Evaluation of CL methods is challenging.

Learned representations are a central component in modern ML systems, serving a multitude of downstream tasks. When training such representations, it is often the case that computational and statistical constraints for each downstream task are unknown. In this context, rigid fixed-capacity representations can be either over or under-accommodating to the task at hand. This leads us to ask: can we design a flexible representation that can adapt to multiple downstream tasks with varying computational resources?

To integrate the three modalities more effectively and enable inter-modal learning, we design a dynamic fusion scheme with transformers to model the interactions between modalities.

Previous works have proved that recurrent neural networks (RNNs) are Turing-complete.

Addition and scalar multiplication are defined in the obvious way by pa,b q ` λ pc,d q: " p a ` λc,b ` λd q for a,c P H, b,d P p H and λ P C . 'size' by what is called the operator norm, denoted by } } We may then write f " In this case we write R pz, q " p z q It is a standard exercise to show that this is independent of the choice of orthonormal basis. To streamline the argumentation let us first introduce some notation: 18 Notation C.2. Lemma A.1), we find a To investigate the example of Figure 3, we label the vertices of the respective graphs as depicted in Figure 6. Such operators are positive and hence | | " (similarly for r). " 0. Next we note }Jf } " J and determine Ă J It remains to establish (9).

Visual object recognition has been extensively studied in both neuroscience and computer vision. Recently, the most popular class of artificial systems for this task, deep convolutional neural networks (CNNs), has been shown to provide excellent models for its functional analogue in the brain, the ventral stream in visual cortex.