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arxiv: 2605.30356 · v1 · pith:LVDFDTZXnew · submitted 2026-04-22 · 💻 cs.NI

CREWS: Collaborative Robust Edge WiFi Sensing with Asynchronous and Incomplete Observations

Yinan Chen , Yang Zhou , Xiaoxia Huang , Pan Li This is my paper

Pith reviewed 2026-07-05 03:06 UTC · model glm-5.2

classification 💻 cs.NI
keywords WiFi sensingedge computingsplit learningasynchronous distributed learningset aggregationfeature replayrobust sensingconvergence analysis
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The pith

Stale WiFi Data Becomes Training Fuel, Not Trash

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

CREWS reframes delayed and missing sensor data in collaborative WiFi sensing as a training asset rather than a failure mode. The paper's central claim is that a split-learning architecture with three co-designed components — a cardinality-normalized set aggregator, elastic parameter alignment, and staleness-aware adaptive feature replay — can maintain robust sensing accuracy under severe network volatility. The topology-agnostic aggregator treats arriving features as an unordered set, making fusion invariant to which receivers are present and in what order they arrive. Elastic parameter alignment periodically pulls drift-prone edge encoders back toward a shared consensus, preventing representation drift in intermittently connected nodes. The key conceptual move is the replay mechanism: cached features from lagging receivers, though stale and misaligned, are shown to act as system-induced hard samples that regularize the aggregator's decision boundaries — analogous to adversarial training. The paper proves joint convergence of this architecture, showing the optimization error decomposes into convergence rate, aggregator bias, encoder heterogeneity, and system variance terms, all bounded under stated assumptions. On an 8-node heterogeneous hardware testbed, accuracy degradation is held to roughly 2.2 percentage points under 50% dropout or out-of-distribution jitter, and the system maintains 86.4% accuracy with only 2 of 8 receivers available.

Core claim

The paper discovers that stale cached features from intermittently disconnected WiFi receivers, when bounded in staleness, produce representation shifts that are non-negatively aligned with the loss gradient — meaning they function as natural hard samples that regularize the aggregator's decision boundaries. This is established via a first-order Taylor analysis showing the stale-feature perturbation is proportional to the squared gradient norm. Combined with a cardinality-normalized set aggregator that makes gradient norms invariant to the number of active receivers, and elastic parameter alignment that bounds encoder drift, the system converts network-induced asynchrony and incompleteness a

What carries the argument

The cardinality-normalized set aggregator (mean-pooling over available receiver embeddings, yielding O(1) gradient norms independent of subset size); elastic parameter alignment (EMA-based proximal update pulling edge encoders toward a global consensus); staleness-aware adaptive replay (exponentially decaying cache weights combined with rarity-based sampling of missing receivers); and the convergence bound in Theorem 1 decomposing optimization error into four terms governed by complementarity coefficient ν, staleness decay λ_t, and participation rates.

If this is right

  • If stale features genuinely act as hard samples, the same principle could apply to other split-learning or federated systems where stragglers are common — converting infrastructure unreliability into a generalization benefit rather than a cost.
  • The cardinality-normalized aggregator's gradient stability property (Lemma 1) suggests that mean-pooling over set inputs is not just a design convenience but a structural requirement for training stability in systems with variable participation.
  • The optimal replay coefficient formula (Corollary 4) provides a principled way to tune replay strength: when complementarity is high and caches are fresh, replay aggressively; when caches are stale and variance dominates, suppress replay. This could inform adaptive scheduling in other asynchronous distributed learning settings.
  • The testbed results showing graceful degradation under physical device relocation (down to 7.56 pp loss vs. 64.76 pp for baselines) suggest the framework's robustness extends beyond synthetic dropout to genuine distribution shift, which is the practically relevant failure mode for deployed sensing systems.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The complementarity coefficient ν is asserted but not independently estimated from data. A natural extension would be to develop an online estimator for ν based on observed gradient correlations between fresh and replay subsets, enabling the system to detect when replay is counterproductive and automatically suppress it.
  • The hard-sample analogy to adversarial training raises the question of whether the regularization benefit scales with the diversity of staleness patterns — i.e., whether having many different staleness levels in the cache provides richer regularization than uniformly stale features.
  • The framework currently assumes a central server. The convergence analysis suggests that the key mechanism (replay-based bias compression) could in principle operate in a decentralized setting, but the elastic parameter alignment step would need reformulation without a global consensus point.
  • The paper treats receiver availability as exogenous. An interesting extension would be to make the deadline W adaptive — tightening it when the system is well-trained and loosening it when coverage gaps are detected — creating a feedback loop between sensing quality and communication latency tolerance.

