State-space models have gained popularity in sequence modelling due to their simple and efficient network structures. However, the absence of nonlinear activation along the temporal direction limits the model's capacity.

Comments on Theorem 3.2 With the primal problem in (6) in the paper, Theorem 3.2 provides Additionally, [27] presents the optimization w.r.t. a single projection direction in Therefore, our KSVD is more general in the data setups. Remark 3.3, we show that the values can be regarded as playing the role of the dual variables Using data-dependent projection weights does not affect the derivation of the shifted eigenvalue problem in the dual. With the derivations of the primal-dual optimization problems above, the primal-dual model representation of our KSVD problem can be provided correspondingly. Lemma 4.2 evaluates the objective value Moreover, as in the proof of Theorem 3.2, we note that the regularization coefficient This section provides the implementation details of all experiments included in the paper. This will be illustrated in details in the following.Algorithm 1 Learning with Primal-AttentionRequire: X:= [ x UEA Time Series The UEA time series benchmark [31] consists of 30 datasets. Following the setup in [11], we select 10 datasets for evaluation.

Most crucially, they require prohibitively large amounts of additional memory since they rely on backpropagation which allocates almost twice as much GPU memory as the forward pass. This renders it difficult, if not impossible, to use explanations in production.

Transformer-based language models have found many diverse applications requiring them to process sequences of increasing length.

Large language models(LLMs) have sparked a new wave of exciting AI applications. Hosting these models at scale requires significant memory resources.

Here we omit the computation of HJ PDEs for concisity. The model is trained for 90, 000 iterations. The model is also trained for 90, 000 iterations. For the disentanglement methods, we largely enrich the original MNIST dataset by adding the transformed images of the whole sequence. The generalization ability ( i.e., validation accuracy) can be thus regarded as a reasonable surrogate for the disentanglement ability.

To evaluate TSLD's efficiency, we detail training speeds and GPU memory consumption for various Our analysis of confidence disparity in token predictions, detailed in Section 4.2, extends beyond a In fact, this observed trend is consistently present across various GLM models. These errors are visualized using a heatmap plot (Fig. A2 top), For the OPT -6.7B model, quantization error is measured for the 5th and 15th layers. LLaMA-7B model, quantization errors are depicted for input sequence lengths of 128 and 512. From left to right: OPT -6.7B, LLaMA-7B, and LLaMA-2-7B. However, as we delve deeper into the layers of OPT -6.7B or introduce longer input sequences to LLaMA-7B, this phenomenon becomes less pronounced.

Generative Language Models (GLMs) have shown impressive performance in tasks such as text generation, understanding, and reasoning. However, the large model size poses challenges for practical deployment.