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What Makes Recurrence Effective in Looped Language Models?

Xinlin Zhuang, Siyuan Wang, Imran Razzak, Weiyang Liu

arXiv:2609.36636v1cs.LGcs.CL

TL;DR

It remains unclear whether LoopLMs gain useful computation beyond their training horizon and which architectural choices govern that behavior. Through controlled experiments, the paper varies inference depth, recurrent placement, and conditioning; recurrence can help reasoning while harming knowledge, with outcomes depending on design. The study also proposes a lightweight joint conditioning design for extended inference budgets.

  • Problem

    It remains unclear whether additional depth beyond the training horizon provides useful computation and what factors determine LoopLM scaling behavior.

    Source: §1 · p. 1

  • Method

    The paper uses controlled experiments to examine how recurrent placement and conditioning shape test-time scaling across inference regimes.

    Source: §1 · p. 2

  • Results

    Beyond the training horizon, recurrence can improve reasoning while degrading knowledge, and scaling behavior depends on task and recurrent configuration.

    Source: §1 · p. 2

  • Takeaways & Limitations

    Channel-wise history-state injection combined with timestep conditioning is a lightweight design that outperforms either variant alone and the unconditioned baseline under extended inference budgets.

    Source: §1 · p. 2

    Experiments cover models up to roughly 1B parameters and fixed multiples of the training horizon, without adaptive per-input iteration counts.

    Source: A LIMITATIONS · p. 15

Abstract

from arXiv · show

Looped language models (LoopLMs) increase computational depth through parameter sharing, offering a path to scale inference computation without adding parameters. However, it remains unclear when additional recurrence is beneficial and how architectural choices affect its effectiveness. Through controlled experiments, we systematically examine (1) when recurrence helps, (2) where it should be applied, and (3) how its conditioning affects performance. Our evaluation covers inference budgets below, within, and beyond the training horizon under knowledge and reasoning tasks. (1) We find that recurrence can improve reasoning beyond the training horizon while degrading knowledge performance, but harder reasoning instances do not consistently benefit more. (2) Performance also depends on how distinct layers and recurrent iterations are allocated, showing that effective depth alone is insufficient to predict behavior. Non-recurrent output layers improve robustness to under-unrolling, while the preferred placement of input and output layers varies with inference budget. (3) Finally, we find that conventional initial-state injection offers limited robustness to varying recurrence depth. We therefore propose history-state injection as an alternative, and show that channel-wise history-state injection combined with timestep conditioning offers a low-cost and more effective design, better preserving knowledge under extended unrolling while improving robustness across inference budgets. Overall, our results clarify when recurrent computation helps, where it fails, and offer practical guidelines for designing LoopLMs across variable inference budgets.

1 INTRODUCTION

LoopLMs reuse parameters to add inference depth, but whether computation beyond the training horizon helps—and which design choices govern its effectiveness—remains unclear. Controlled experiments show that recurrence’s effects depend on task and architecture, and examine how recurrent placement and conditioning shape scaling.

1 INTRODUCTION

  • Beyond the training horizon, additional loops can improve reasoning while degrading knowledge, and scaling also varies with reasoning demand and the allocation of physical depth versus recurrent iterations.Models with the same effective training depth can have markedly different scaling behavior.Source: §1 · p. 2
  • Non-recurrent output blocks improve knowledge robustness to under-unrolling, while input-side allocation tends to support reasoning extrapolation; preferred allocation varies with inference budget.Near the training horizon, performance is less sensitive to boundary-block allocation.Source: §1 · p. 2
  • The paper proposes lightweight channel-wise conditioning that combines history-state injection with timestep conditioning and outperforms either variant alone and the unconditioned baseline under extended inference budgets.The contributions also frame the study as a characterization of recurrent scaling and the factors governing extrapolation.Source: §1 · p. 2

2 PRELIMINARIES AND EVALUATION SETTINGS

The section defines LoopLM components and depth measures, specifies controlled model comparisons, and describes evaluation across task demands and inference budgets.

