Seijin Kobayashi

Johannes von Oswald, Maximilian Schlegel, Alexander Meulemans et al. · deepmind

Some autoregressive models exhibit in-context learning capabilities: being able to learn as an input sequence is processed, without undergoing any parameter changes, and without being explicitly trained to do so. The origins of this phenomenon are still poorly understood. Here we analyze a series of Transformer models trained to perform synthetic sequence prediction tasks, and discover that standard next-token prediction error minimization gives rise to a subsidiary learning algorithm that adjusts the model as new inputs are revealed. We show that this process corresponds to gradient-based optimization of a principled objective function, which leads to strong generalization performance on unseen sequences. Our findings explain in-context learning as a product of autoregressive loss minimization and inform the design of new optimization-based Transformer layers.

Seijin Kobayashi, Simon Schug, Yassir Akram et al. · deepmind

Many tasks can be composed from a few independent components. This gives rise to a combinatorial explosion of possible tasks, only some of which might be encountered during training. Under what circumstances can transformers compositionally generalize from a subset of tasks to all possible combinations of tasks that share similar components? Here we study a modular multitask setting that allows us to precisely control compositional structure in the data generation process. We present evidence that transformers learning in-context struggle to generalize compositionally on this task despite being in principle expressive enough to do so. Compositional generalization becomes possible only when introducing a bottleneck that enforces an explicit separation between task inference and task execution.

Elvis Nava, Seijin Kobayashi, Yifei Yin et al. · eth-zurich, mit

We introduce meta-learning algorithms that perform zero-shot weight-space adaptation of neural network models to unseen tasks. Our methods repurpose the popular generative image synthesis techniques of natural language guidance and diffusion models to generate neural network weights adapted for tasks. We first train an unconditional generative hypernetwork model to produce neural network weights; then we train a second "guidance" model that, given a natural language task description, traverses the hypernetwork latent space to find high-performance task-adapted weights in a zero-shot manner. We explore two alternative approaches for latent space guidance: "HyperCLIP"-based classifier guidance and a conditional Hypernetwork Latent Diffusion Model ("HyperLDM"), which we show to benefit from the classifier-free guidance technique common in image generation. Finally, we demonstrate that our approaches outperform existing multi-task and meta-learning methods in a series of zero-shot learning experiments on our Meta-VQA dataset.

Alexander Meulemans, Simon Schug, Seijin Kobayashi et al.

To make reinforcement learning more sample efficient, we need better credit assignment methods that measure an action's influence on future rewards. Building upon Hindsight Credit Assignment (HCA), we introduce Counterfactual Contribution Analysis (COCOA), a new family of model-based credit assignment algorithms. Our algorithms achieve precise credit assignment by measuring the contribution of actions upon obtaining subsequent rewards, by quantifying a counterfactual query: 'Would the agent still have reached this reward if it had taken another action?'. We show that measuring contributions w.r.t. rewarding states, as is done in HCA, results in spurious estimates of contributions, causing HCA to degrade towards the high-variance REINFORCE estimator in many relevant environments. Instead, we measure contributions w.r.t. rewards or learned representations of the rewarding objects, resulting in gradient estimates with lower variance. We run experiments on a suite of problems specifically designed to evaluate long-term credit assignment capabilities. By using dynamic programming, we measure ground-truth policy gradients and show that the improved performance of our new model-based credit assignment methods is due to lower bias and variance compared to HCA and common baselines. Our results demonstrate how modeling action contributions towards rewarding outcomes can be leveraged for credit assignment, opening a new path towards sample-efficient reinforcement learning.

Alexander Meulemans, Nicolas Zucchet, Seijin Kobayashi et al.

Equilibrium systems are a powerful way to express neural computations. As special cases, they include models of great current interest in both neuroscience and machine learning, such as deep neural networks, equilibrium recurrent neural networks, deep equilibrium models, or meta-learning. Here, we present a new principle for learning such systems with a temporally- and spatially-local rule. Our principle casts learning as a least-control problem, where we first introduce an optimal controller to lead the system towards a solution state, and then define learning as reducing the amount of control needed to reach such a state. We show that incorporating learning signals within a dynamics as an optimal control enables transmitting activity-dependent credit assignment information, avoids storing intermediate states in memory, and does not rely on infinitesimal learning signals. In practice, our principle leads to strong performance matching that of leading gradient-based learning methods when applied to an array of problems involving recurrent neural networks and meta-learning. Our results shed light on how the brain might learn and offer new ways of approaching a broad class of machine learning problems.