Load-bearing premise

The convergence guarantee depends on the assumption that stale cached features from missing receivers are complementary to fresh features — formally, that a complementarity coefficient ν is bounded away from zero. If missing nodes carry redundant rather than complementary views, replay could increase bias rather than compress it, and the theoretical benefit would vanish. The paper does not independently measure ν from data; it is posited as a modeling assumption.

What would settle it

Deploy CREWS in an environment where missing receivers consistently carry redundant (not complementary) views — for example, where spatially clustered receivers drop out together. If ν approaches zero, the aggregator bias term (1−2νλ_t+λ_t²)σ₁² should exceed the no-replay baseline, and accuracy should degrade below a simple discard-and-predict strategy.

Figures

Figures reproduced from arXiv: 2605.30356 by Pan Li, Xiaoxia Huang, Yang Zhou, Yinan Chen.

Figure 1
Figure 1. Figure 1: Transient disconnections in our 8-node testbed and [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: The overall architecture of CREWS. Following a split-learning paradigm, edge receivers (bottom models) extract [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: UMAP visualizations for rare participation nodes [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: Loss landscapes under different training configu [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Robustness under different system heterogeneity. [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Illustration of the data collection and deployment [PITH_FULL_IMAGE:figures/full_fig_p008_7.png] view at source ↗
Figure 10
Figure 10. Figure 10: Hardware deployment results on the heteroge [PITH_FULL_IMAGE:figures/full_fig_p009_10.png] view at source ↗
Figure 9
Figure 9. Figure 9: Performance and complexity comparison under [PITH_FULL_IMAGE:figures/full_fig_p009_9.png] view at source ↗
read the original abstract

Existing collaborative WiFi sensing systems rely on perfect node synchronization and complete data availability. However, real-world edge deployments suffer from heterogeneous computing and network dropouts, leading to asynchronous and incomplete features. We propose CREWS, a robust collaborative sensing framework that inherently resists these network volatility. First, CREWS employs a topology-agnostic aggregator invariant to the arrival order and subset size of incoming features. Second, rather than discarding delayed observations, it utilizes a staleness-aware adaptive replay mechanism. By treating stale features from lagging nodes as system-induced hard samples, CREWS transforms synchronization delays into beneficial training regularization. We theoretically prove the joint convergence of this architecture and demonstrate how replay bounds the bias-variance trade-off. Extensive evaluations and an 8-node heterogeneous hardware testbed demonstrate its superior resilience. Under severe conditions i.e., 50\% transient dropout rate or out-of-distribution jitter, CREWS restricts accuracy degradation to merely 2.2 percentage points, substantially outperforming state-of-the-art baselines.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 8 minor

Summary. This paper proposes CREWS, a collaborative edge WiFi sensing framework that addresses asynchronous and incomplete observations in real-world deployments. The system has three components: (1) a topology-agnostic, cardinality-normalized set aggregator based on the DeepSets formulation, which is permutation-invariant and scale-invariant to subset size; (2) Elastic Parameter Alignment (EPA), which periodically synchronizes edge encoder parameters via an EMA update to counteract gradient starvation in intermittently participating receivers; and (3) a staleness-aware adaptive feature replay mechanism that treats delayed cached features as system-induced hard samples, with freshness-weighted and rarity-weighted sampling. The paper provides a joint convergence analysis (Theorem 1) showing O(1/T) convergence under stated assumptions, with the aggregator bias governed by a complementarity coefficient ν. Empirical evaluation is conducted on the public Widar 3.0 dataset and a self-collected CoSense dataset, plus an 8-node heterogeneous Jetson testbed. Under 50% dropout or straggler reversal conditions, CREWS substantially outperforms baselines (OneFi, FewSense, EfficientFi, PlugVFL).

