Horizon Activation Mapping for Neural Networks in Time Series Forecasting

• URL: http://arxiv.org/abs/2601.02094v2
• Date: Wed, 14 Jan 2026 13:10:20 GMT
• Title: Horizon Activation Mapping for Neural Networks in Time Series Forecasting
• Authors: Hans Krupakar, V A Kandappan,
• Abstract summary: Horizon Activation Mapping (HAM) is a visual interpretability inspired by grad-CAM.<n>Ham can be used for granular model selection, validation set choices and comparisons across different neural network model families.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Neural networks for time series forecasting have relied on error metrics and architecture-specific interpretability approaches for model selection that don't apply across models of different families. To interpret forecasting models agnostic to the types of layers across state-of-the-art model families, we introduce Horizon Activation Mapping (HAM), a visual interpretability technique inspired by grad-CAM that uses gradient norm averages to study the horizon's subseries where grad-CAM studies attention maps over image data. We introduce causal and anti-causal modes to calculate gradient update norm averages across subseries at every timestep and lines of proportionality signifying uniform distributions of the norm averages. Optimization landscape studies with respect to changes in batch sizes, early stopping, train-val-test splits, architectural choices, univariate forecasting and dropouts are studied with respect to performances and subseries in HAM. Interestingly, batch size based differences in activities seem to indicate potential for existence of an exponential approximation across them per epoch relative to each other. Multivariate forecasting models including MLP-based CycleNet, N-Linear, N-HITS, self attention-based FEDformer, Pyraformer, SSM-based SpaceTime and diffusion-based Multi-Resolution DDPM over different horizon sizes trained over the ETTm2 dataset are used for HAM plots in this study. NHITS' neural approximation theorem and SpaceTime's exponential autoregressive activities have been attributed to trends in HAM plots over their training, validation and test sets. In general, HAM can be used for granular model selection, validation set choices and comparisons across different neural network model families.

Related papers

• Nonparametric Data Attribution for Diffusion Models [57.820618036556084]
  Data attribution for generative models seeks to quantify the influence of individual training examples on model outputs.<n>We propose a nonparametric attribution method that operates entirely on data, measuring influence via patch-level similarity between generated and training images.
  arXiv  Detail & Related papers  (2025-10-16T03:37:16Z)
• A Review of the Long Horizon Forecasting Problem in Time Series Analysis [0.0]
  The long horizon forecasting (LHF) problem has come up in the time series literature for over the last 35 years or so.<n>Deep learning has incorporated variants of trend, seasonality, fourier and wavelet transforms, misspecification bias reduction and bandpass filters.<n>We highlight time series decomposition techniques, input data preprocessing and dataset windowing schemes that improve performance.
  arXiv  Detail & Related papers  (2025-06-15T10:49:50Z)
• Temporal Difference Flows [82.24174052059352]
  Geometric Horizon Models (GHMs) offer a compelling alternative by directly making predictions of future states.<n>Existing methods are negatively affected by bootstrapping predictions at train time and struggle to generate high-quality predictions at long horizons.<n>This paper introduces Temporal Difference Flows (TD-Flow), which leverages the structure of a novel Bellman equation on probability paths alongside flow-matching techniques to learn accurate GHMs at over 5x the horizon length of prior methods.
  arXiv  Detail & Related papers  (2025-03-12T20:30:07Z)
• Amortizing intractable inference in diffusion models for vision, language, and control [89.65631572949702]
  This paper studies amortized sampling of the posterior over data, $mathbfxsim prm post(mathbfx)propto p(mathbfx)r(mathbfx)$, in a model that consists of a diffusion generative model prior $p(mathbfx)$ and a black-box constraint or function $r(mathbfx)$.<n>We prove the correctness of a data-free learning objective, relative trajectory balance, for training a diffusion model that samples from
  arXiv  Detail & Related papers  (2024-05-31T16:18:46Z)
• PDETime: Rethinking Long-Term Multivariate Time Series Forecasting from the perspective of partial differential equations [49.80959046861793]
  We present PDETime, a novel LMTF model inspired by the principles of Neural PDE solvers. Our experimentation across seven diversetemporal real-world LMTF datasets reveals that PDETime adapts effectively to the intrinsic nature of the data.
  arXiv  Detail & Related papers  (2024-02-25T17:39:44Z)
• RPMixer: Shaking Up Time Series Forecasting with Random Projections for Large Spatial-Temporal Data [33.0546525587517]
  We propose a all-Multi-Layer Perceptron (all-MLP) time series forecasting architecture called RPMixer. Our method capitalizes on the ensemble-like behavior of deep neural networks, where each individual block behaves like a base learner in an ensemble model.
  arXiv  Detail & Related papers  (2024-02-16T07:28:59Z)
• From Reactive to Proactive Volatility Modeling with Hemisphere Neural Networks [0.0]
  We reinvigorate maximum likelihood estimation (MLE) for macroeconomic density forecasting through a novel neural network architecture with dedicated mean and variance hemispheres. Our Hemisphere Neural Network (HNN) provides proactive volatility forecasts based on leading indicators when it can, and reactive volatility based on the magnitude of previous prediction errors when it must.
  arXiv  Detail & Related papers  (2023-11-27T21:37:50Z)
• Insights into Closed-form IPM-GAN Discriminator Guidance for Diffusion Modeling [11.68361062474064]
  We propose a theoretical framework to analyze the effect of the GAN discriminator on Langevin-based sampling.<n>We show that the proposed approach can be combined with existing accelerated-diffusion techniques to improve latent-space image generation.
  arXiv  Detail & Related papers  (2023-06-02T16:24:07Z)
• Mixed Effects Neural ODE: A Variational Approximation for Analyzing the Dynamics of Panel Data [50.23363975709122]
  We propose a probabilistic model called ME-NODE to incorporate (fixed + random) mixed effects for analyzing panel data. We show that our model can be derived using smooth approximations of SDEs provided by the Wong-Zakai theorem. We then derive Evidence Based Lower Bounds for ME-NODE, and develop (efficient) training algorithms.
  arXiv  Detail & Related papers  (2022-02-18T22:41:51Z)
• Spatial machine-learning model diagnostics: a model-agnostic distance-based approach [91.62936410696409]
  This contribution proposes spatial prediction error profiles (SPEPs) and spatial variable importance profiles (SVIPs) as novel model-agnostic assessment and interpretation tools. The SPEPs and SVIPs of geostatistical methods, linear models, random forest, and hybrid algorithms show striking differences and also relevant similarities. The novel diagnostic tools enrich the toolkit of spatial data science, and may improve ML model interpretation, selection, and design.
  arXiv  Detail & Related papers  (2021-11-13T01:50:36Z)
• Dynamic Time Warping as a New Evaluation for Dst Forecast with Machine Learning [0.0]
  We train a neural network to make a forecast of the disturbance storm time index at origin time $t$ with a forecasting horizon of 1 up to 6 hours. Inspection of the model's results with the correlation coefficient and RMSE indicated a performance comparable to the latest publications. A new method is proposed to measure whether two time series are shifted in time with respect to each other.
  arXiv  Detail & Related papers  (2020-06-08T15:14:13Z)
• A Multi-Channel Neural Graphical Event Model with Negative Evidence [76.51278722190607]
  Event datasets are sequences of events of various types occurring irregularly over the time-line. We propose a non-parametric deep neural network approach in order to estimate the underlying intensity functions.
  arXiv  Detail & Related papers  (2020-02-21T23:10:50Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.