There are no explicit equations for the cerebellum traditionally also has access to a desired state ds (in particular, one can consider this a and forward DNI, respectively; L denotes the loss function. In addition, the inverse model of the of a motor area and sensory area, respectively; CB,CF denotes the computation of backward DNI Notation is largely consistent with section 2 of the main text: hm,hs denotes the hidden activity properties of the inverse model of the cerebellum can be set against those of forward DNI (red). Controller Neocortex Main model Cerebellum Synthesiser Forward Model Backward DNIInverse Model Forward DNI be summarised in table S1. In general, the likeness in formulation between DNI and the cerebellar internal model hypothesis can backward DNI where the main model is an motor-associated RNN. In fact, it was recently suggested that the cerebellum out that though the temporal case of forward DNI was not originally considered in [5], there remain learns to mimic the forward computations which then take place in the neocortex.

Overall, our work offers a novel perspective on the cerebellum as a brainneuronal observations while making several testable predictions across multiple mental observations. Moreover, our model also explains recent behavioural and learning while reducing ataxia-like behaviours, consistent with classical experishown to be cerebellar-dependent. In all tasks, we observe that ccRNNs facilitates and cognitive tasks (pattern recognition and caption generation) that have been network (ccRNN) model on a number of sensorimotor (line and digit drawing) tions from a cerebellar module. We test this cortico-cerebellar recurrent neural in which a recurrent cortical network receives online temporal feedback predicdemonstrate the potential of this framework we introduce a systems-level model lum, helps the cerebral cortex solve similar locking problems akin to DNIs.

AForster transform is an operation that turns a distribution into one with good anticoncentration properties. While a Forster transform does not always exist, we show that any distribution can be efficiently decomposed as a disjoint mixture of few distributions for which a Forster transform exists and can be computed efficiently. As the main application of this result, we obtain the first polynomial-time algorithm for distribution-independent PAC learning of halfspaces in the Massart noise model with strongly polynomial sample complexity, i.e., independent of the bit complexity of the examples. Previous algorithms for this learning problem incurred sample complexity scaling polynomially with the bit complexity, even though such a dependence is not information-theoretically necessary.

Bayesian optimization (BO) conventionally relies on handcrafted acquisition functions (AFs) to sequentially determine the sample points. However, it has been widely observed in practice that the best-performing AF in terms of regret can vary significantly under different types of black-box functions. It has remained a challenge to design one AF that can attain the best performance over a wide variety of black-box functions. This paper aims to attack this challenge through the perspective of reinforced few-shot AF learning (FSAF). Specifically, we first connect the notion of AFs with Q-functions and view a deep Q-network (DQN) as a surrogate differentiable AF. While it serves as a natural idea to combine DQN and an existing few-shot learning method, we identify that such a direct combination does not perform well due to severe overfitting, which is particularly critical in BO due to the need of a versatile sampling policy. To address this, we present a Bayesian variant of DQN with the following three features: (i) It learns a distribution of Q-networks as AFs based on the Kullback-Leibler regularization framework. This inherently provides the uncertainty required in sampling for BO and mitigates overfitting.

This format not only enables few-shot learning via interleaving independent supervised (image, text) examples, but also, more complex prompts involving interaction between images, e.g., "What do image A and image B have in common?" To support this interface, pretraining occurs over web corpora that similarly contain interleaved images+text. To date, however, large-scale data of this form have not been publicly available. We release Multimodal C4 (mmc4), an augmentation of the popular text-only c4 corpus2 with images interleaved. We use a linear assignment algorithm to place images into longer bodies of text using CLIP features [24], a process that we show outperforms alternatives.

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