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Rethinking Neural Thickets Without Weight Perturbations

Nicolas Dufour, Elouan Gardès, Amil Dravid, Patrick Pérez, Loic Landrieu

arXiv:2610.40649v1cs.LGcs.AIcs.CV

TL;DR

The paper asks whether Neural Thickets' gains require nearby task experts in weight space. It formalizes perturb-select-vote (PSV) and tests output-logit perturbations, finding that a frozen model can match or exceed full-weight perturbations on reasoning tasks and that logit perturbations also recover gains under vision domain shift.

  • Problem

    Neural Thickets attributes gains from random weight perturbations to nearby task-specific experts, raising whether that weight-space explanation is necessary for the observed improvements.

    Source: §1 · p. 1, §6 · p. 10

  • Method

    The paper formalizes PSV as generating perturbed predictors, selecting high-performing members on a small validation set, and aggregating their predictions, including via output-logit perturbations of a frozen model.

    Source: §1 · pp. 1–2, §3 · p. 3

  • Results

    Logit PSV matches or exceeds full-weight perturbations on reasoning tasks, including 81.3% versus 74.7% MATH-500 accuracy, and recovers full-weight gains under vision domain shift.

    Source: §1 · pp. 1–2, §6 · p. 10

  • Takeaways & Limitations

    The studied gains can be obtained through output diversity, selection, and voting without requiring useful local structure in weight space.

    Source: §1 · p. 2, §6 · p. 10

    Language experiments stop at 7B parameters, PSV requires a labeled selection set and answer-comparison method, and it requires K model evaluations per test input.

    Source: §6 · p. 10

Abstract

from arXiv · show

The Neural Thickets hypothesis posits that pretrained language models lie in dense neighborhoods of task-specific experts in weight space, which random Gaussian perturbations can uncover. We reproduce the reported gains, but show that they do not require this geometric explanation. Perturbing a single decoder block already recovers much of the improvement, while keeping the model entirely frozen and adding a random bias to its output logits matches or exceeds full-weight perturbations on most reasoning tasks. This suggests an alternative explanation based on output diversity, validation-based selection, and voting. We formalize this view as Perturb-Select-Vote (PSV), a general procedure that generates perturbed predictors, selects high-performing members on a small validation set, and aggregates their predictions. This interpretation connects Neural Thickets to established inference-time methods, including sampling, self-consistency, and verifier-guided selection. A first-order analysis further shows that small weight perturbations act primarily through their induced logit shifts. We extend this analysis to vision, where logit PSV substantially improves performance under domain shift, including on Earth observation, while full-weight perturbations provide little additional benefit. Together, these results suggest that the gains attributed to nearby weight-space experts can instead be obtained through output diversity, selection, and voting. Logit PSV realizes these benefits with a fully frozen model, providing a simple, training-free alternative to full-weight perturbation ensembles across language and vision.

1 INTRODUCTION

Neural Thickets attributes gains from random weight perturbations to nearby task-specific experts, but this paper finds that full-network perturbation is not required. It reframes the gains through output diversity, validation-based selection, and voting, and extends the output-space approach to vision.

1 INTRODUCTION

  • 81.3% MATH-500 accuracy with logit-only PSV compares with 74.7% for full-weight perturbations, from 63.3% for the OLMo-3-7B-Instruct base model.The model remains frozen and receives a random Gaussian bias on its output logits.Source: §1 · p. 1
  • PSV interprets the gains as output diversity followed by validation-based selection and voting, connecting the procedure to sampling, self-consistency, and verifier-guided selection.The paper also reports that tuned sampling and majority voting match full-weight PSV on strong base models, while validation-based filtering remains important on weaker models.Source: §1 · pp. 1–2
  • Under domain shift, logit perturbations recover full-weight PSV gains for pretrained vision models and often improve out-of-domain performance while leaving the backbone unchanged.The vision comparison uses one probe with perturbed class logits versus a perturbed backbone and one probe per member.Source: §1 · p. 2
  • The results show that useful local structure in weight space is not required to obtain the gains studied, without ruling out that such structure exists.The paper presents PSV as a training-free output-space procedure for specialized tasks and domains.Source: §1 · p. 2

2 RELATED WORK

Related work situates Neural Thickets among inference-time sampling and selection methods, methods that control frozen-model logits, and research on local weight-space structure and perturbation.

