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Dynamic Influence-Weighted Distillation for Single-IMU Activity Recognition

Bingxuan Xie

arXiv:2608.24904v1cs.LGcs.HC

TL;DR

The paper investigates whether multi-position IMUs available only during training can improve a model deployed with a right-arm IMU, addressing the burden of multi-sensor inference. It introduces DIW, which uses one-step meta feedback to gate logit and feature distillation separately for each sample. On WEAR, DIW raises pooled OOF macro-F1 to 0.638451 while retaining the same 80,915-parameter right-arm student at inference.

  • Problem

    Additional body-worn sensors broaden activity coverage but increase deployment burden, motivating training with four synchronized IMUs while retaining only a right-arm IMU for fitting and inference.

  • Method

    DIW evaluates a detached one-step candidate update on a fold-internal meta set and assigns separate sample-wise gates to logit and feature teacher targets.

  • Results

    0.638451 pooled OOF macro-F1 is achieved by DIW versus 0.561820 for Supervised and 0.571623 for Fixed-weight KD on WEAR.

  • Takeaways & Limitations

    DIW converts training-only multi-position information into a stronger single-IMU model without changing the deployed input or student forward graph under the tested protocol.

  • Takeaways & Limitations

    The study uses one dataset, one retained sensor location, one random seed, and one teacher–student family, while DIW alone receives fold-internal meta-participant labels.

Abstract

from arXiv · show

Inertial sensors at multiple body locations can improve activity recognition, but requiring every sensor at inference increases the deployment burden. We study whether four synchronized IMUs available during training can improve a student that uses only the right-arm IMU during fitting and inference. A frozen four-IMU teacher provides logit and feature targets. Fixed-weight knowledge distillation applies each target with the same strength to every fitting sample, although the student may not benefit equally from them. We introduce dynamic influence weighting (DIW), which tests a one-step candidate update on separate fold-internal training participants. DIW then assigns separate sample-wise gates to the logit and feature losses. On WEAR, we evaluate 19 labels and 68,298 complete windows from 22 participants using subject-disjoint five-fold cross-validation. Pooled out-of-fold macro-F1 is 0.561820 for Supervised and 0.571623 for Fixed-weight KD. DIW reaches 0.638451, gains of 7.66 and 6.68 percentage points, respectively. It exceeds Supervised for 18 of 19 labels and 21 of 22 held-out participants. All three routes retain the same 80,915-parameter right-arm student at inference. Under this protocol, DIW converts training-only multi-position information into a stronger single-IMU model without changing deployed sensing or the student forward graph.

1 Introduction

The paper asks whether training-only multi-position sensing can strengthen a right-arm-only activity-recognition model without increasing inference burden. It introduces DIW to adaptively select teacher guidance and reports improved WEAR performance under a controlled single-IMU deployment protocol.

  • Motivation: Four synchronized training IMUs provide broader motion coverage, but requiring every device at inference increases wearing, synchronization, power, and maintenance burdens.The final classifier therefore receives only the right-arm IMU.
  • Motivation: Fixed-weight KD applies logit and feature targets uniformly, although a four-IMU teacher may rely on motion unavailable to the right-arm student.This creates a mismatch between teacher information and the student’s restricted input.
  • Method: DIW uses a detached one-step candidate update and fold-internal meta evaluation to estimate separate sample-wise gates for logit and feature distillation.Teacher, meta-set, and gate-estimation operations are used only during training.
  • Evaluation: 0.638451 pooled OOF macro-F1 is achieved by DIW, compared with 0.561820 for Supervised and 0.571623 for Fixed-weight KD on WEAR.The evaluation uses subject-disjoint five-fold cross-validation.
  • Results: DIW exceeds Supervised for 18 of 19 labels and 21 of 22 held-out participants while retaining identical single-IMU inference across deployable routes.The contribution protocol keeps the deployed input and model unchanged.

2 Related Work

Prior work transfers training-only information from richer sensing or stronger models to predictors with restricted deployment inputs. Related approaches adapt representations, modalities, examples, objectives, or distillation components rather than treating all guidance identically.

