Alex Infanger

Aditya Cowsik, Kfir Dolev, Alex Infanger

We present a complete mechanistic description of the algorithm learned by a minimal non-linear sparse data autoencoder in the limit of large input dimension. The model, originally presented in arXiv:2209.10652, compresses sparse data vectors through a linear layer and decompresses using another linear layer followed by a ReLU activation. We notice that when the data is permutation symmetric (no input feature is privileged) large models reliably learn an algorithm that is sensitive to individual weights only through their large-scale statistics. For these models, the loss function becomes analytically tractable. Using this understanding, we give the explicit scalings of the loss at high sparsity, and show that the model is near-optimal among recently proposed architectures. In particular, changing or adding to the activation function any elementwise or filtering operation can at best improve the model's performance by a constant factor. Finally, we forward-engineer a model with the requisite symmetries and show that its loss precisely matches that of the trained models. Unlike the trained model weights, the low randomness in the artificial weights results in miraculous fractal structures resembling a Persian rug, to which the algorithm is oblivious. Our work contributes to neural network interpretability by introducing techniques for understanding the structure of autoencoders. Code to reproduce our results can be found at https://github.com/KfirD/PersianRug .

Henrik Marklund, Alex Infanger, Benjamin Van Roy

Because human preferences are too complex to codify, AIs operate with misspecified objectives. Optimizing such objectives often produces undesirable outcomes; this phenomenon is known as reward hacking. Such outcomes are not necessarily catastrophic. Indeed, most examples of reward hacking in previous literature are benign. And typically, objectives can be modified to resolve the issue. We study the prospect of catastrophic outcomes induced by AIs operating in complex environments. We argue that, when capabilities are sufficiently advanced, pursuing a fixed consequentialist objective tends to result in catastrophic outcomes. We formalize this by establishing conditions that provably lead to such outcomes. Under these conditions, simple or random behavior is safe. Catastrophic risk arises due to extraordinary competence rather than incompetence. With a fixed consequentialist objective, avoiding catastrophe requires constraining AI capabilities. In fact, constraining capabilities the right amount not only averts catastrophe but yields valuable outcomes. Our results apply to any objective produced by modern industrial AI development pipelines.

Henrik Marklund, Alex Infanger, Benjamin Van Roy

Reward functions, learned or manually specified, are rarely perfect. Instead of accurately expressing human goals, these reward functions are often distorted by human beliefs about how best to achieve those goals. Specifically, these reward functions often express a combination of the human's terminal goals -- those which are ends in themselves -- and the human's instrumental goals -- those which are means to an end. We formulate a simple example in which even slight conflation of instrumental and terminal goals results in severe misalignment: optimizing the misspecified reward function results in poor performance when measured by the true reward function. This example distills the essential properties of environments that make reinforcement learning highly sensitive to conflation of instrumental and terminal goals. We discuss how this issue can arise with a common approach to reward learning and how it can manifest in real environments.