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Transparent Networks for Multivariate Time Series

Conference: AAAI 2026 arXiv: 2410.10535 Code: https://github.com/gim4855744/GATSM Area: Time Series Keywords: Interpretable Models, Generalized Additive Models, Time Series, Transparent Networks, Attention Mechanism

TL;DR

This paper proposes GATSM (Generalized Additive Time Series Model), a transparent neural network for time series that employs weight-sharing feature networks to learn feature representations and masked multi-head attention to capture temporal patterns. GATSM achieves performance comparable to black-box models such as Transformers while maintaining full interpretability.

Background & Motivation

State of the Field

In high-stakes domains such as healthcare and fraud detection, model transparency (interpretability) is critical. Existing interpretability approaches fall into two categories: - Post-hoc XAI: Methods such as LIME and SHAP explain already-trained black-box models, but may produce incorrect or unfaithful explanations that do not reflect the true contribution of input features. - Inherently Interpretable Models: Models whose structure is interpretable by design, such as Generalized Additive Models (GAMs).

Limitations of Prior Work

Classic GAMs take the form \(g(\mathbb{E}(y|\mathbf{x})) = \sum_{i=1}^M f_i(x_i)\), where each feature has an independent function that directly reveals its contribution. However, applying GAMs to time series faces three challenges:

Inability to handle sequential data: Conventional tabular GAMs assume static feature vectors and cannot process temporal sequences.

Inability to capture temporal patterns: NATM naively applies independent functions \(f_{i,j}(x_{i,j})\) at each time step without cross-step interactions, preventing the model from learning temporal dependencies.

Fixed-length constraint: NATM requires fixed-length inputs and cannot handle variable-length time series (e.g., patient stays of unpredictable duration in clinical settings).

Paper Goals

The authors define a novel temporal GAM formulation:

\[g(\mathbb{E}(y_t | \mathbf{X}_{:t})) = \sum_{i=1}^{t} \sum_{j=1}^{M} f_{i,j}(x_{i,j}, \mathbf{X}_{:t})\]

The key distinction is that each function \(f_{i,j}\) can take the entire historical sequence \(\mathbf{X}_{:t}\) as an additional input, enabling temporal pattern capture while preserving the additive structure. GATSM is the first transparent model to realize this formulation.

Method

Overall Architecture

GATSM consists of two modules: 1. Time-Sharing NBM (Neural Basis Model): Learns nonlinear feature representations. 2. Masked MHA (Masked Multi-Head Attention): Captures temporal patterns.

Key Designs

1. Time-Sharing NBM

Problem: Assigning independent functions to every time step and feature requires \(T \times M\) functions, leading to parameter explosion.

Solution: Share basis function weights across all time steps.

\[\tilde{x}_{i,j} = f_j(x_{i,j}) = \sum_{k=1}^{B} h_k(x_{i,j}) w_{j,k}^{nbm}\]
  • \(B = 100\) basis functions \(h_k(\cdot)\) implemented as MLPs.
  • Basis functions are shared across all features and time steps, substantially reducing parameters.
  • Each feature retains independent weights \(w_{j,k}^{nbm}\) to preserve feature specificity.
  • Parameter count is reduced from \(T \times M\) to \(B\).

Design Motivation: The basis strategy of NBM is particularly well-suited for time series — the same nonlinear transformation can be shared across time steps for a given feature, while feature-specific weights maintain discriminative capacity.

2. Masked MHA

A two-layer attention mechanism (derived from GAT) is adopted instead of simple dot-product attention to achieve greater expressive power.

Step 1: Transform feature representations and add positional encodings.

\[\mathbf{v}_i = \tilde{\mathbf{x}}_i^\intercal \mathbf{Z} + \mathbf{pe}_i\]
  • \(\mathbf{Z} \in \mathbb{R}^{M \times D}\) is a learnable weight matrix.
  • Sinusoidal positional encodings (rather than learnable ones) are used to support variable-length sequences.

Step 2: Compute attention scores.

\[e_{k,i,j} = \sigma([\mathbf{v}_i | \mathbf{v}_j]^\intercal \mathbf{w}_k^{attn}) m_{i,j}\]
\[a_{k,i,j} = \frac{\exp(e_{k,i,j})}{\sum_{t=1}^{T} \exp(e_{k,i,t})}\]
  • A causal mask \(m_{i,j}\) ensures that time step \(i\) attends only to time steps \(j \leq i\).
  • The nonlinear activation \(\sigma(\cdot)\) enhances expressive power.

3. Inference and Interpretability

The final prediction is:

\[\hat{y}_t = \sum_{k=1}^{K} \mathbf{a}_{k,t}^\intercal \tilde{\mathbf{X}} \mathbf{w}_k^{out}\]

Expanding into scalar form:

\[= \sum_{u=1}^{t} \sum_{m=1}^{M} \underbrace{\sum_{k=1}^{K} \sum_{b=1}^{B} a_{k,t,u} h_b(x_{u,m}) w_{m,b}^{nbm} w_{k,m}^{out}}_{f_{u,m}(x_{u,m}, \mathbf{X}_{:t})}\]

This demonstrates that GATSM satisfies the temporal GAM definition (Definition 3.1) and supports three levels of interpretability:

  1. Time step importance: \(a_{k,t,u}\) quantifies the importance of time step \(u\) in the prediction at time step \(t\).
  2. Time-independent feature contribution: \(h_b(x_{u,m}) w_{m,b}^{nbm} w_{k,m}^{out}\) reflects the intrinsic contribution of feature \(m\).
  3. Time-dependent feature contribution: \(a_{k,t,u} h_b(x_{u,m}) w_{m,b}^{nbm} w_{k,m}^{out}\) captures the contribution of feature \(m\) at a specific time step.