Significance. The paper addresses a practically important problem — robust collaborative WiFi sensing under dynamic receiver availability — that is underexplored relative to cross-domain adaptation work. The split-learning architecture with set-based fusion is well-motivated by the exchangeability argument (de Finetti's theorem). The convergence analysis in Appendix C is self-contained and follows standard SGD techniques (polarization identity, smoothness-based descent). The derivation of the optimal replay coefficient (Corollary 4, Eq. 41) from the bias-variance trade-off function B(λ) is a clean, parameter-free result. The 8-node heterogeneous Jetson testbed with real WiFi CSI collection and the physical relocation experiments (Section 6.2) add significant practical value. The ablation in Table 2 isolating replay and EPA contributions is informative.

major comments (3)
  1. §4.3, Theorem 1 (Eq. 16) and Appendix C.2, Lemma 2 (Eq. 27): There is a gap between the tighter bias bound in Lemma 2 and the looser bound stated in Theorem 1. Lemma 2 establishes that the aggregator bias satisfies ˜σ₁² ≤ [(1−2νλ_t+λ_t²)/(1+λ_t)²]·σ₁², which is always ≤ σ₁² for ν ≥ 0 and λ_t ∈ [0,1]. However, Theorem 1 (Eq. 16) and Theorem 2 (Eq. 29) drop the (1+λ_t)² denominator, yielding the looser term (1−2νλ_t+λ_t²)σ₁², which can exceed σ₁² when ν is near zero. The proof of Theorem 2 (between Eqs. 31–33) makes this step by noting (1+λ_t) ≥ 1, but this loses the key property that replay never worsens the bias. Since the tighter bound is already proven in Lemma 2, the main theorem should present the tighter result or explicitly justify the looseness. This matters because the paper's narrative (§4.3, discussion of the aggregator bias term) emphasizes that replay 'compresses' the bias, a
  2. §4.3, Assumption 1(ii): The complementarity coefficient ν ∈ (0,1] is the load-bearing premise for bias compression, positing E[⟨Δ₁, Δ̄₂⟩] ≤ −νE[‖Δ₁‖²]. The paper acknowledges that ν quantifies 'spatial complementarity between S_t and R_t' but does not provide any independent estimate or empirical validation of this quantity. The concern is substantive: if missing receivers carry redundant rather than complementary views (e.g., similar angular projections per §3.1), their gradient biases would be positively correlated, and ν could be near zero. The ablation in Table 2 (B+R vs B under Straggler Reversal: 83.6% vs 69.6%) provides indirect evidence that replay helps in practice, but this is an accuracy-level observation, not a validation of the gradient-level geometric assumption. The authors should either (a) provide an empirical estimate of ν from the gradient statistics of trained models,
  3. §4.2, Eqs. (10)–(13) and Algorithm 1: The staleness-aware adaptive sampling mechanism introduces numerous free parameters (γ, β, ξ, η_s, κ, λ₀, μ, T_align, W). The paper does not provide a sensitivity analysis or guidance on how these were selected for the experiments. Given that the functional forms in Eqs. (12)–(13) are acknowledged as non-critical (footnote 1), it would strengthen the paper to show that performance is robust to reasonable variations in these hyperparameters, particularly γ (staleness decay) and β (rarity up-weighting), which most directly govern the replay behavior.
minor comments (8)
  1. §3.1, Eq. (1): The notation uses both 𝑓 (italic) for subcarrier frequency and 𝑓_𝑘(·) for the encoder function, which could cause confusion. Consider using a different symbol for one of them.
  2. Figure 2: The diagram is dense and some labels are difficult to read (e.g., gradient flow arrows, cache update paths). Consider simplifying or enlarging key components.
  3. §5.1: The CoSense dataset description is brief. Details on the 6 activities, number of samples per activity, and train/test split ratios would aid reproducibility.
  4. Table 1: The 'Own' in the caption appears to be a typo for 'CoSense'.
  5. §5.3, Table 2: The 'Balanced Loss' row shows B+R (94.1%) slightly underperforming B+F (96.2%), and the full model B+F+R (96.3%) barely improves over B+F. This suggests replay adds minimal value under uniform dropout. The paper should discuss this asymmetry between the Straggler Reversal and Balanced Loss settings more explicitly.
  6. Appendix B, Eq. (24): The approximation δ_t^(k) ≈ η J_k J_k^T ∇_{z_virt} L assumes one-step parameter lag. The extension to multi-step lag (general age_t(k)) is mentioned qualitatively but not formalized. A brief statement on how the bound degrades with age would strengthen the hard-sample argument.
  7. §6.2, Fig. 10(b): The '2-Group Swap' and '4-Group Swap' conditions are described in text but the figure only shows three bars per method. Clarify which deployment conditions correspond to which bars.
  8. References: Some 2025–2026 references (e.g., [17], [24], [40]) may be preprints; please verify final publication status and update citations accordingly.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the careful and constructive review. All three major comments are well-taken. We will (1) tighten the main theorem to use the sharper bound from Lemma 2, (2) add an empirical estimate of the complementarity coefficient ν from trained models, and (3) include a hyperparameter sensitivity analysis. Details are below.