  • Training-only information: Learning using privileged information allows auxiliary observations during training while the deployed predictor operates without them.Distillation transfers training-only information into a model defined on the deployment input.
  • Wearable sensing: Wearable-sensing studies use additional sensors, cross-location representation alignment, and virtual fusion to improve recognition from a retained single sensor.These approaches preserve restricted single-sensor inference after richer training-time sensing.
  • Heterogeneous and teacher–student systems: MESEN, TSAK, and Sensor-to-Sensor Procedural Co-learning transfer heterogeneous or multi-position information to smaller or sensor-limited activity-recognition models.They use multimodal data, semantic representations, input adaptation, and multi-level feature objectives.
  • Distillation: Classical and feature-based KD align softened outputs or internal representations, while combining objectives commonly uses constant loss coefficients across fitting samples.The related literature frames adaptive weighting as a departure from identical treatment of every sample.
  • Adaptive weighting: Validation-guided methods use training–validation gradient agreement, meta-learned mappings, student state, or training stage to adapt sample or objective contributions.These methods derive weighting feedback beyond the instantaneous training loss.
  • Adaptive distillation: Adaptive distillation can act on teacher combinations, individual training examples, or the teacher’s own update, including finite-difference influence estimates.This positions DIW among methods that adapt how distillation information enters learning.

3 Method

The method trains a right-arm student with privileged four-IMU teacher information, while DIW adaptively gates logit and feature distillation using fold-internal meta feedback. Only the student remains at inference, preserving the single-IMU deployment graph.

  • Problem setting: A synchronized example contains right-arm, right-leg, left-leg, and left-arm inputs, but the student uses only right-arm input during fitting and inference.The teacher’s non-right-arm inputs are privileged training information rather than inputs the student reconstructs.
  • Inputs and networks: The student uses a compact temporal convolutional architecture with 80,915 trainable parameters, while the four-IMU teacher uses a shared encoder and fusion projection.The teacher produces detached logit and fused-feature targets for distillation.
  • Dynamic influence weighting: DIW independently gates logit and feature distillation according to whether reducing each loss aligns locally with lowering the meta objective.The influence estimate is recomputed at every fitting step for both components.
  • Dynamic influence weighting: DIW evaluates a detached one-step candidate update on fold-internal meta participants before estimating training-sample influence.The candidate mirrors the optimizer transition but does not modify persistent optimizer state.
  • Dynamic influence weighting: Influence is retained only when positive beyond numerical resolution, then maximum-normalized within the fitting mini-batch and clamped to [0, 1].A zero gate indicates no resolved positive evidence for that sample–component pair at the current step, not permanent harm.
  • Deployment: DIW changes only training: inference removes the teacher, meta set, look-ahead state, probes, and non-right-arm streams.All deployable routes retain the same right-arm input tensor and 80,915-parameter forward graph.

4 Experimental Setup

The study evaluates three right-arm deployment routes on WEAR under participant-disjoint five-fold cross-validation. DIW is compared with supervised training and fixed-weight distillation using common data, architecture, and evaluation procedures.

  • Dataset: WEAR contributes 22 participants, 19 labels, and 68,298 complete non-overlapping windows from four synchronized IMU positions.The labels comprise 18 exercise activities and a null class; video is not used.
  • Cross-validation: Five-fold StratifiedGroupKFold uses participant identity for grouping, with three outer-training participants reserved as Dmeta in each fold.DIW accesses only right-arm windows and labels from Dmeta, while Supervised and Fixed-weight KD train on Dfit.
  • Compared routes: The three deployable routes are Supervised, Fixed-weight KD, and DIW, all using the same right-arm student architecture.The four-IMU teacher is reported separately as a non-deployable reference.
  • Uncertainty: Participant-cluster bootstrap with 10,000 resamples produces percentile 95% intervals for pooled and per-label estimates.The reported route differences are descriptive.
  • Diagnostics: Fold-0 gate diagnostics characterize training behavior rather than providing a separate accuracy estimate or cross-fold mechanism claim.The diagnostics cover 49,113 fitting samples at epochs 6, 8, 16, and 32.

