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As AI model size grows, neural scaling laws have become a crucial tool to predict the improvements of large models when increasing capacity and the size of original (human or natural) training data. Yet, the widespread use of popular models means that the ecosystem of online data and text will co-evolve to progressively contain increased amounts of synthesized data. In this paper we ask: How will the scaling laws change in the inevitable regime where synthetic data makes its way into the training corpus? Will future models, still improve, or be doomed to degenerate up to total (model) collapse? We develop a theoretical framework of model collapse through the lens of scaling laws. We discover a wide range of decay phenomena, analyzing loss of scaling, shifted scaling with number of generations, the ''un-learning" of skills, and grokking when mixing human and synthesized data. Our theory is validated by large-scale experiments with a transformer on an arithmetic task and text generation using the large language model Llama2. 

Adversarial examples have been shown to cause neural networks to fail on a wide range of vision and language tasks, but recent work has claimed that {\em Bayesian} neural networks (BNNs) are inherently robust to adversarial perturbations. In this work, we examine this claim. To study the adversarial robustness of BNNs, we investigate whether it is possible to successfully break state-of-the-art BNN inference methods and prediction pipelines using even relatively unsophisticated attacks for three tasks: (1) label prediction under the posterior predictive mean, (2) adversarial example detection with Bayesian predictive uncertainty, and (3) semantic shift detection. We find that BNNs trained with state-of-the-art approximate inference methods, and even BNNs trained with Hamiltonian Monte Carlo, are highly susceptible to adversarial attacks. We also identify various conceptual and experimental errors in previous works that claimed inherent adversarial robustness of BNNs and conclusively demonstrate that BNNs and uncertainty-aware Bayesian prediction pipelines are {\em not} inherently robust against adversarial attacks. 

Dataset distillation extracts a small set of synthetic training samples from a large dataset with the goal of achieving competitive performance on test data when trained on this sample. In this work, we tackle dataset distillation at its core by treating it directly as a bilevel optimization problem. Re-examining the foundational back-propagation through time method, we study the pronounced variance in the gradients, computational burden, and long-term dependencies. We introduce an improved method: Random Truncated Backpropagation Through Time (RaT-BPTT) to address them. RaT-BPTT incorporates a truncation coupled with a random window, effectively stabilizing the gradients and speeding up the optimization while covering long dependencies. This allows us to establish new state-of-the-art for a variety of standard dataset benchmarks. A deeper dive into the nature of distilled data unveils pronounced intercorrelation. In particular, subsets of distilled datasets tend to exhibit much worse performance than directly distilled smaller datasets of the same size. Leveraging RaT-BPTT, we devise a boosting mechanism that generates distilled datasets that contain subsets with near optimal performance across different data budgets. 

As AI model size grows, neural scaling laws have become a crucial tool to predict the improvements of large models when increasing capacity and the size of original (human or natural) training data. Yet, the widespread use of popular models means that the ecosystem of online data and text will co-evolve to progressively contain increased amounts of synthesized data. In this paper we ask: How will the scaling laws change in the inevitable regime where synthetic data makes its way into the training corpus? Will future models, still improve, or be doomed to degenerate up to total (model) collapse? We develop a theoretical framework of model collapse through the lens of scaling laws. We discover a wide range of decay phenomena, analyzing loss of scaling, shifted scaling with number of generations, ``un-learning" of skills, and grokking when mixing human and synthesized data. Our theory is validated by large-scale experiments with a transformer on an arithmetic task and text generation using the large language model Llama2. 

Training of large-scale models in general requires enormous amounts of traning data. Dataset distillation aims to extract a small set of synthetic training samples from a large dataset with the goal of achieving competitive performance on test data when trained on this sample, thus reducing both dataset size and training time. In this work, we tackle dataset distillation at its core by treating it directly as a bilevel optimization problem. Re-examining the foundational back-propagation through time method, we study the pronounced variance in the gradients, computational burden, and long-term dependencies. We introduce an improved method: Random Truncated Backpropagation Through Time (RaT-BPTT) to address them. RaT-BPTT incorporates a truncation coupled with a random window, effectively stabilizing the gradients and speeding up the optimization while covering long dependencies. This allows us to establish new dataset distillation state-of-the-art for a variety of standard dataset benchmarks.