read point-by-point responses

  1. Referee: §4.3, Theorem 1 (Eq. 16) and Appendix C.2, Lemma 2 (Eq. 27): There is a gap between the tighter bias bound in Lemma 2 and the looser bound stated in Theorem 1. Lemma 2 establishes that the aggregator bias satisfies σ̃₁² ≤ [(1−2νλ_t+λ_t²)/(1+λ_t)²]·σ₁², which is always ≤ σ₁² for ν ≥ 0 and λ_t ∈ [0,1]. However, Theorem 1 (Eq. 16) and Theorem 2 (Eq. 29) drop the (1+λ_t)² denominator, yielding the looser term (1−2νλ_t+λ_t²)σ₁², which can exceed σ₁² when ν is near zero. The proof of Theorem 2 (between Eqs. 31–33) makes this step by noting (1+λ_t) ≥ 1, but this loses the key property that replay never worsens the bias. Since the tighter bound is already proven in Lemma 2, the main theorem should present the tighter result or explicitly justify the looseness.

    Authors: The referee is correct. The tighter bound from Lemma 2, which includes the (1+λ_t)² denominator and guarantees that the aggregator bias never exceeds σ₁², is already proven in our appendix. Dropping this denominator in Theorems 1 and 2 was an unnecessary loosening that loses the important property that replay never worsens the bias. We will revise Theorem 1 (Eq. 16) and Theorem 2 (Eq. 29) to present the tighter bound [(1−2νλ_t+λ_t²)/(1+λ_t)²]·σ₁² directly. We will also update the discussion in §4.3 to explicitly note that the bias is uniformly bounded by σ₁², which strengthens the narrative that replay compresses rather than inflates the aggregator bias. The proof in Appendix C.3 already derives the tighter form at the intermediate step (using η̃_t = η_φ(1+λ_t) combined with Lemma 2); we will simply retain it rather than relaxing it. revision: yes

  2. Referee: §4.3, Assumption 1(ii): The complementarity coefficient ν ∈ (0,1] is the load-bearing premise for bias compression, positing E[⟨Δ₁, Δ̄₂⟩] ≤ −νE[‖Δ₁‖²]. The paper acknowledges that ν quantifies 'spatial complementarity between S_t and R_t' but does not provide any independent estimate or empirical validation of this quantity. The concern is substantive: if missing receivers carry redundant rather than complementary views (e.g., similar angular projections per §3.1), their gradient biases would be positively correlated, and ν could be near zero. The ablation in Table 2 (B+R vs B under Straggler Reversal: 83.6% vs 69.6%) provides indirect evidence that replay helps in practice, but this is an accuracy-level observation, not a validation of the gradient-level geometric assumption. The authors should either (a) provide an empirical estimate of ν from the gradient statistics of trained models,