5 Results

DIW delivers the strongest right-arm-only student performance, with gains distributed broadly across labels and held-out participants. Gate diagnostics and ablations indicate that DIW’s adaptive, component-specific selection outperforms fixed or reduced alternatives under the common protocol.

  • 5.1 Selective distillation improves the right-arm student: 0.638451 pooled OOF macro-F1 is achieved by DIW, versus 0.571623 for Fixed-weight KD and 0.561820 for Supervised.DIW gains 7.66 percentage points over Supervised and 6.68 points over Fixed-weight KD.
  • 5.2 Gains extend across labels and held-out participants: 18 of 19 labels and 21 of 22 held-out participants improve with DIW over Supervised, while gains over Fixed-weight KD occur for 18 labels and 20 participants.The improvement is broad but not universal across the evaluation cohort.
  • 5.1 Selective distillation improves the right-arm student: All three student routes retain identical right-arm-only inference with the same 80,915-parameter forward graph.The four-IMU teacher is a contextual reference rather than a directly comparable student route because it uses richer inputs and a larger fusion model.
  • 5.3 Gate selection varies by component, stage, and activity class: DIW gate trajectories diverge by component: positive logit-gate rates fall from 79.4% to 69.5%, while feature-gate rates rise from 61.1% to 71.3% between epochs 6 and 32.Median gate values rise for both components over the same period.
  • 5.4 Full DIW exceeds coefficient- and structure-reduced controls: 0.625185 for the Static gate map and 0.599342 for Mean-matched KD remain below Full DIW at 0.638451.No look-ahead and Batch-shared gates reach 0.616044 and 0.606234, respectively.
  • 5.4 Full DIW exceeds coefficient- and structure-reduced controls: Recalculating gates, evaluating guidance after the candidate optimizer step, and assigning component weights per sample are each supported by targeted variant comparisons.These comparisons are not a full factorial estimate of each component’s independent causal effect.

6 Discussion

The results support selective, component-specific teacher guidance for a right-arm student, while limiting interpretation to the tested protocol and acknowledging added training costs and confounds.

  • The teacher exceeds the supervised student by 14.30 percentage points, but Fixed-weight KD recovers only 0.98 points.The gap is plausible because the teacher observes motion absent from the right-arm input.
  • Logit and feature gates follow different trajectories, so one shared schedule cannot express their observed behavior.The both-positive state remains common, suggesting the two knowledge sources often remain complementary.
  • Mean-matched KD does not reproduce Full DIW, while static gates retain much of the gain and online gates perform better as the student changes.These targeted comparisons support sample- and component-specific selection but do not establish class-level causal effects.
  • DIW increases training cost through a candidate AdamW update, meta-batch evaluation, and two finite-difference probes after warm-up.Hardware-normalized training time, memory use, and on-device performance remain unmeasured.
  • Interpretation is constrained by one dataset, retained sensor location, random seed, teacher–student family, and DIW-only access to fold-internal meta labels.Equivalent meta-label access is needed to separate gating effects from additional labeled feedback.

7 Conclusion

The conclusion examines whether training-only multi-position signals can improve a right-arm-only classifier and reports that DIW does so under the tested WEAR protocol.

  • DIW assigns separate sample-wise gates to logit and feature targets using feedback from a one-step candidate update.
  • Pooled OOF macro-F1 rises from 0.561820 to 0.638451 under subject-disjoint five-fold evaluation on WEAR.The deployed model remains the same 80,915-parameter right-arm student.
  • Lowering average KD strength alone does not reproduce the Full DIW result.The findings support selective privileged distillation under the tested protocol.
  • Equivalent meta-label access and broader replication are needed to isolate the reported effects.

Data Availability

The WEAR dataset is available from the official project website and is described by Bock et al.

  • The WEAR dataset is available from the official project website and is described by Bock et al. [13].

Code Availability

A public PyTorch implementation provides the paper’s student, teacher, training objectives, and DIW components.

  • A PyTorch reference implementation includes the right-arm student, four-IMU teacher, three training objectives, and DIW meta-probe and gate mapping.
  • The repository is available at github.com/1304126986/wear-right-arm-privileged-distillation.
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