2.1 FORMULATION

  • A LoopLM decoder combines a Prelude, a shared recurrent core applied K times during training, and a Coda; inference varies loop count r to under-unroll, match, or exceed the training horizon.Optional auxiliary signals γ_t condition the recurrent trajectory, while setting γ_t = ∅ gives standard recurrence.Source: §2.1 · p. 2
  • Physical depth counts independently parameterized layers, while effective depth counts per-token compute at a given loop count; BaseLoop has no non-recurrent boundary blocks, whereas CoreLoop has at least one.Comparisons match physical depth, training and inference effective depths, and the training pipeline.Source: §2.1 · p. 3, §2.2 · p. 3

2.3 EVALUATION ACROSS COMPUTATIONAL DEMANDS

  • Evaluation varies inference loop count below, at, and beyond the training horizon, and reports knowledge and reasoning groups plus reasoning-depth strata for ProofWriter and CLUTRR.The task groups distinguish fact retrieval with limited composition from tasks requiring multiple inference steps.Source: §2.3 · pp. 3–4

3 WHEN DOES RECURRENCE HELP?

Under fixed effective training depth, test-time scaling depends on task and on how physical layers and recurrent iterations are allocated. Reasoning can improve beyond the training horizon while knowledge declines, and harder reasoning instances do not consistently benefit more.

Additional recurrence can improve reasoning beyond the training horizon

  • Reasoning rises 28.52 to 31.49 from L(r) = 20 to 40, while Knowledge falls 62.80 to 52.11 for BaseLoop 2 × 10.The reasoning gain is 2.97 percentage points, achieved at test time without parameter updates.Source: §3 · p. 4

Gains vary across reasoning demands and complexities

  • ProofWriter gains around 7.5 percentage points at proof depths 3–5, but CLUTRR gains are smaller or decline for longer relation chains.At L(r) = 24, CLUTRR accuracy reaches 31.6 for length 2 and 23.4 for length 3; harder long-chain instances do not automatically benefit more from added loops.Source: §3 · p. 4

Physical depth and recurrent loops require a balanced allocation

  • At the same effective training depth L(K) = 20, 2 × 10 degrades and 10 × 2 gains little under extrapolation, while 5 × 4 peaks at L(r) = 30 and 4 × 5 improves to L(r) = 40.The results indicate that effective scaling depends on balancing physical depth and recurrent iterations, not effective depth alone.Source: §3 · p. 4

Additional computation enables recurrent models to surpass the non-recurrent upper-bound

  • 31.88 reasoning at L(r) = 30 for BaseLoop 5 × 4 and 31.49 at L(r) = 40 for 4 × 5 exceed NonLoop’s 30.25.These variants share NonLoop’s effective training depth and training FLOPs while using fewer distinct physical Transformer layers.Source: §3 · pp. 4–5

4 WHICH COMPUTATIONS SHOULD BE RECURRENT?

Matched effective-depth and token-budget comparisons of BaseLoop and CoreLoop show that boundary-layer placement has different trade-offs across inference budgets. Coda layers mitigate under-unrolling, while Prelude-heavy configurations can better support reasoning extrapolation.

Boundary-layer allocation across inference regimes

  • The optimal allocation of non-recurrent boundary layers varies by inference budget, with distinct trade-offs across under-unrolling, the training horizon, and extrapolation.The study compares BaseLoop with CoreLoop configurations that reserve non-recurrent Prelude and/or Coda blocks around a shared core under matched effective training depth and token budget.Source: §4 · p. 5

Coda alleviates knowledge decay during under-unrolling

  • Coda blocks substantially mitigate BaseLoop’s rapid knowledge degradation under under-unrolling, alongside smaller angular changes and more stable recurrent states.The authors suggest that separating the output-side transformation from the recurrent core helps align under-executed states with the final readout.Source: §4 · p. 6

Performance is strong and robust to boundary allocation at the training horizon

  • Around L(K) = 20, models generally show strong, stable overall, knowledge, and reasoning performance, with smaller differences across Prelude–Coda allocations.This is the computation regime encountered during training, where recurrent-core representations are described as aligned with the trained output pathway.Source: §4 · p. 6

Prelude-heavy allocations better support reasoning extrapolation

  • Beyond the training horizon, Prelude-heavy allocations can better sustain or improve reasoning, although this trend is not universal.Examples include 2 + 2 × 9 + 0 in the four-layer setting and 5 + 5 × 3 + 0 and 4 + 5 × 3 + 1 in the ten-layer setting.Source: §4 · p. 6

Convergence alone does not explain useful extrapolation

  • Beyond the training horizon, angular distance and relative update norm decrease while recurrent-state variance grows, even as downstream performance can deteriorate.The authors suggest that small per-iteration updates may accumulate and drift states away from the training distribution, so decreasing updates alone do not establish useful extrapolation.Source: §4 · p. 6

5 HOW SHOULD RECURRENCE BE CONDITIONED?

The section examines whether state and timestep conditioning make recurrent computation more robust when inference depth differs from training depth. It finds that their effectiveness depends on the conditioning design, recurrent architecture, and inference budget.