    Authors: This is a fair and substantive concern. We agree that ν is the load-bearing premise for bias compression and that the current manuscript lacks a direct empirical validation of this gradient-level geometric assumption. We will address this by adding an empirical estimate of ν from trained models. Specifically, we will instrument the training process to compute E[⟨Δ₁, Δ̄₂⟩] and E[‖Δ₁‖²] from the actual gradient statistics of the aggregator at multiple checkpoints on both the Widar 3.0 and CoSense datasets, and report the resulting ν estimates. We will also examine the regime the referee raises — when missing receivers carry redundant views — by analyzing the correlation between ν and the angular diversity of the receiver deployment (per the directional ambiguity discussion in §3.1). This will show whether the spatial diversity inherent in multi-view WiFi sensing naturally yields positive complementarity, or whether ν degrades in specific configurations. We will include these measurements as a new subsection or table in the revised manuscript. revision: yes

  3. Referee: §4.2, Eqs. (10)–(13) and Algorithm 1: The staleness-aware adaptive sampling mechanism introduces numerous free parameters (γ, β, ξ, η_s, κ, λ₀, μ, T_align, W). The paper does not provide a sensitivity analysis or guidance on how these were selected for the experiments. Given that the functional forms in Eqs. (12)–(13) are acknowledged as non-critical (footnote 1), it would strengthen the paper to show that performance is robust to reasonable variations in these hyperparameters, particularly γ (staleness decay) and β (rarity up-weighting), which most directly govern the replay behavior.

    Authors: The referee is right that a sensitivity analysis would strengthen the paper, especially for γ and β which most directly govern replay behavior. We will add a sensitivity analysis in the revised manuscript showing CREWS performance under systematic variations of γ (staleness decay rate) and β (rarity up-weighting strength), as well as the other key hyperparameters. We expect this to confirm that performance is robust to reasonable variations, consistent with our footnote acknowledging that the specific functional forms are non-critical as long as the calibration is monotonic in both freshness and rarity. We will also add a table listing the specific hyperparameter values used in all experiments and brief guidance on their selection. revision: yes

Circularity Check

0 steps flagged

No significant circularity: convergence theorem is derived from standard assumptions without self-citation chains or fitted-input-as-prediction patterns.

full rationale

The paper's central theoretical claim (Theorem 1, Eq. 16) is derived from Assumption 1 using standard SGD convergence techniques (L-smoothness, polarization identity, Young's inequality) in Appendix C. The proof chain is self-contained: Lemma 2 (bias compression) follows algebraically from the complementarity condition E[⟨Δ₁, Δ̄₂⟩] ≤ −νE[‖Δ₁‖²] stated in Assumption 1(ii); Lemma 3 (variance bound) follows from Assumption 1(i); Theorems 2 and 3 combine these via telescoping. No step reduces to its inputs by construction. The optimal replay coefficient (Corollary 4, Eq. 41) is derived analytically by differentiating the bias-variance trade-off function B(λ) — it is not fitted to data and then presented as a prediction. The adaptive mechanism λ_t = λ₀^{ā_t(R_t)} is explicitly described as a heuristic approximation to λ*, not a fit to the target result. The paper does cite DeepSets [33] and de Finetti's theorem for the set aggregator design, but these are external results used as building blocks, not self-citations that load-bear the central claim. The complementarity coefficient ν is asserted as a modeling assumption rather than independently validated — this is a correctness/assumption-strength concern, not a circularity issue, since the theorem is honestly conditional on Assumption 1(ii) and does not claim to derive ν from data. The empirical evaluation (Tables 1-2, Figs. 6-10) uses external baselines (OneFi, FewSense, EfficientFi, PlugVFL) and real hardware, providing independent benchmarks. No fitted parameter is renamed as a prediction, no self-citation chain forces the conclusion, and no ansatz is smuggled in via citation.