Nicolas Zucchet, Seijin Kobayashi, Yassir Akram et al.

Recent architectural developments have enabled recurrent neural networks (RNNs) to reach and even surpass the performance of Transformers on certain sequence modeling tasks. These modern RNNs feature a prominent design pattern: linear recurrent layers interconnected by feedforward paths with multiplicative gating. Here, we show how RNNs equipped with these two design elements can exactly implement (linear) self-attention, the main building block of Transformers. By reverse-engineering a set of trained RNNs, we find that gradient descent in practice discovers our construction. In particular, we examine RNNs trained to solve simple in-context learning tasks on which Transformers are known to excel and find that gradient descent instills in our RNNs the same attention-based in-context learning algorithm used by Transformers. Our findings highlight the importance of multiplicative interactions in neural networks and suggest that certain RNNs might be unexpectedly implementing attention under the hood.

Seijin Kobayashi, Yanick Schimpf, Maximilian Schlegel et al.

Large-scale autoregressive models pretrained on next-token prediction and finetuned with reinforcement learning (RL) have achieved unprecedented success on many problem domains. During RL, these models explore by generating new outputs, one token at a time. However, sampling actions token-by-token can result in highly inefficient learning, particularly when rewards are sparse. Here, we show that it is possible to overcome this problem by acting and exploring within the internal representations of an autoregressive model. Specifically, to discover temporally-abstract actions, we introduce a higher-order, non-causal sequence model whose outputs control the residual stream activations of a base autoregressive model. On grid world and MuJoCo-based tasks with hierarchical structure, we find that the higher-order model learns to compress long activation sequence chunks onto internal controllers. Critically, each controller executes a sequence of behaviorally meaningful actions that unfold over long timescales and are accompanied with a learned termination condition, such that composing multiple controllers over time leads to efficient exploration on novel tasks. We show that direct internal controller reinforcement, a process we term "internal RL", enables learning from sparse rewards in cases where standard RL finetuning fails. Our results demonstrate the benefits of latent action generation and reinforcement in autoregressive models, suggesting internal RL as a promising avenue for realizing hierarchical RL within foundation models.

Seijin Kobayashi, Pau Vilimelis Aceituno, Johannes von Oswald

Identifying unfamiliar inputs, also known as out-of-distribution (OOD) detection, is a crucial property of any decision making process. A simple and empirically validated technique is based on deep ensembles where the variance of predictions over different neural networks acts as a substitute for input uncertainty. Nevertheless, a theoretical understanding of the inductive biases leading to the performance of deep ensemble's uncertainty estimation is missing. To improve our description of their behavior, we study deep ensembles with large layer widths operating in simplified linear training regimes, in which the functions trained with gradient descent can be described by the neural tangent kernel. We identify two sources of noise, each inducing a distinct inductive bias in the predictive variance at initialization. We further show theoretically and empirically that both noise sources affect the predictive variance of non-linear deep ensembles in toy models and realistic settings after training. Finally, we propose practical ways to eliminate part of these noise sources leading to significant changes and improved OOD detection in trained deep ensembles.

Johannes von Oswald, Seijin Kobayashi, Yassir Akram et al.

Randomization is a powerful tool that endows algorithms with remarkable properties. For instance, randomized algorithms excel in adversarial settings, often surpassing the worst-case performance of deterministic algorithms with large margins. Furthermore, their success probability can be amplified by simple strategies such as repetition and majority voting. In this paper, we enhance deep neural networks, in particular transformer models, with randomization. We demonstrate for the first time that randomized algorithms can be instilled in transformers through learning, in a purely data- and objective-driven manner. First, we analyze known adversarial objectives for which randomized algorithms offer a distinct advantage over deterministic ones. We then show that common optimization techniques, such as gradient descent or evolutionary strategies, can effectively learn transformer parameters that make use of the randomness provided to the model. To illustrate the broad applicability of randomization in empowering neural networks, we study three conceptual tasks: associative recall, graph coloring, and agents that explore grid worlds. In addition to demonstrating increased robustness against oblivious adversaries through learned randomization, our experiments reveal remarkable performance improvements due to the inherently random nature of the neural networks' computation and predictions.