Test-time sampling, selection, and voting

  • Inference-time scaling includes self-consistency voting and best-of-N verifier selection; Neural Thickets combines perturbations, validation-based selection, and voting, with a connection to perturb-and-MAP sampling.The cited works include Wang et al. (2023), Cobbe et al. (2021), Papandreou & Yuille (2011), and Maddison et al. (2017).Source: §2 · p. 3

Logit-space control

  • Frozen-model logit methods include classifier-free guidance, contrastive decoding, calibration, and watermarking, whereas logit PSV uses task-agnostic random biases with selection and voting.The passage cites Ho & Salimans (2022), Li et al. (2023), Guo et al. (2017), and Kirchenbauer et al. (2023).Source: §2 · p. 3

Perturbations in weight space

  • Prior weight-space work studies mode connectivity, model averaging, low-dimensional adaptation, and random perturbations for evolution strategies or zeroth-order optimization; this paper asks which perturbations PSV needs.The passage cites Garipov et al. (2018), Izmailov et al. (2018), Wortsman et al. (2022), Li et al. (2018), Hu et al. (2022), and Salimans et al. (2017).Source: §2 · p. 3

3 THE PERTURB-SELECT-VOTE FRAMEWORK

The section formalizes perturb-select-vote (PSV) as a test-time template whose perturbation space, selection set, and aggregation rule can vary. It relates Neural Thickets to full-weight PSV and reports reproduced gains alongside evidence that highly localized perturbations recover much of the gain.

Perturb-select-vote

  • PSV samples perturbed predictors, scores each on a task-specific selection set, retains the top K, and aggregates their predictions, typically by majority vote.Its defining choices are the perturbation space, selection set, and aggregation rule; K = 1 selects the single best perturbation.Source: §3 · p. 3

Empirical effect

  • On Countdown with K = 50, perturbing any single first-decoder-block component in OLMo-3-7B-Instruct recovers at least 85% of the full-weight PSV gain, from 66.6% base accuracy to 90.8%.Source: Figure 3 · p. 4

Neural Thickets as full-weight PSV

  • Neural Thickets instantiates PSV by perturbing every model parameter, evaluating members on 200 target-task examples, and ensembling the top K by majority vote.The reported setup uses N = 1000 to 5000 perturbations and K values from 1 to 50.Source: §3 · p. 4

Empirical effect

  • For OLMo-3-7B-Instruct on Countdown, the reported full-weight PSV gain is +20.2 points over greedy decoding, while the released-code reproduction obtains +25.2 points.The paper reports that reproduced final accuracies are within 3.7 points of the reported ones on six tasks and 6.8 points higher on Countdown.Source: §3 · p. 4

Weight-space interpretation

  • The weight-space interpretation treats nearby perturbations as task experts, and the experiments ask whether PSV's gains require perturbing the full weight vector.The interpretation is framed through density, task specialization, and competitiveness claims.Source: §3 · p. 4

4 WEIGHT PERTURBATIONS ARE NOT NECESSARY

The section progressively localizes perturbations from model weights to output logits, arguing that full-network perturbation is unnecessary. It interprets the gains through output diversity, validation-based selection, and voting.

4.2 PERTURBING ONLY THE LOGITS

  • Logit PSV matches or exceeds full-weight PSV across reasoning tasks: it wins 13 of 15 cells and is within 0.6 points on the other two, closely tracking across scales.At matched N=5000, the methods are statistically indistinguishable on 22 of 28 model–task pairs. On USPTO, logit PSV has higher accuracy (42.7% vs. 39.4%) but lower balanced accuracy (26.7% vs. 29.7%).Source: Figure 4 · p. 5, §4.2 · pp. 5–6

4.1 LOCAL WEIGHT PERTURBATIONS SUFFICE

  • On Countdown, the base model scores 66.6% versus 90.8% for full-weight PSV; perturbing any single decoder block recovers much of the gain, especially later blocks.Within the first block, components writing directly to the residual stream recover the full gain; value and feed-forward input projections recover 96–99%, while the query/key path recovers 85–89%. Qwen2.5 shows the same pattern from 0.5B to 3B.Source: §4.1 · p. 5

