RWKV-LM

We propose the RWKV language model, with alternating time-mix and channel-mix layers:

$\begin{align*} \text{Time-mix :} && \text{TM}_{t,c} &&=&&\text{sigmoid}(\text{R}_{t,c}) &&\cdot&& &&\textstyle\sum_{u} &&\textbf{W}_{t,u,c} &&\cdot&& \text{softmax}_t(\text{K}_{u,c}) &&\cdot&& \text{V}_{u,c}\\ \text{Channel-mix :} && \text{CM}_{t,c} &&=&&\text{sigmoid}(\text{R}_{t,c}) &&\cdot&& &&\textstyle\sum_d &&\textbf{W}_{c,d} &&\cdot&& \text{gelu}(\text{K}_{t,d}) &&\cdot&& \text{V}_{t,d} \end{align*}$

The R, K, V are generated by linear transforms of input, and W is parameter. The idea of RWKV is to decompose attention into R(target) * W(src, target) * K(src). So we can call R "receptance", and sigmoid means it's in 0~1 range.
The Time-mix is similar to AFT (https://arxiv.org/abs/2105.14103). There are two differences.

(1) We changed the normalization (denominator). For masked language models, we define:

$\text{softmax}_t(\text{K}_{u,c}) = \frac{\exp(\text{K}_{u,c})}{\sum_{v \leq t}\exp(\text{K}_{v,c})}$

(2) We decompose W_{t,u,c} and introduce multi-head W (here h is the corresponding head of c):

$W_{t,u,c}=f_h(t-u)\cdot \alpha_h(u) \cdot \beta_h(t)$

(3) You don't need LayerNorm for Time-mix. In fact, the model converges faster when LayerNorm is removed.

Moreover we multiply the final output of Time-mix layer by γ(t). The reason for the α β γ factors, is because the context size is smaller when t is small, and this can be compensated using the α β γ factors.

The Channel-mix is similar to GeGLU (https://arxiv.org/abs/2002.05202) with an extra R factor.
Finally, we add extra time-mixing as in (https://github.com/BlinkDL/minGPT-tuned). You can try reducing the amt of time-mixing in upper layers of deep models.

We also propose a new sampling method (as in src/utils.py):

(1) Find the max probability p_max after softmax.

(2) Remove all entries whose probability is lower than 0.02 * pow(p_max, 2)

(3) Feel free to tune the 0.02 and 2 factor.

Training loss, RWKV vs MHA+Rotary+GeGLU:

RWKV-vs-MHA