Seijin Kobayashi, Yassir Akram, Johannes Von Oswald

The effect of regularizers such as weight decay when training deep neural networks is not well understood. We study the influence of weight decay as well as $L2$-regularization when training neural network models in which parameter matrices interact multiplicatively. This combination is of particular interest as this parametrization is common in attention layers, the workhorse of transformers. Here, key-query, as well as value-projection parameter matrices, are multiplied directly with each other: $W_K^TW_Q$ and $PW_V$. We extend previous results and show on one hand that any local minimum of a $L2$-regularized loss of the form $L(AB^\top) + λ(\|A\|^2 + \|B\|^2)$ coincides with a minimum of the nuclear norm-regularized loss $L(AB^\top) + λ\|AB^\top\|_*$, and on the other hand that the 2 losses become identical exponentially quickly during training. We thus complement existing works linking $L2$-regularization with low-rank regularization, and in particular, explain why such regularization on the matrix product affects early stages of training. Based on these theoretical insights, we verify empirically that the key-query and value-projection matrix products $W_K^TW_Q, PW_V$ within attention layers, when optimized with weight decay, as usually done in vision tasks and language modelling, indeed induce a significant reduction in the rank of $W_K^TW_Q$ and $PW_V$, even in fully online training. We find that, in accordance with existing work, inducing low rank in attention matrix products can damage language model performance, and observe advantages when decoupling weight decay in attention layers from the rest of the parameters.

Simon Schug, Seijin Kobayashi, Yassir Akram et al. · deepmind

Many complex tasks can be decomposed into simpler, independent parts. Discovering such underlying compositional structure has the potential to enable compositional generalization. Despite progress, our most powerful systems struggle to compose flexibly. It therefore seems natural to make models more modular to help capture the compositional nature of many tasks. However, it is unclear under which circumstances modular systems can discover hidden compositional structure. To shed light on this question, we study a teacher-student setting with a modular teacher where we have full control over the composition of ground truth modules. This allows us to relate the problem of compositional generalization to that of identification of the underlying modules. In particular we study modularity in hypernetworks representing a general class of multiplicative interactions. We show theoretically that identification up to linear transformation purely from demonstrations is possible without having to learn an exponential number of module combinations. We further demonstrate empirically that under the theoretically identified conditions, meta-learning from finite data can discover modular policies that generalize compositionally in a number of complex environments.

Johannes von Oswald, Nino Scherrer, Seijin Kobayashi et al. · deepmind

Sequence modeling is currently dominated by causal transformer architectures that use softmax self-attention. Although widely adopted, transformers require scaling memory and compute linearly during inference. A recent stream of work linearized the softmax operation, resulting in powerful recurrent neural network (RNN) models with constant memory and compute costs such as DeltaNet, Mamba or xLSTM. These models can be unified by noting that their recurrent layer dynamics can all be derived from an in-context regression objective, approximately optimized through an online learning rule. Here, we join this line of work and introduce a numerically stable, chunkwise parallelizable version of the recently proposed Mesa layer (von Oswald et al., 2024), and study it in language modeling at the billion-parameter scale. This layer again stems from an in-context loss, but which is now minimized to optimality at every time point using a fast conjugate gradient solver. Through an extensive suite of experiments, we show that optimal test-time training enables reaching lower language modeling perplexity and higher downstream benchmark performance than previous RNNs, especially on tasks requiring long context understanding. This performance gain comes at the cost of additional flops spent during inference time. Our results are therefore intriguingly related to recent trends of increasing test-time compute to improve performance -- here by spending compute to solve sequential optimization problems within the neural network itself.

Alexander Meulemans, Seijin Kobayashi, Johannes von Oswald et al.

Self-interested individuals often fail to cooperate, posing a fundamental challenge for multi-agent learning. How can we achieve cooperation among self-interested, independent learning agents? Promising recent work has shown that in certain tasks cooperation can be established between learning-aware agents who model the learning dynamics of each other. Here, we present the first unbiased, higher-derivative-free policy gradient algorithm for learning-aware reinforcement learning, which takes into account that other agents are themselves learning through trial and error based on multiple noisy trials. We then leverage efficient sequence models to condition behavior on long observation histories that contain traces of the learning dynamics of other agents. Training long-context policies with our algorithm leads to cooperative behavior and high returns on standard social dilemmas, including a challenging environment where temporally-extended action coordination is required. Finally, we derive from the iterated prisoner's dilemma a novel explanation for how and when cooperation arises among self-interested learning-aware agents.

Alexander Meulemans, Rajai Nasser, Maciej Wołczyk et al.

