**Funnel Transformer** is a type of [Transformer](https://paperswithcode.com/methods/category/transformers) that gradually compresses the sequence of hidden states to a shorter one and hence reduces the computation cost. By re-investing the saved FLOPs from length reduction in constructing a deeper or wider model, the model capacity is further improved. In addition, to perform token-level predictions as required by common pretraining objectives, Funnel-[transformer](https://paperswithcode.com/method/transformer) is able to recover a deep representation for each token from the reduced hidden sequence via a decoder.

The proposed model keeps the same overall skeleton of interleaved S-[Attn](https://paperswithcode.com/method/scaled) and P-[FFN](https://paperswithcode.com/method/dense-connections) sub-modules wrapped by [residual connection](https://paperswithcode.com/method/residual-connection) and [layer normalization](https://paperswithcode.com/method/layer-normalization). But differently, to achieve representation compression and computation reduction, THE model employs an encoder that gradually reduces the sequence length of the hidden states as the layer gets deeper. In addition, for tasks involving per-token predictions like pretraining, a simple decoder is used to reconstruct a full sequence of token-level representations from the compressed encoder output. Compression is achieved via a pooling operation,

**Exponential Decay** is a learning rate schedule where we decay the learning rate with more iterations using an exponential function:

$$ \text{lr} = \text{lr}\_{0}\exp\left(-kt\right) $$

Image Credit: [Suki Lau](https://towardsdatascience.com/learning-rate-schedules-and-adaptive-learning-rate-methods-for-deep-learning-2c8f433990d1)

Exponential Decay

Funnel Transformer

Funnel-Transformer: Filtering out Sequential Redundancy for Efficient Language Processing

**DIME**, or **Distance to Modelled Embedding**, is a method for detecting out-of-distribution examples during prediction time. Given a trained neural network, the training data drawn from some high-dimensional distribution in data space $X$ is transformed into the model’s intermediate feature vector space $\mathbb{R}^{p}$. The training set embedding is linearly approximated as a hyperplane. When we then receive new observations it is difficult to assess if observations are out-of-distribution directly in data space, so we transform them into the same intermediate feature space. Finally, the Distance-to-Modelled-Embedding (DIME) can be used to assess whether new observations fit into the expected embedding covariance structure.

Source	Funnel-Transformer: Filtering out Sequential Redundancy for Efficient Language Processing
Year	2000
Data Source	CC BY-SA - https://paperswithcode.com