# 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) 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. *** Character-level loss on simplebooks-92 dataset https://dldata-public.s3.us-east-2.amazonaws.com/simplebooks.zip ![RWKV-vs-MHA](RWKV-vs-MHA.png) Gray: usual MHA+Rotary+GeGLU - performance not as good. Red: RWKV ("linear" attention) - VRAM friendly - quite faster when ctx window is long - good performance. Black: MHA_pro (MHA with various tweaks & RWKV-type-FFN) - slow - needs more VRAM - good performance. parameters count: 17.2 vs 18.5 vs 18.5.