Wu's Method can Boost Symbolic AI to Rival Silver Medalists and AlphaGeometry to Outperform Gold Medalists at IMO Geometry

Proving geometric theorems constitutes a hallmark of visual reasoning combining both intuitive and logical skills. Therefore, automated theorem proving of Olympiad-level geometry problems is considered a notable milestone in human-level automated reasoning. The introduction of AlphaGeometry, a neuro-symbolic model trained with 100 million synthetic samples, marked a major breakthrough. It solved 25 of 30 International Mathematical Olympiad (IMO) problems whereas the reported baseline based on Wu's method solved only ten. In this note, we revisit the IMO-AG-30 Challenge introduced with AlphaGeometry, and find that Wu's method is surprisingly strong. Wu's method alone can solve 15 problems, and some of them are not solved by any of the other methods. This leads to two key findings: (i) Combining Wu's method with the classic synthetic methods of deductive databases and angle, ratio, and distance chasing solves 21 out of 30 methods by just using a CPU-only laptop with a time limit of 5 minutes per problem. Essentially, this classic method solves just 4 problems less than AlphaGeometry and establishes the first fully symbolic baseline strong enough to rival the performance of an IMO silver medalist. (ii) Wu's method even solves 2 of the 5 problems that AlphaGeometry failed to solve. Thus, by combining AlphaGeometry with Wu's method we set a new state-of-the-art for automated theorem proving on IMO-AG-30, solving 27 out of 30 problems, the first AI method which outperforms an IMO gold medalist.

No "Zero-Shot" Without Exponential Data: Pretraining Concept Frequency Determines Multimodal Model Performance

Web-crawled pretraining datasets underlie the impressive "zero-shot" evaluation performance of multimodal models, such as CLIP for classification/retrieval and Stable-Diffusion for image generation. However, it is unclear how meaningful the notion of "zero-shot" generalization is for such multimodal models, as it is not known to what extent their pretraining datasets encompass the downstream concepts targeted for during "zero-shot" evaluation. In this work, we ask: How is the performance of multimodal models on downstream concepts influenced by the frequency of these concepts in their pretraining datasets? We comprehensively investigate this question across 34 models and five standard pretraining datasets (CC-3M, CC-12M, YFCC-15M, LAION-400M, LAION-Aesthetics), generating over 300GB of data artifacts. We consistently find that, far from exhibiting "zero-shot" generalization, multimodal models require exponentially more data to achieve linear improvements in downstream "zero-shot" performance, following a sample inefficient log-linear scaling trend. This trend persists even when controlling for sample-level similarity between pretraining and downstream datasets, and testing on purely synthetic data distributions. Furthermore, upon benchmarking models on long-tailed data sampled based on our analysis, we demonstrate that multimodal models across the board perform poorly. We contribute this long-tail test set as the "Let it Wag!" benchmark to further research in this direction. Taken together, our study reveals an exponential need for training data which implies that the key to "zero-shot" generalization capabilities under large-scale training paradigms remains to be found.

Lifelong Benchmarks: Efficient Model Evaluation in an Era of Rapid Progress

Standardized benchmarks drive progress in machine learning. However, with repeated testing, the risk of overfitting grows as algorithms over-exploit benchmark idiosyncrasies. In our work, we seek to mitigate this challenge by compiling ever-expanding large-scale benchmarks called Lifelong Benchmarks. As exemplars of our approach, we create Lifelong-CIFAR10 and Lifelong-ImageNet, containing (for now) 1.69M and 1.98M test samples, respectively. While reducing overfitting, lifelong benchmarks introduce a key challenge: the high cost of evaluating a growing number of models across an ever-expanding sample set. To address this challenge, we also introduce an efficient evaluation framework: Sort \& Search (S&S), which reuses previously evaluated models by leveraging dynamic programming algorithms to selectively rank and sub-select test samples, enabling cost-effective lifelong benchmarking. Extensive empirical evaluations across 31,000 models demonstrate that S&S achieves highly-efficient approximate accuracy measurement, reducing compute cost from 180 GPU days to 5 GPU hours (1000x reduction) on a single A100 GPU, with low approximation error. As such, lifelong benchmarks offer a robust, practical solution to the "benchmark exhaustion" problem.

