfect proxy reward often leads to the behaviour predicted by Goodhart's law for a wide range of environments and reward functions. We then provide a geometric explanation for why Goodhart's law occurs in Markov decision processes. We use these theoretical insights to propose an optimal early stopping method that provably avoids the aforementioned pitfall and derive theoretical regret bounds for this method. Moreover, we derive a training method that maximises worst-case reward, for the setting where there is uncertainty about the true reward function. Finally, we evaluate our early stopping method experimentally. Our results support a foundation for a theoretically-principled study of reinforcement learning under reward misspecification.
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Dataset distillation aims to generate a smaller but representative subset from a large dataset, which allows a model to be trained efficiently, meanwhile evaluating on the original testing data distribution to achieve decent performance. Many prior works have aimed to align with diverse aspects of the original datasets, such as matching the training weight trajectories, gradient, feature/BatchNorm distributions, etc. In this work, we show how to distill various large-scale datasets such as full ImageNet-1K/21K under a conventional input resolution of 224$\times$224 to achieve the best accuracy over all previous approaches, including SRe$^2$L, TESLA and MTT. To achieve this, we introduce a simple yet effective ${\bf C}$urriculum ${\bf D}$ata ${\bf A}$ugmentation ($\texttt{CDA}$) during data synthesis that obtains the accuracy on large-scale ImageNet-1K and 21K with 63.2% under IPC (Images Per Class) 50 and 36.1% under IPC 20, respectively. Finally, we show that, by integrating all our enhancements together, the proposed model beats the current state-of-the-art by more than 4% Top-1 accuracy on ImageNet-1K/21K and for the first time, reduces the gap to its full-data training counterpart to less than absolute 15%. Moreover, this work represents the inaugural success in dataset distillation on larger-scale ImageNet-21K under the standard 224$\times$224 resolution. Our code and distilled ImageNet-21K dataset of 20 IPC, 2K recovery budget are available at //github.com/VILA-Lab/SRe2L/tree/main/CDA.
Fractional derivatives are a well-studied generalization of integer order derivatives. Naturally, for optimization, it is of interest to understand the convergence properties of gradient descent using fractional derivatives. Convergence analysis of fractional gradient descent is currently limited both in the methods analyzed and the settings analyzed. This paper aims to fill in these gaps by analyzing variations of fractional gradient descent in smooth and convex, smooth and strongly convex, and smooth and non-convex settings. First, novel bounds will be established bridging fractional and integer derivatives. Then, these bounds will be applied to the aforementioned settings to prove $O(1/T)$ convergence for smooth and convex functions and linear convergence for smooth and strongly convex functions. Additionally, we prove $O(1/T)$ convergence for smooth and non-convex functions using an extended notion of smoothness that is more natural for fractional derivatives. Finally, empirical results will be presented on the potential speed up of fractional gradient descent over standard gradient descent as well as the challenges of predicting which will be faster in general.
Programs using random values can either make all choices in advance (eagerly) or sample as needed (lazily). In formal proofs, we focus on indistinguishability between two lazy programs, a common requirement in the random oracle model (ROM). While rearranging sampling instructions often solves this, it gets complex when sampling is spread across procedures. The traditional approach, introduced by Bellare and Rogaway in 2004, converts programs to eager sampling, but requires assuming finite memory, a polynomial bound, and artificial resampling functions. We introduce a novel approach in probabilistic Relational Hoare Logic (pRHL) that directly proves indistinguishability, eliminating the need for conversions and the mentioned assumptions. We also implement this approach in the EasyCrypt theorem prover, showing that it can be a convenient alternative to the traditional method.
As artificial intelligence (AI) models continue to scale up, they are becoming more capable and integrated into various forms of decision-making systems. For models involved in moral decision-making, also known as artificial moral agents (AMA), interpretability provides a way to trust and understand the agent's internal reasoning mechanisms for effective use and error correction. In this paper, we provide an overview of this rapidly-evolving sub-field of AI interpretability, introduce the concept of the Minimum Level of Interpretability (MLI) and recommend an MLI for various types of agents, to aid their safe deployment in real-world settings.
Reasoning is a fundamental aspect of human intelligence that plays a crucial role in activities such as problem solving, decision making, and critical thinking. In recent years, large language models (LLMs) have made significant progress in natural language processing, and there is observation that these models may exhibit reasoning abilities when they are sufficiently large. However, it is not yet clear to what extent LLMs are capable of reasoning. This paper provides a comprehensive overview of the current state of knowledge on reasoning in LLMs, including techniques for improving and eliciting reasoning in these models, methods and benchmarks for evaluating reasoning abilities, findings and implications of previous research in this field, and suggestions on future directions. Our aim is to provide a detailed and up-to-date review of this topic and stimulate meaningful discussion and future work.