Axiom & Free-Parameter Ledger

10 free parameters · 4 axioms · 1 invented entities

The paper introduces 10 free parameters (γ, β, ξ, η_s, κ, μ, T_align, W, λ₀, learning rates) none of which are tabulated with fitted values in the main text. The convergence analysis relies on three assumptions, of which Assumption 1(ii) is the most ad hoc: it posits a complementarity coefficient ν that is load-bearing for the bias-compression claim but is never independently estimated. One invented entity (ν) is introduced without independent empirical grounding.

free parameters (10)
  • γ (staleness decay rate) = not stated
    Controls exponential decay of cached feature weight w_t(k) = exp(-γ·age). Value not reported in main text.
  • β (rarity up-weighting strength) = not stated
    Controls how strongly underrepresented receivers are prioritized in Eq. 11. Value not reported.
  • ξ (smoothing constant) = not stated
    Smoothing in rarity score r_t(k). Value not reported.
  • η_s (rarity-freshness balance) = not stated
    Balances rarity against freshness in priority score u_t(k). Value not reported.
  • κ (sigmoid sharpness) = not stated
    Controls sharpness of selection probability in Eq. 13. Value not reported.
  • μ (EMA alignment coefficient) = not stated
    Controls how much local encoders are pulled toward global consensus in Eq. 9. Value not reported.
  • T_align (alignment interval) = not stated
    Periodicity of elastic parameter alignment. Value not reported.
  • W (deadline window) = not stated
    Maximum wait time for feature arrival. Value not reported.
  • λ₀ (base replay coefficient) = not stated
    Base scaling for replay loss in λ_t = λ₀^{ā_t(R_t)}. Value not reported.
  • η_ϕ, η_θ (learning rates) = constrained by η_ϕ ≤ 1/(2L₁), η_θ ≤ 1/(4L₂)
    Learning rates for aggregator and encoders. Specific values not reported.
axioms (4)
  • domain assumption Assumption 1(i): L_nom and L_rep are L₁-smooth in ϕ; F is L₂-smooth in each θ_k; stochastic gradients satisfy E[‖g−∇F‖²] ≤ σ²_B.
    Standard SGD smoothness and bounded-variance assumptions. Invoked in §4.3 and Appendix C.
  • ad hoc to paper Assumption 1(ii): Gradient biases of fresh subset and replay subset relative to global gradient are bounded by σ₁², and complementarity ν ∈ (0,1] exists such that E[⟨Δ₁, Δ̄₂⟩] ≤ −νE[‖Δ₁‖²].
    Load-bearing for the aggregator bias term. The complementarity ν is not independently estimated; it is posited as a property of the system. Invoked in §4.3 and Appendix C.2.
  • domain assumption Assumption 1(iii): Participation-conditioned gradient of each encoder satisfies E[‖E[∇_{θ_k} L_nom | k ∈ S_t] − ∇_{θ_k} F‖²] ≤ σ₂².
    Bounds the bias introduced by stochastic participation. Standard in federated/distributed learning analysis. Invoked in §4.3 and Appendix C.4.
  • domain assumption Short-delay, same-label assumption for staleness analysis: y_{t'_k} = y_t and X^{(k)}_{t'_k} ≈ X^{(k)}_t.
    Required for the first-order staleness analysis in Appendix B to reduce to parameter-lag-dominated shift. Reasonable for short delays but unvalidated for longer delays.
invented entities (1)
  • Complementarity coefficient ν no independent evidence
    purpose: Quantifies the spatial complementarity between fresh subset S_t and replay subset R_t in the convergence bound.
    Introduced in Assumption 1(ii) as a modeling parameter. No independent measurement or estimation of ν from the testbed data is provided. The convergence bound depends on ν but the paper does not report its empirical value.

pith-pipeline@v1.1.0-glm · 30837 in / 4222 out tokens · 339142 ms · 2026-07-05T03:06:52.239332+00:00 · methodology

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    can be rewritten as 𝜙𝑡+1 =𝜙 𝑡 − ˜𝜂𝑡 ˆ𝑔𝑡 . The weights1 /(1 +𝜆 𝑡 ) and 𝜆𝑡 /(1 +𝜆 𝑡 ) sum to one, so ˆ𝑔𝑡 is a convex combination of the fresh and replay gradients. this rewriting merely redistributes the scaling between the learning rate and the gradient direction, without altering the actual parameter update. C.2 Auxiliary Lemmas Define the gradient biases...

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