5.1 STATE CONDITIONING

  • Dense initial-state injection collapses overall and knowledge accuracy during extrapolation, while lightweight variants avoid collapse but offer negligible net gains and reasoning remains largely flat.The authors attribute the static reference’s limited value to redundant input semantics in the residual stream.Source: §5.1 · p. 7
  • History-state injection conditions updates on recent intermediate states using relative differences, and a dense one-step window sustains extrapolation accuracy near NonLoop.For Dense mapping, larger windows progressively diminish extrapolation performance; low-capacity Scalar and Channel-wise variants offer limited gains and slightly hurt reasoning.Source: §5.1 · pp. 7–8

5.2 TIMESTEP CONDITIONING

  • Timestep variants use continuous time features, with inference rescaling the time grid so the normalized interval [0, 1] is divided into the requested number of steps.Loop Gating scales the shared-stack update, Branch Gating gates attention and MLP residual branches, and AdaLN modulates RMSNorm outputs and residual branches.Source: §5.2 · p. 8
  • At L(r) = 56 in the 7 × 4 setup, BG scores 38.46 and LG 36.91 overall, above BaseLoop’s 36.59; gains are smaller or negative in other configurations.The authors conclude that timestep gating must be assessed jointly with recurrent architecture and intended inference budget.Source: §5.2 · p. 8, Figure 6 · p. 8
  • For 7 × 4 at L(r) = 56, BG exceeds AdaLN overall (38.46 vs 38.01) and in reasoning (30.88 vs 29.12), while AdaLN better preserves knowledge.LG and BG use scalar modulation and require fewer conditioning parameters than channel-wise AdaLN; preferred granularity varies by architecture.Source: §5.2 · p. 8

6 WHEN ARE CONDITIONING MECHANISMS COMPOSABLE?

The authors compare pairwise and three-way combinations of state and timestep conditioning, then analyze how earlier recurrent computation relates to later updates. History-state plus timestep conditioning is strongest under deep extrapolation, alongside increased cross-loop interaction.

6 WHEN ARE CONDITIONING MECHANISMS COMPOSABLE?

  • At D = 84, H+LG reaches 37.30 Overall accuracy, exceeding I+H (36.91) and I+LG (36.33); adding initial-state conditioning provides no further benefit.The three-way combinations remain below H+LG.Source: Figure 7 · p. 9, §6 · p. 9
  • Computational interaction measures the relative change in a downstream block’s update after an earlier block occurrence is skipped, capturing dependence beyond representation change.The analysis reports that large state transformations need not imply strong interaction; Coda layers reduce the terminal-to-core response ratio from 0.85–0.89 to 0.48–0.50.Source: §6 · p. 9
  • At D = 84, H+LG has 18.6% and 10.4% higher mean interaction over lags 1–6 than I+H and I+LG, with its advantage appearing mainly across loops.H+LG has a smaller within-loop response than I+H; the authors suggest history exposes evolving states while timestep conditioning modulates each iteration’s shared update.Source: §6 · p. 9, Figure 8 · p. 9
  • Adding initial-state conditioning to H+LG reduces mean interaction over lags 2–6 by 7.4% at D = 56 and 4.2% at D = 84, alongside lower three-way accuracy.The authors say this may explain the lack of additive gains, while noting the pattern is not universal across lags and gating variants.Source: §6 · pp. 9–10

A LIMITATIONS

The limitations section bounds the experiments and geometry analyses. The extended literature review surveys work on recurrent scaling, architectures, retrofitting, and recurrent dynamics.

