Memory in Deep Time-Series Models

Deep learning models, particularly recurrent neural networks and their variants, such as long short-term memory, have significantly advanced time series analysis. These models capture complex, sequential patterns in time series, enabling real-time assessments. However, their high computational complexity and large model sizes pose challenges for deployment in resource-constrained environments, such as wearable devices and edge computing platforms. Knowledge Distillation (KD) offers a solution by transferring knowledge from a large, complex model (teacher) to a smaller, more efficient model (student), thereby retaining high performance while reducing computational demands. Current KD methods, originally designed for computer vision tasks, neglect the unique temporal dependencies and memory retention characteristics of time series models. To bridge this gap, we propose a novel KD framework termed Memory-Discrepancy Knowledge Distillation (MemKD). MemKD leverages a specialized loss function to capture memory retention discrepancies between the teacher and student models across subsequences within time series data, ensuring that the student model effectively mimics the teacher's behaviour. This approach facilitates the development of compact, high-performing recurrent neural networks suitable for real-time, time series analysis tasks. We provide additional experiments, in-depth theoretical analysis, and insights into the proposed framework across extended time series benchmarks. Our experiments demonstrate that MemKD significantly outperforms state-of-the-art KD methods. Additionally, we demonstrate that it can match the teacher model's performance across a wide range of compression levels, achieving notable reductions in parameter count and memory usage without a significant loss in accuracy.

Test-time memorization of sequential information is a foundational capability for any intelligent system that needs to rapidly store and retrieve data, as demonstrated by the attention mechanism in large language models. However, Transformers and linear attention variants are trained via backpropagation through time (BPTT), which has drawbacks such as its enormous memory requirements. Predictive coding (PC), an algorithm that optimizes a prediction-error energy function with local updates, offers a compelling solution but still lacks test-time memory for sequential data. We develop a solution to this problem by treating the per-step memory update $ΔS_t$ as a latent variable, as opposed to a slow weight to be learned. By taking the log probability of a standard PC-based probabilistic model, we derive a PC-native solution for verbatim sequence memory, and relate our update rule to common choices in the linear attention literature (e.g., DeltaNet). We present an extensive set of empirical tests to probe our system's properties, including its scaling capacity, memory footprint, and ability to infer a context from evidence (e.g., bank (river) vs. bank (money)). We show how DeltaNet-PC can be used for storing single sequences of data, multiple sequences of data, and key-value associative memory pairs with perfect recall accuracy.

Retrieval-augmented forecasting for Web and online services supplements a forecaster with the continuations of historical segments that resemble the current context. Most existing methods build the retrieval memory once from the training segment, leaving observations revealed after deployment unavailable as references, and generally do not calibrate how much retrieved information should influence a frozen forecaster. We identify two key determinants of retrieval utility for a frozen forecaster: the timeliness of the retrieved history and its complementarity, i.e., whether the correction it induces aligns with the forecaster's residual errors; this alignment can shift between validation and deployment when the memory becomes stale. We propose FreshCast, a plug-in retrieval framework for frozen forecasters: a non-parametric streaming memory keeps writing in new observations, relational kernel regression weights candidate readouts into a memory forecast, and its correction weight is calibrated in closed form on the validation segment. Under a simplified generative model, we characterize the optimal combination gain through the second-order relation between forecaster error and memory correction, and show that periodic memory information can become redundant once the forecaster captures it. Across seven datasets, ten forecasters, and three input lengths, FreshCast reduces average MSE for every forecaster and input length, by 14.0% and 5.7% at L = 96 and 720, and achieves lower average MSE than the evaluated retrieval-augmented and online updating baselines in their comparison settings. Ablations show that post-training observations are a primary source of the gain: freezing the memory at the end of training removes most of it. For a frozen forecaster, similarity alone is not enough: useful retrieval must stay timely and provide information that the forecaster still misses.