4.4 DISENTANGLING THE SOURCE OF PSV GAINS

  • TT-MV can explain much of the gain on strong models: on MATH-500, it reaches 77.7% versus 74.7% for full-weight PSV, while weaker samplers benefit from validation selection.On USPTO with Qwen2.5-1.5B-Instruct, TT-MV stays at or below 6.9% for all temperatures, while full-weight PSV reaches 24.9%; that result remains below the 31.9% majority-class baseline.Source: Figure 5 · p. 6, §4.4 · p. 7

4.3 CONNECTION TO SAMPLING, SELECTION, AND VOTING

  • A fixed bias reused across decoding turns greedy outputs into perturb-and-MAP samples; PSV votes like self-consistency but selects persistent biases on validation data, unlike test-time best-of-N.Temperature sampling instead resamples at each step and input, while best-of-N uses a test-time verifier or reward model.Source: §4.3 · pp. 6–7

4.5 INTERNAL PERTURBATIONS INDUCE LOGIT PERTURBATIONS

  • Linearized logits reproduce 89.7% of exact-model argmax-token flips at the experimental perturbation scale, supporting induced logit shifts as the main effect.Internal perturbations propagate to logits; their location affects the magnitude and structure of the shift, and the approximation degrades as σ increases.Source: Table 2 · p. 8, §4.5 · p. 8

5 EXTENDING PSV TO VISION

The vision experiments compare weight-space perturbations with output-space perturbations under domain shift. Logit PSV and closed-form recalibration improve shifted-domain performance, while weight-space variants have little effect and no method substantially improves balanced ImageNet.

5 EXTENDING PSV TO VISION

  • The vision test defines a domain expert as a perturbed backbone whose frozen representations support a better linear probe on a target domain.It compares full-weight PSV, patch-embedding PSV, and logit PSV using a self-supervised DINOv3 backbone.Source: §5 · p. 8
  • Full-weight PSV perturbs the backbone and refits a probe per member; logit PSV keeps the backbone and single probe fixed, perturbing only class logits.Patch PSV perturbs only the patch-embedding module and refits the probe; logit PSV is cheaper because the probe is fitted once.Source: §5 · p. 9
  • Logit PSV improves worst-group accuracy by 5–6 points under shift, while full-weight and patch PSV improve it by at most one point; none substantially helps balanced ImageNet.Table 3 reports improvements over linear probing on frozen DINOv3-7B, using worst-region accuracy for FMoW, worst-group accuracy for Waterbirds, and balanced top-1 accuracy for ImageNet.Source: §5 · p. 9, Table 3 · p. 9
  • Closed-form recalibration recovers most of logit PSV’s gain on FMoW and matches it on Waterbirds, but provides no meaningful improvement on ImageNet.On binary Waterbirds, the correction effectively selects an improved decision threshold.Source: §5 · pp. 9–10
  • Gains appear when the output distribution is modified, not when random backbone perturbations are followed by probe refitting, even at 6.7B parameters.The authors interpret the shifted-dataset gains as primarily a recalibration effect, contrasting them with balanced ImageNet, where train and evaluation distributions are aligned.Source: §5 · pp. 9–10

6 DISCUSSION

The discussion argues that the studied Neural Thickets gains do not require weight-space experts: comparable improvements arise from a single decoder block or frozen-model logits. It also identifies limits on model scale, task applicability, analysis assumptions, and inference cost.

6 DISCUSSION

  • Comparable improvements arise from perturbing a single decoder block or only the logits of a frozen model, so the studied gains do not require perturbing the full model.The findings do not rule out useful local structure in weight space.Source: §6 · p. 10
  • Language experiments stop at 7B parameters, and larger models may exhibit weight-space effects that logit perturbations fail to capture.The first-order analysis is valid only for sufficiently small σ.Source: §6 · p. 10
  • PSV requires a labeled selection set and a way to compare generated answers for voting, limiting its applicability to open-ended generation.Like full-weight PSV, logit PSV requires K model evaluations per test input, increasing inference cost relative to a single prediction.Source: §6 · p. 10
  • All datasets and pretrained models are publicly available, and the paper documents protocols and settings; complete LLM experiment code is slated for release upon publication.The authors report that AI-assisted outputs were reviewed and verified, and that they take responsibility for the final content.Source: REPRODUCIBILITY STATEMENT · p. 10, AI USE STATEMENT · p. 10
  • The work evaluates logit PSV only on standard reasoning, chemistry, and image-recognition benchmarks; it inherits the biases and failure modes of its pretrained model.The authors do not expect it to introduce risks beyond those of the pretrained models it builds on.Source: ETHICS STATEMENT · p. 10