A LIMITATIONS

  • Experiments cover models up to roughly 1B parameters under a fixed token budget and extrapolation only to a fixed multiple of the training horizon, without adaptive per-input iteration.The relationship between computational-interaction geometry and downstream performance needs further study.Source: A LIMITATIONS · p. 15

B EXTENDED LITERATURE REVIEW

  • From-scratch LoopLM research studies recurrent scaling, dynamic or elastic recurrence, stability at larger loop counts, and alternative ways to allocate or route recurrent computation.The review also describes scaling-law work on recurrence depth and its relation to model size, data, and compute.Source: B EXTENDED LITERATURE REVIEW · pp. 15–16
  • Retrofitting research converts pretrained Transformers into recurrent models through selected repeated layers, recurrence curricula, input-conditioned modulation, or continual training.The reviewed approaches aim to add inference-time computation while preserving capabilities or enabling extrapolation beyond supervised recurrence depth.Source: B EXTENDED LITERATURE REVIEW · pp. 15–16
  • Other reviewed studies analyze recurrent trajectories, token-dependent convergence, adaptive halting, timestep encoding, systematic generalization, overthinking, and signal propagation.These works connect recurrent behavior to internal dynamics, optimization, and theoretical properties.Source: B EXTENDED LITERATURE REVIEW · p. 16

C.1 MODELS AND DATA

This section specifies the model backbones, training data, and recurrent configurations used in the experiments. It also describes the injection and timestep-conditioning implementations and how inference depth is varied.

C.1 MODELS AND DATA

  • The from-scratch decoder-only backbones are Llama3.1-1B with 20 layers and Qwen3-0.6B with 28 layers; their non-recurrent references contain approximately 1B and 596,049,920 parameters, respectively.Both use pre-normalization, causal self-attention, grouped-query attention, RoPE, and SwiGLU feed-forward networks.Source: §C.1 · p. 17, Table 1 · p. 17
  • Models use FineWeb-Edu-350BT with no data curriculum; Llama and Qwen experiments process approximately 20.15B and 12B packed tokens, respectively.Token streams are packed into non-overlapping sequences of length 2,048.Source: §C.1 · p. 17
  • Architectures use p + s × K + c blocks: Prelude and Coda blocks run once, while the s recurrent-core blocks are reused K times.Physical depth is p + s + c, and training effective depth is p + Ks + c; BaseLoop and CoreLoop configurations hold effective depth fixed while varying allocation.Source: §C.1 · pp. 17–18, Table 2 · p. 18
  • Inference depth is Linference(r) = p + rs + c, and comparisons at different r account for operator-level compute rather than equating models by raw loop counts.Source: §C.1 · p. 18
  • Initial-state injection places a shared adapter at the entrance to the recurrent stack; tested parameterizations add 1, 2d, 2d, or 2d² parameters.The four variants are Scalar, Channel-wise, Residual Channel-wise, and Dense; the injection maps are initialized to act as the identity on the current state.Source: §C.1 · p. 18
  • History-state injection weights differences between recent completed states and the current state by relative lag, excluding the current state and h0 from its history window.History-only injection adds w trainable scalars in the scalar form; buffered states remain attached so gradients propagate during training.Source: §C.1 · pp. 18–19
  • Timestep conditioning uses normalized time and step-size features; inference can retain the training grid for prefix runs or rescale the grid to support budgets above or below training.Loop Gating, Branch Gating, and AdaLN add 8, 16K, and 32Kd trainable parameters, respectively.Source: §C.1 · pp. 19–20

C.2 TRAINING

LoopLMs are trained from scratch with a next-token language-modeling objective and a fixed loop count, with gradients propagated through every recurrent iteration. The training setup also specifies optimizer groups, a warmup-stable-decay schedule, and gradient accumulation and clipping.

C.2 TRAINING

  • Each model is trained from scratch with mean next-token cross-entropy, and gradients pass through all K recurrent iterations without detachment.The loss is averaged over non-masked target tokens.Source: §C.2 · p. 20
  • Muon optimizes matrix-valued attention and feed-forward weights, while AdamW handles embeddings, the language-model head, normalization, and other vector- or scalar-valued parameters.Muon uses 0.95 momentum, Nesterov momentum, and five-step Newton-Schulz iterations; AdamW uses (β1, β2) = (0.9, 0.95) and ϵAdamW = 10−8.Source: §C.2 · p. 20
  • The WSD learning rate warms up for 5% of updates, stays at its peak for 85%, then decays linearly over the final 10%.The terminal rate is 0.1ηmax, and the learning rate at update t is η(t) = ηmaxλ(t).Source: §C.2 · p. 20
  • Llama3.1-1B runs use micro-batches of 38 with six-way gradient accumulation, while Qwen3-0.6B runs use micro-batches of 32 with eight-way accumulation.The global gradient ℓ2 norm is clipped to 1.0 before each optimizer update; Table 3 reports exact schedule lengths and batch sizes.Source: §C.2 · p. 20, Table 3 · p. 21
  • Training uses bfloat16 parameters and mixed-precision computation, independently Gaussian-initialized linear and embedding weights with standard deviation 0.02, and random seed 42.Source: §C.2 · p. 21

C.3 EVALUATION

Evaluation aggregates zero-shot task accuracies into knowledge and reasoning groups, while geometry probing measures recurrent-state changes and block interactions. The probes use fixed held-out token selections and explicitly distinguish block-level from loop-level measurements.