Following unprecedented success on the natural language tasks, Transformers have been successfully applied to several computer vision problems, achieving state-of-the-art results and prompting researchers to reconsider the supremacy of convolutional neural networks (CNNs) as {de facto} operators. Capitalizing on these advances in computer vision, the medical imaging field has also witnessed growing interest for Transformers that can capture global context compared to CNNs with local receptive fields. Inspired from this transition, in this survey, we attempt to provide a comprehensive review of the applications of Transformers in medical imaging covering various aspects, ranging from recently proposed architectural designs to unsolved issues. Specifically, we survey the use of Transformers in medical image segmentation, detection, classification, reconstruction, synthesis, registration, clinical report generation, and other tasks. In particular, for each of these applications, we develop taxonomy, identify application-specific challenges as well as provide insights to solve them, and highlight recent trends. Further, we provide a critical discussion of the field's current state as a whole, including the identification of key challenges, open problems, and outlining promising future directions. We hope this survey will ignite further interest in the community and provide researchers with an up-to-date reference regarding applications of Transformer models in medical imaging. Finally, to cope with the rapid development in this field, we intend to regularly update the relevant latest papers and their open-source implementations at \url{//github.com/fahadshamshad/awesome-transformers-in-medical-imaging}.
This manuscript portrays optimization as a process. In many practical applications the environment is so complex that it is infeasible to lay out a comprehensive theoretical model and use classical algorithmic theory and mathematical optimization. It is necessary as well as beneficial to take a robust approach, by applying an optimization method that learns as one goes along, learning from experience as more aspects of the problem are observed. This view of optimization as a process has become prominent in varied fields and has led to some spectacular success in modeling and systems that are now part of our daily lives.
In the era of deep learning, modeling for most NLP tasks has converged to several mainstream paradigms. For example, we usually adopt the sequence labeling paradigm to solve a bundle of tasks such as POS-tagging, NER, Chunking, and adopt the classification paradigm to solve tasks like sentiment analysis. With the rapid progress of pre-trained language models, recent years have observed a rising trend of Paradigm Shift, which is solving one NLP task by reformulating it as another one. Paradigm shift has achieved great success on many tasks, becoming a promising way to improve model performance. Moreover, some of these paradigms have shown great potential to unify a large number of NLP tasks, making it possible to build a single model to handle diverse tasks. In this paper, we review such phenomenon of paradigm shifts in recent years, highlighting several paradigms that have the potential to solve different NLP tasks.
We propose a novel method for automatic reasoning on knowledge graphs based on debate dynamics. The main idea is to frame the task of triple classification as a debate game between two reinforcement learning agents which extract arguments -- paths in the knowledge graph -- with the goal to promote the fact being true (thesis) or the fact being false (antithesis), respectively. Based on these arguments, a binary classifier, called the judge, decides whether the fact is true or false. The two agents can be considered as sparse, adversarial feature generators that present interpretable evidence for either the thesis or the antithesis. In contrast to other black-box methods, the arguments allow users to get an understanding of the decision of the judge. Since the focus of this work is to create an explainable method that maintains a competitive predictive accuracy, we benchmark our method on the triple classification and link prediction task. Thereby, we find that our method outperforms several baselines on the benchmark datasets FB15k-237, WN18RR, and Hetionet. We also conduct a survey and find that the extracted arguments are informative for users.
It is important to detect anomalous inputs when deploying machine learning systems. The use of larger and more complex inputs in deep learning magnifies the difficulty of distinguishing between anomalous and in-distribution examples. At the same time, diverse image and text data are available in enormous quantities. We propose leveraging these data to improve deep anomaly detection by training anomaly detectors against an auxiliary dataset of outliers, an approach we call Outlier Exposure (OE). This enables anomaly detectors to generalize and detect unseen anomalies. In extensive experiments on natural language processing and small- and large-scale vision tasks, we find that Outlier Exposure significantly improves detection performance. We also observe that cutting-edge generative models trained on CIFAR-10 may assign higher likelihoods to SVHN images than to CIFAR-10 images; we use OE to mitigate this issue. We also analyze the flexibility and robustness of Outlier Exposure, and identify characteristics of the auxiliary dataset that improve performance.
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