The standard theory of model-free reinforcement learning assumes that the environment dynamics are stationary and that agents are decoupled from their environment, such that policies are treated as being separate from the world they inhabit. This leads to theoretical challenges in the multi-agent setting where the non-stationarity induced by the learning of other agents demands prospective learning based on prediction models. To accurately model other agents, an agent must account for the fact that those other agents are, in turn, forming beliefs about it to predict its future behavior, motivating agents to model themselves as part of the environment. Here, building upon foundational work on universal artificial intelligence (AIXI), we introduce a mathematical framework for prospective learning and embedded agency centered on self-prediction, where Bayesian RL agents predict both future perceptual inputs and their own actions, and must therefore resolve epistemic uncertainty about themselves as part of the universe they inhabit. We show that in multi-agent settings, self-prediction enables agents to reason about others running similar algorithms, leading to new game-theoretic solution concepts and novel forms of cooperation unattainable by classical decoupled agents. Moreover, we extend the theory of AIXI, and study universally intelligent embedded agents which start from a Solomonoff prior. We show that these idealized agents can form consistent mutual predictions and achieve infinite-order theory of mind, potentially setting a gold standard for embedded multi-agent learning.

Simon Schug, Seijin Kobayashi, Yassir Akram et al.

Transformers can under some circumstances generalize to novel problem instances whose constituent parts might have been encountered during training, but whose compositions have not. What mechanisms underlie this ability for compositional generalization? By reformulating multi-head attention as a hypernetwork, we reveal that a composable, low-dimensional latent code specifies key-query specific operations. We find empirically that this latent code is predictive of the subtasks the network performs on unseen task compositions, revealing that latent codes acquired during training are reused to solve unseen problem instances. To further examine the hypothesis that the intrinsic hypernetwork of multi-head attention supports compositional generalization, we ablate whether making the hypernetwork-generated linear value network nonlinear strengthens compositionality. We find that this modification improves compositional generalization on abstract reasoning tasks. In particular, we introduce a symbolic version of the Raven's Progressive Matrices human intelligence test, which gives us precise control over the problem compositions encountered during training and evaluation. We demonstrate on this task how scaling model size and data enables compositional generalization in transformers and gives rise to a functionally structured latent space.

Johannes von Oswald, Dominic Zhao, Seijin Kobayashi et al.

Finding neural network weights that generalize well from small datasets is difficult. A promising approach is to learn a weight initialization such that a small number of weight changes results in low generalization error. We show that this form of meta-learning can be improved by letting the learning algorithm decide which weights to change, i.e., by learning where to learn. We find that patterned sparsity emerges from this process, with the pattern of sparsity varying on a problem-by-problem basis. This selective sparsity results in better generalization and less interference in a range of few-shot and continual learning problems. Moreover, we find that sparse learning also emerges in a more expressive model where learning rates are meta-learned. Our results shed light on an ongoing debate on whether meta-learning can discover adaptable features and suggest that learning by sparse gradient descent is a powerful inductive bias for meta-learning systems.

Christian Henning, Maria R. Cervera, Francesco D'Angelo et al.

Learning a sequence of tasks without access to i.i.d. observations is a widely studied form of continual learning (CL) that remains challenging. In principle, Bayesian learning directly applies to this setting, since recursive and one-off Bayesian updates yield the same result. In practice, however, recursive updating often leads to poor trade-off solutions across tasks because approximate inference is necessary for most models of interest. Here, we describe an alternative Bayesian approach where task-conditioned parameter distributions are continually inferred from data. We offer a practical deep learning implementation of our framework based on probabilistic task-conditioned hypernetworks, an approach we term posterior meta-replay. Experiments on standard benchmarks show that our probabilistic hypernetworks compress sequences of posterior parameter distributions with virtually no forgetting. We obtain considerable performance gains compared to existing Bayesian CL methods, and identify task inference as our major limiting factor. This limitation has several causes that are independent of the considered sequential setting, opening up new avenues for progress in CL.

Johannes von Oswald, Seijin Kobayashi, Alexander Meulemans et al.

The largely successful method of training neural networks is to learn their weights using some variant of stochastic gradient descent (SGD). Here, we show that the solutions found by SGD can be further improved by ensembling a subset of the weights in late stages of learning. At the end of learning, we obtain back a single model by taking a spatial average in weight space. To avoid incurring increased computational costs, we investigate a family of low-dimensional late-phase weight models which interact multiplicatively with the remaining parameters. Our results show that augmenting standard models with late-phase weights improves generalization in established benchmarks such as CIFAR-10/100, ImageNet and enwik8. These findings are complemented with a theoretical analysis of a noisy quadratic problem which provides a simplified picture of the late phases of neural network learning.