SGD, can serve as the inner-loop optimizer, and the derived lookahead generally enjoys remarkable test performance improvement over the vanilla optimizer. But theoretical understandings on the test performance improvement of lookahead remain absent yet. To solve this issue, we theoretically justify the advantages of lookahead in terms of the excess risk error which measures the test performance. Specifically, we prove that lookahead using SGD as its inner-loop optimizer can better balance the optimization error and generalization error to achieve smaller excess risk error than vanilla SGD on (strongly) convex problems and nonconvex problems with Polyak-{\L}ojasiewicz condition which has been observed/proved in neural networks. Moreover, we show the stagewise optimization strategy~\cite{barshan2015stage} which decays learning rate several times during training can also benefit lookahead in improving its optimization and generalization errors on strongly convex problems. Finally, we propose a stagewise locally-regularized lookahead (SLRLA) algorithm which sums up the vanilla objective and a local regularizer to minimize at each stage and provably enjoys optimization and generalization improvement over the conventional (stagewise) lookahead. Experimental results on CIFAR10/100 and ImageNet testify its advantages.

Until recently, research on artificial neural networks was largely restricted to systems with only two types of variable: Neural activities that represent the current or recent input and weights that learn to capture regularities among inputs, outputs and payoffs. There is no good reason for this restriction. Synapses have dynamics at many different time-scales and this suggests that artificial neural networks might benefit from variables that change slower than activities but much faster than the standard weights. These ``fast weights'' can be used to store temporary memories of the recent past and they provide a neurally plausible way of implementing the type of attention to the past that has recently proven helpful in sequence-to-sequence models. By using fast weights we can avoid the need to store copies of neural activity patterns.

Until recently, research on artificial neural networks was largely restricted to systems with only two types of variable: Neural activities that represent the current or recent input and weights that learn to capture regularities among inputs, outputs and payoffs. There is no good reason for this restriction. Synapses have dynamics at many different time-scales and this suggests that artificial neural networks might benefit from variables that change slower than activities but much faster than the standard weights. These "fast weights" can be used to store temporary memories of the recent past and they provide a neurally plausible way of implementing the type of attention to the past that has recently proved very helpful in sequence-to-sequence models. By using fast weights we can avoid the need to store copies of neural activity patterns.

Neural Information Processing Systems http://nips.cc/

Large language models display in-context learning as an emergent effect of scale, but they rely on static weights during inference. In contrast, biological systems continually adapt via synaptic plasticity. We investigate whether explicit, biologically inspired plasticity can endow Transformers with faster in-sequence adaptation. To this end, we augment decoder-only Transformers with fast-weight modules updated either by (i) a neuromodulated Hebbian rule or (ii) the gradient-based plasticity mechanism of Duan et al. (2023). Across copying, regression, and few-shot classification tasks (CIF AR-FS, Omniglot), Hebbian plasticity consistently achieves lower loss and stronger few-shot generalization, while gradient-based updates perform best on long-horizon credit assignment. When associations are short and linearly separable, static weights suffice, defining a clear boundary condition for when plasticity helps. Analysis of learned modulatory signals reveals that gradient-based rules maintain large, persistent updates, whereas Hebbian plasticity is sharply gated around salient events. Together, these results show that explicit plasticity complements attention by enabling rapid, task-specific adaptation, and clarify when different plasticity mechanisms are most effective.

We find that Lookahead is less sensitive to suboptimal hyperparameters and therefore lessens the need for extensive hyperparameter tuning.

Major comments: This paper contains a nice idea, namely, a weight matrix which is architecturally constrained to use a certain learning rule and update itself at various points during processing. This general scheme seems likely to lead to many variants in the future. The performance on the tasks considered is solid, and makes the technique worthy of further consideration. This paper makes a solid contribution to machine learning, but the results in the paper do not support the claim in the conclusion that "the main contribution is to computational neuroscience and cognitive science." The paper makes no contact with experimental data, whether neural or psychological.

Until recently, research on artificial neural networks was largely restricted to systems with only two types of variable: Neural activities that represent the current or recent input and weights that learn to capture regularities among inputs, outputs and payoffs. There is no good reason for this restriction. Synapses have dynamics at many different time-scales and this suggests that artificial neural networks might benefit from variables that change slower than activities but much faster than the standard weights. These "fast weights" can be used to store temporary memories of the recent past and they provide a neurally plausible way of implementing the type of attention to the past that has recently proved very helpful in sequence-to-sequence models. By using fast weights we can avoid the need to store copies of neural activity patterns.

We reformulate the problem of supervised learning as learning to learn with two nested loops (i.e. The inner loop learns on each individual instance with self-supervision before final prediction. The outer loop learns the self-supervised task used by the inner loop, such that its final prediction improves. Our inner loop turns out to be equivalent to linear attention when the inner-loop learner is only a linear model, and to self-attention when it is a kernel estimator. For practical comparison with linear or self-attention layers, we replace each of them in a transformer with an inner loop, so our outer loop is equivalent to training the architecture. When each inner-loop learner is a neural network, our approach vastly outperforms transformers with linear attention on ImageNet from 224 224 raw pixels in both accuracy and FLOPs, while (regular) transformers cannot run. Test-time training (TTT) is an algorithmic framework for machine learning. The core idea is that each test instance defines its own learning problem, with its own target of generalization (Sun et al., 2020). Since the test instance comes without its label, TTT is performed with a self-supervised task such as reconstruction. Performance should improve on this particular instance for the selfsupervised task, because that is the objective optimized by TTT. But will such a process lead to better performance for the main task we actually care about? If improvement for a self-supervised task transfers to a given main task, we say the two tasks are aligned (Sun et al., 2020). In prior work, task alignment has been an art, combining ingenuity with trial and error (Gandelsman et al., 2022; Wang et al., 2023). Crucially, the amount of ingenuity in task design does not scale with more data and compute.

The Lookahead optimizer improves the training stability of deep neural networks by having a set of fast weights that "look ahead" to guide the descent direction. Here, we combine this idea with sharpness-aware minimization (SAM) to stabilize its multi-step variant and improve the loss-sharpness trade-off. We propose Lookbehind, which computes $k$ gradient ascent steps ("looking behind") at each iteration and combine the gradients to bias the descent step toward flatter minima. We apply Lookbehind on top of two popular sharpness-aware training methods -- SAM and adaptive SAM (ASAM) -- and show that our approach leads to a myriad of benefits across a variety of tasks and training regimes. Particularly, we show increased generalization performance, greater robustness against noisy weights, and higher tolerance to catastrophic forgetting in lifelong learning settings.