Corrective Machine Unlearning

Machine Learning models increasingly face data integrity challenges due to the use of large-scale training datasets drawn from the internet. We study what model developers can do if they detect that some data was manipulated or incorrect. Such manipulated data can cause adverse effects like vulnerability to backdoored samples, systematic biases, and in general, reduced accuracy on certain input domains. Often, all manipulated training samples are not known, and only a small, representative subset of the affected data is flagged. We formalize "Corrective Machine Unlearning" as the problem of mitigating the impact of data affected by unknown manipulations on a trained model, possibly knowing only a subset of impacted samples. We demonstrate that the problem of corrective unlearning has significantly different requirements from traditional privacy-oriented unlearning. We find most existing unlearning methods, including the gold-standard retraining-from-scratch, require most of the manipulated data to be identified for effective corrective unlearning. However, one approach, SSD, achieves limited success in unlearning adverse effects with just a small portion of the manipulated samples, showing the tractability of this setting. We hope our work spurs research towards developing better methods for corrective unlearning and offers practitioners a new strategy to handle data integrity challenges arising from web-scale training.

RanDumb: A Simple Approach that Questions the Efficacy of Continual Representation Learning

We propose RanDumb to examine the efficacy of continual representation learning. RanDumb embeds raw pixels using a fixed random transform which approximates an RBF-Kernel, initialized before seeing any data, and learns a simple linear classifier on top. We present a surprising and consistent finding: RanDumb significantly outperforms the continually learned representations using deep networks across numerous continual learning benchmarks, demonstrating the poor performance of representation learning in these scenarios. RanDumb stores no exemplars and performs a single pass over the data, processing one sample at a time. It complements GDumb, operating in a low-exemplar regime where GDumb has especially poor performance. We reach the same consistent conclusions when RanDumb is extended to scenarios with pretrained models replacing the random transform with pretrained feature extractor. Our investigation is both surprising and alarming as it questions our understanding of how to effectively design and train models that require efficient continual representation learning, and necessitates a principled reinvestigation of the widely explored problem formulation itself. Our code is available at https://github.com/drimpossible/RanDumb.

From Categories to Classifier: Name-Only Continual Learning by Exploring the Web

Continual Learning (CL) often relies on the availability of extensive annotated datasets, an assumption that is unrealistically time-consuming and costly in practice. We explore a novel paradigm termed name-only continual learning where time and cost constraints prohibit manual annotation. In this scenario, learners adapt to new category shifts using only category names without the luxury of annotated training data. Our proposed solution leverages the expansive and ever-evolving internet to query and download uncurated webly-supervised data for image classification. We investigate the reliability of our web data and find them comparable, and in some cases superior, to manually annotated datasets. Additionally, we show that by harnessing the web, we can create support sets that surpass state-of-the-art name-only classification that create support sets using generative models or image retrieval from LAION-5B, achieving up to 25% boost in accuracy. When applied across varied continual learning contexts, our method consistently exhibits a small performance gap in comparison to models trained on manually annotated datasets. We present EvoTrends, a class-incremental dataset made from the web to capture real-world trends, created in just minutes. Overall, this paper underscores the potential of using uncurated webly-supervised data to mitigate the challenges associated with manual data labeling in continual learning.