C.3 EVALUATION

  • Zero-shot benchmark scores are evaluated independently at each inference loop count; length-normalized accuracy is used for variable-length multiple-choice options and plain accuracy for fixed-form options.Knowledge and reasoning scores are unweighted averages of task headline metrics, giving each task equal influence regardless of test-set size.Source: §C.3 · p. 21
  • PIQA is assigned to the knowledge group because its instances are resolved through stored knowledge of object affordances and material properties.The knowledge group contains SciQ, ARC-Easy, and PIQA; the reasoning group contains eight tasks.Source: §C.3 · p. 21, Table 4 · p. 21, Table 5 · p. 21
  • The selected 14 BBH subtasks cover complementary reasoning abilities, but other BBH subtasks were excluded because results near task-specific guessing baselines offered little model-discriminative signal.The excluded subtasks were not included in the aggregate score.Source: §C.3 · pp. 21–22, Table 6

C.4 GEOMETRY PROBING

  • Geometry probes use identical selected token examples across configurations and depths, drawing 100,000 next-token positions from 49 packed sequences per model comparison.Angular distance and relative update norm use one selected position per sequence; variance and update-response scores use all selected positions.Source: §C.4 · p. 22
  • Effective depth is D = a + sL + b, and recurrent-state probes measure the state after complete loops while excluding the coda and final output normalization.A complete loop includes state injection, shared blocks, and any loop-level mixing or gating; block probes instead use each block’s own boundaries.Source: §C.4 · p. 22
  • Angular distance captures directional change, whereas relative update norm measures update magnitude against the incoming state; small updates alone establish neither convergence nor task usefulness.The angular metric is insensitive to positive rescaling away from its numerical floor.Source: §C.4 · p. 23
  • Variance growth is attributed stage-by-stage using ratios for injection, core, and mixing, which telescope for positive variances but are not additive contribution fractions.State variance is within-token feature dispersion averaged over tokens, and plot normalization sets variance at the training loop count to one.Source: §C.4 · pp. 23–24
  • Computational interaction compares a normal run with one that skips a single block occurrence, measuring how that change affects a later block’s update.Lag curves aggregate pairs at different positions and counts; they do not track one fixed perturbation as it travels through the network.Source: §C.4 · p. 24

D.1 OPTIMIZER EXPERIMENT

The appendix compares optimizer choices and architectural configurations, then tests initial-state injection, history-state injection, and timestep conditioning across inference depths. Results show that preferred layouts and conditioning effects vary by task, configuration, and inference budget.

D.1 OPTIMIZER EXPERIMENT

  • Muon improves average scores over AdamW for every architecture successfully trained with both optimizers, and Muon trains Huginn where AdamW fails.Table 7 reports averages including 41.95 to 42.04 for the 12-layer non-recurrent Transformer and 39.98 to 40.74 for BaseLoop; Muon’s Huginn average is 41.72.Source: Table 7 · p. 26, §D.1 · p. 26

D.2 BASELOOP AND CORELOOP

  • At D = 56, BaseLoop has higher Overall and Reasoning scores than all three CoreLoop variants, while the best CoreLoop layout changes with inference depth.The coda-only layout scores higher Overall at reduced depths but loses Knowledge more strongly during extrapolation; the balanced layout leads Overall and Knowledge at D = 28.Source: §D.2 · p. 26, Figure 9 · p. 27
  • At the training loop count, displayed CoreLoop variants have smaller loop angular distances and relative updates than BaseLoop, while extrapolation combines small angular changes with growing normalized state variance.With two physical layers, prelude-only allocation ends with smaller recurrent updates and less normalized variance growth than coda-only allocation.Source: §D.2 · pp. 26–27, Figure 10 · p. 27

