Factorial Hidden Markov Models (FHMMs) are powerful models for sequential data but they do not scale well with long sequences. We propose a scalable inference and learning algorithm for FHMMs that draws on ideas from the stochastic variational inference, neural network and copula literatures. Unlike existing approaches, the proposed algorithm requires no message passing procedure among latent variables and can be distributed to a network of computers to speed up learning. Our experiments corroborate that the proposed algorithm does not introduce further approximation bias compared to the proven structured mean-field algorithm, and achieves better performance with long sequences and large FHMMs.

Large language models (LLMs) have emerged as a cornerstone in real-world applications with lengthy streaming inputs (e.g., LLM-driven agents). However, existing LLMs, pre-trained on sequences with a restricted maximum length, cannot process longer sequences due to the out-of-domain and distraction issues. Common solutions often involve continual pre-training on longer sequences, which will introduce expensive computational overhead and uncontrollable change in model capabilities. In this paper, we unveil the intrinsic capacity of LLMs for understanding extremely long sequences without any fine-tuning. To this end, we introduce a training-free memory-based method, InfLLM. Specifically, InfLLM stores distant contexts into additional memory units and employs an efficient mechanism to lookup token-relevant units for attention computation.

Learning long-term dependencies in extended temporal sequences requires credit assignment to events far back in the past. The most common method for training recurrent neural networks, back-propagation through time (BPTT), requires credit information to be propagated backwards through every single step of the forward computation, potentially over thousands or millions of time steps. This becomes computationally expensive or even infeasible when used with long sequences. Importantly, biological brains are unlikely to perform such detailed reverse replay over very long sequences of internal states (consider days, months, or years.) However, humans are often reminded of past memories or mental states which are associated with the current mental state. We consider the hypothesis that such memory associations between past and present could be used for credit assignment through arbitrarily long sequences, propagating the credit assigned to the current state to the associated past state. Based on this principle, we study a novel algorithm which only back-propagates through a few of these temporal skip connections, realized by a learned attention mechanism that associates current states with relevant past states. We demonstrate in experiments that our method matches or outperforms regular BPTT and truncated BPTT in tasks involving particularly long-term dependencies, but without requiring the biologically implausible backward replay through the whole history of states. Additionally, we demonstrate that the proposed method transfers to longer sequences significantly better than LSTMs trained with BPTT and LSTMs trained with full self-attention.

Sequences of millions of bytes are ubiquitous; for example, music, image, or video files typically consist of multiple megabytes.

In speech separation, time-domain approaches have successfully replaced the time-frequency domain with latent sequence feature from a learnable encoder.

We introduce a simple sequence model inspired by control systems thatgeneralizes these approaches while addressing their shortcomings.

We consider the class of noisy multi-layered sigmoid recurrent neural networks with $w$ (unbounded) weights for classification of sequences of length $T$, where independent noise distributed according to $\mathcal{N}(0,\sigma^2)$ is added to the output of each neuron in the network. Our main result shows that the sample complexity of PAC learning this class can be bounded by $O (w\log(T/\sigma))$. For the non-noisy version of the same class (i.e., $\sigma=0$), we prove a lower bound of $\Omega (wT)$ for the sample complexity. Our results indicate an exponential gap in the dependence of sample complexity on $T$ for noisy versus non-noisy networks. Moreover, given the mild logarithmic dependence of the upper bound on $1/\sigma$, this gap still holds even for numerically negligible values of $\sigma$.

Transformer-based language models have found many diverse applications requiring them to process sequences of increasing length. For these applications, the causal self-attention---which is the only component scaling quadratically w.r.t. the sequence length---becomes a central concern. While many works have proposed schemes to sparsify the attention patterns and reduce the computational overhead of self-attention, those are often limited by implementation concerns and end up imposing a simple and static structure over the attention matrix. Conversely, implementing more dynamic sparse attention often results in runtimes significantly slower than computing the full attention using the Flash implementation from Dao et al. (2022). We extend FlashAttention to accommodate a large class of attention sparsity patterns that, in particular, encompass key/query dropping and hashing-based attention. This leads to implementations with no computational complexity overhead and a multi-fold runtime speedup on top of FlashAttention. Even with relatively low degrees of sparsity, our method improves visibly upon FlashAttention as the sequence length increases. Without sacrificing perplexity, we increase the training speed of a transformer language model by $2.0\times$ and $3.3\times$ for sequences of respectively $8k$ and $16k$ tokens.