Inverse Scaling: When Bigger Isn't Better

Work on scaling laws has found that large language models (LMs) show predictable improvements to overall loss with increased scale (model size, training data, and compute). Here, we present evidence for the claim that LMs may show inverse scaling, or worse task performance with increased scale, e.g., due to flaws in the training objective and data. We present empirical evidence of inverse scaling on 11 datasets collected by running a public contest, the Inverse Scaling Prize, with a substantial prize pool. Through analysis of the datasets, along with other examples found in the literature, we identify four potential causes of inverse scaling: (i) preference to repeat memorized sequences over following in-context instructions, (ii) imitation of undesirable patterns in the training data, (iii) tasks containing an easy distractor task which LMs could focus on, rather than the harder real task, and (iv) correct but misleading few-shot demonstrations of the task. We release the winning datasets at https://inversescaling.com/data to allow for further investigation of inverse scaling. Our tasks have helped drive the discovery of U-shaped and inverted-U scaling trends, where an initial trend reverses, suggesting that scaling trends are less reliable at predicting the behavior of larger-scale models than previously understood. Overall, our results suggest that there are tasks for which increased model scale alone may not lead to progress, and that more careful thought needs to go into the data and objectives for training language models.

Rapid Adaptation in Online Continual Learning: Are We Evaluating It Right?

We revisit the common practice of evaluating adaptation of Online Continual Learning (OCL) algorithms through the metric of online accuracy, which measures the accuracy of the model on the immediate next few samples. However, we show that this metric is unreliable, as even vacuous blind classifiers, which do not use input images for prediction, can achieve unrealistically high online accuracy by exploiting spurious label correlations in the data stream. Our study reveals that existing OCL algorithms can also achieve high online accuracy, but perform poorly in retaining useful information, suggesting that they unintentionally learn spurious label correlations. To address this issue, we propose a novel metric for measuring adaptation based on the accuracy on the near-future samples, where spurious correlations are removed. We benchmark existing OCL approaches using our proposed metric on large-scale datasets under various computational budgets and find that better generalization can be achieved by retaining and reusing past seen information. We believe that our proposed metric can aid in the development of truly adaptive OCL methods. We provide code to reproduce our results at https://github.com/drimpossible/EvalOCL.

Online Continual Learning Without the Storage Constraint

Online continual learning (OCL) research has primarily focused on mitigating catastrophic forgetting with fixed and limited storage allocation throughout the agent's lifetime. However, the growing affordability of data storage highlights a broad range of applications that do not adhere to these assumptions. In these cases, the primary concern lies in managing computational expenditures rather than storage. In this paper, we target such settings, investigating the online continual learning problem by relaxing storage constraints and emphasizing fixed, limited economical budget. We provide a simple algorithm that can compactly store and utilize the entirety of the incoming data stream under tiny computational budgets using a kNN classifier and universal pre-trained feature extractors. Our algorithm provides a consistency property attractive to continual learning: It will never forget past seen data. We set a new state of the art on two large-scale OCL datasets: Continual LOCalization (CLOC), which has 39M images over 712 classes, and Continual Google Landmarks V2 (CGLM), which has 580K images over 10,788 classes -- beating methods under far higher computational budgets than ours in terms of both reducing catastrophic forgetting of past data and quickly adapting to rapidly changing data streams. We provide code to reproduce our results at \url{https://github.com/drimpossible/ACM}.

Computationally Budgeted Continual Learning: What Does Matter?

Continual Learning (CL) aims to sequentially train models on streams of incoming data that vary in distribution by preserving previous knowledge while adapting to new data. Current CL literature focuses on restricted access to previously seen data, while imposing no constraints on the computational budget for training. This is unreasonable for applications in-the-wild, where systems are primarily constrained by computational and time budgets, not storage. We revisit this problem with a large-scale benchmark and analyze the performance of traditional CL approaches in a compute-constrained setting, where effective memory samples used in training can be implicitly restricted as a consequence of limited computation. We conduct experiments evaluating various CL sampling strategies, distillation losses, and partial fine-tuning on two large-scale datasets, namely ImageNet2K and Continual Google Landmarks V2 in data incremental, class incremental, and time incremental settings. Through extensive experiments amounting to a total of over 1500 GPU-hours, we find that, under compute-constrained setting, traditional CL approaches, with no exception, fail to outperform a simple minimal baseline that samples uniformly from memory. Our conclusions are consistent in a different number of stream time steps, e.g., 20 to 200, and under several computational budgets. This suggests that most existing CL methods are particularly too computationally expensive for realistic budgeted deployment. Code for this project is available at: https://github.com/drimpossible/BudgetCL.