D.4 HISTORY-STATE INPUT INJECTION

  • At D = 84, Scalar history injection with w = 4 exceeds BaseLoop by 1.64 Overall and 6.89 Knowledge percentage points, while Dense history’s preferred window varies by metric and depth.Channel-wise w = 2 leads the history variants in Overall at all reported depths but does not beat initial-state injection at D = 84; larger Dense windows can weaken extrapolation.Source: §D.4 · p. 28

D.5 TIMESTEP CONDITIONING

  • Timestep conditioning has configuration- and task-dependent effects: Branch Gating improves Qwen 7 × 4 Overall at D = 56, but no variant improves Overall for 2 × 14 at either reported depth.On Llama3.1-1B, all three variants improve Overall and Knowledge at D = 40, but none matches BaseLoop in Reasoning.Source: §D.5 · p. 28

D.3 INITIAL-STATE INPUT INJECTION

  • Initial-state injection improves Overall at D = 20 for all four 4 × 5 variants, but all fall below BaseLoop at D = 40.Dense injection shows pronounced Knowledge degradation; Scalar and Channel-wise retain higher Knowledge than BaseLoop at D = 40 but score lower on Reasoning and Overall.Source: §D.3 · p. 27, Figure 13 · p. 29, Table 8 · p. 29

D.6 COMBINATION EXPERIMENTS

The combination experiments test initial-state, history-state, and timestep mechanisms individually and jointly. Channel-wise history combined with timestep conditioning shows the clearest extended-depth gains, while adding all three mechanisms does not yield consistent additive improvement.

D.6 COMBINATION EXPERIMENTS

  • Channel-wise initial-state plus history-state injection with w = 2 reaches 37.74 Overall at D = 56, above initial-state-only and history-only scores of 36.67 and 36.77.Scalar combinations remain more stable than dense combinations beyond training depth, but scalar history alone reaches higher Knowledge than the scalar combination at D = 84.Source: §D.6 · p. 29, Table 10 · p. 30
  • At D = 84, channel-wise history with w = 2 and LG scores 37.30 Overall and 56.32 Knowledge, exceeding initial-state plus LG at 36.33 Overall and 52.92 Knowledge.Channel-wise history uses 2,048 injection weights at d = 1024 and w = 2, versus 2,097,152 for dense history.Source: §D.6 · pp. 30–31
  • Adding all three mechanisms does not consistently outperform two-mechanism alternatives; at D = 56, none of the four three-way configurations exceeds its best matched individual component.Their Overall scores are 35.69–36.60, below the reported 37.74 for initial-state plus history-state and 37.49 for channel-wise history plus LG.Source: §D.6 · p. 31, Figure 14 · p. 32, Figure 15 · p. 32
  • Initial-state injection combined with timestep conditioning provides almost no consistent benefit over its individual components across the evaluated depths.At D = 28, combined Overall is 35.89 with BG and 35.99 with LG, below the corresponding gating-only scores of 37.16 and 36.68.Source: §D.6 · p. 30, Figure 17 · p. 33

E.1 INPUT NOISE INITIALIZATION ABLATION

Geometry probes show stronger H+LG responses than the pairwise comparisons, while adding initial-state conditioning has heterogeneous effects. Initialization noise has only minor downstream effects and no consistent advantage across variants or metrics.

E.1 INPUT NOISE INITIALIZATION ABLATION

  • At 84 effective layers, adding initialization noise had only minor effects and no consistent advantage across injection variants or metrics, so noise-free initialization is the default.The comparison used Qwen3-0.6B BaseLoop 4 × 7, with four shared layers trained for seven loops and a noise scale of 0.03.Source: §E.1 · pp. 33–35, Figure 22 · p. 36

E.2 GEOMETRY ANALYSIS

  • At D = 84, H+LG's mean raw response is 6.4% higher than I+H and 10.2% higher than I+LG across lags 1-6, with higher relative response in all 16 pairings.The response advantage also appears in the unnormalized numerator, not only in relative response.Source: Figure 23 · p. 36, §E.2 · p. 36
  • Adding initial-state conditioning to H+LG reduces mean raw response over lags 2-6 by 10.5% at D = 56 and 6.0% at D = 84, but effects vary across gates and pairings.At D = 84, the LG triple has lower mean C in 9/16 pairings; the remaining pairings increase, while BG aggregate responses stay close to H+BG.Source: Figure 23 · p. 36, §E.2 · p. 36
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