Loss & Training

  • Regression: MSE
  • Binary classification: Binary Cross-Entropy
  • Multi-class classification: Cross-Entropy
  • Optimizer: AdamW
  • Early stopping: training halts if validation loss does not improve for 20 epochs
  • Hyperparameters: automatically tuned via Optuna

Key Experimental Results

Main Results

Single-step prediction performance on 8 public time series datasets:

Model Type Model Energy (R²↑) Rainfall (R²↑) AirQuality (R²↑) Heartbeat (AUROC↑) LSST (Acc↑) NATOPS (Acc↑) Avg. Rank
Black-box temporal GRU 0.435 0.089 0.701 0.694 0.629 0.931 4.500
Black-box temporal Transformer 0.263 0.098 0.711 0.690 0.679 0.967 4.125
Transparent tabular NAM 0.363 0.006 0.300 0.645 0.400 0.242 9.375
Transparent tabular NBM 0.330 0.007 0.301 0.716 0.388 0.189 9.250
Transparent temporal NATM 0.304 0.038 0.548 0.724 0.452 0.878 6.833
Transparent temporal GATSM 0.493 0.073 0.583 0.843 0.570 0.956 3.375

GATSM achieves the best average rank (3.375) across all models, outperforming the Transformer (4.125) while substantially surpassing all prior transparent models.

Ablation Study

Feature Function Selection

Feature Function Energy Rainfall AirQuality Heartbeat LSST NATOPS
Linear 0.283 0.071 0.563 0.766 — —
NAM — — — — — —
NBM 0.493 0.073 0.583 0.843 0.570 0.956

The basis strategy of NBM achieves the best performance on 6 of 8 datasets.

Temporal Module Design

Configuration Energy Heartbeat LSST NATOPS Description
Base Poor Poor Poor Poor No temporal module
Base + PE Similar to Base Similar to Base Similar to Base Similar to Base Positional encoding alone is insufficient
Base + MHA Moderate Moderate Moderate Moderate Attention is beneficial
Base + PE + MHA Best Best Best Best PE and MHA exhibit synergy

Positional encodings and multi-head attention must be used together to effectively capture temporal patterns.

Key Findings

  1. GATSM surpasses the Transformer in average rank: This is the first time a transparent model has outperformed a classic black-box temporal model in overall ranking.
  2. Temporal patterns matter: On datasets with strong temporal structure (Rainfall, AirQuality, LSST, NATOPS), temporal models substantially outperform tabular models.
  3. Variable-length sequence support: GATSM handles variable-length datasets such as Mortality and Sepsis, whereas NATM cannot.
  4. Clinical data characteristics: The performance gap between temporal and tabular models is small on Mortality and Sepsis, possibly because current patient state already encodes historical information.
  5. Multi-level interpretability: GATSM simultaneously provides time step importance, global feature contributions, and local time-dependent feature contributions.

Highlights & Insights

  1. Theoretical rigor: A formal definition of temporal GAMs (Definition 3.1) is proposed, and GATSM is rigorously proven to satisfy it.
  2. Elegant weight-sharing design: Sharing basis functions across time steps achieves an excellent balance between parameter efficiency and expressive power.
  3. Three-level interpretability: Explanations at different granularities — time step importance, time-independent feature contributions, and time-dependent feature contributions — are highly valuable in practice.
  4. No performance compromise: GATSM maintains full transparency while matching or exceeding Transformer performance, challenging the conventional trade-off between interpretability and accuracy.

Limitations & Future Work

  1. First-order additive effects only: The GAM structure inherently cannot capture feature interactions (e.g., second-order terms as in GA²M), leading to performance gaps on certain datasets (e.g., AirQuality) relative to black-box models.
  2. Primarily single-step prediction: Although multi-step forecasting is discussed, experiments are conducted mainly on single-step tasks; multi-step performance remains to be verified.
  3. Limited attention capacity: The expressiveness of multi-head attention is constrained by the number of heads and hidden dimensionality, which may be insufficient for highly complex temporal patterns.
  4. No native missing value handling: The current approach relies on simple imputation strategies for missing values.
  5. Scalability: Computational efficiency on very long time series or high-dimensional feature settings is not discussed.
  • NBM: The feature network of GATSM directly extends NBM; the basis strategy proves highly effective for time series.
  • NAM / NodeGAM / EBM: Other transparent tabular models, none of which can handle sequential data.
  • NATM: The only prior transparent temporal model, but incapable of capturing temporal patterns and restricted to fixed-length inputs.
  • GAT: The source of the two-layer attention mechanism, which is better suited to the GAM setting than dot-product attention.
  • Insight: Combining the interpretability advantages of GAMs with modern deep learning components is a direction worthy of further exploration.

Rating

  • Novelty: ⭐⭐⭐⭐⭐ — First transparent GAM capable of capturing temporal patterns, with a rigorous formal definition.
  • Experimental Thoroughness: ⭐⭐⭐⭐ — 8 datasets, 15 baselines, complete ablations, though mainly on single-step tasks.
  • Writing Quality: ⭐⭐⭐⭐⭐ — Clear logic, complete theoretical derivations, and well-presented interpretability analysis.
  • Value: ⭐⭐⭐⭐⭐ — A breakthrough contribution to the important direction of interpretable temporal modeling.