Perturbations

The related-work discussion places perturb-select-vote among inference-time sampling and selection methods, distinguishes its random logit biases from task-specific logit modifications, and contrasts random selection with approaches that explicitly optimize or structure weight perturbations.

A EXTENDED RELATED WORK

  • Neural Thickets fits a broader inference-time family: perturbations generate diversity, validation selection favors high-reward members, and voting aggregates predictions.Related approaches include self-consistency, best-of-N, minimum Bayes risk decoding, and perturb-and-MAP sampling.Source: A EXTENDED RELATED WORK · p. 15
  • Unlike task-specific logit modifications such as calibration or watermarking, logit PSV samples task-agnostic random biases.The related work also covers guidance, contrastive decoding, decoding-time experts, and proxy-tuning.Source: A EXTENDED RELATED WORK · p. 15
  • Weight-space merging and connectivity work studies combining solutions or shared low-loss regions, including model soups, task vectors, and mode connectivity.These approaches concern structured relationships among solutions rather than the PSV procedure described here.Source: A EXTENDED RELATED WORK · p. 15
  • Low-dimensional adaptation and evolution-strategy work use structured directions or optimize perturbations, whereas Neural Thickets selects among unstructured random draws.Related local-neighborhood methods consolidate rewarded perturbations or use Bayesian optimization to find strong experts with fewer evaluations.Source: A EXTENDED RELATED WORK · pp. 15–16

Perturbations

  • Logit PSV draws random biases, scores members on validation data, retains the top K, and returns their majority vote at test time.Its procedure is presented as a frozen-model perturb-select-vote algorithm.Source: A EXTENDED RELATED WORK · p. 16

B PERSISTENT PERTURBATIONS, SELECTION, AND VOTING: FORMAL STATEMENTS

This appendix formalizes logit PSV as persistent vocabulary-bias members followed by validation selection and answer voting, and analyzes how persistence changes their sampling and voting behavior.

B.1 EACH MEMBER RECALIBRATES THE VOCABULARY

  • A logit-PSV member reuses one vocabulary bias across decoding steps and inputs, equivalent to greedy decoding under token probabilities multiplied by fixed factors.The bias is held constant throughout autoregressive generation.Source: §B.1 · p. 16

B.2 VOTING RETURNS THE MOST FREQUENT ANSWER

  • With independent unselected members, plurality returns the unique modal answer with probability at least 1 − (|A_x| − 1)e^(−Kγ²/2), and is asymptotically correct when that mode is correct.The bound assumes a positive margin between the most frequent answer and its competitors.Source: §B.2 · pp. 16–17

B.3 SELECTION EXPLOITS PERSISTENCE ACROSS INPUTS

  • Selection changes test-answer frequencies only when validation reward is informative across persistent members; it can help or hurt, and members may overfit the 200-example set.Selection is most useful when the unselected answer distribution is unreliable.Source: §B.3 · pp. 17–18

B.4 RELATION TO TEMPERATURE SAMPLING

  • Logit PSV reuses its perturbation across decoding steps and inputs, unlike temperature sampling, which resamples noise at every step.The appendix calls these persistent and resampled perturbations, respectively.Source: §B.4 · p. 18

B.4.1 RESAMPLED GUMBEL PERTURBATIONS RECOVER TEMPERATURE SAMPLING

  • Fresh independent Gumbel noise yields temperature-T sequence sampling at T = σ, making its K-vote exactly temperature-T majority voting with no selection effect.The equality between noise scale and temperature is exact for this Gumbel construction.Source: §B.4.1 · pp. 18–19

B.4.2 PERSISTENT PERTURBATIONS INTRODUCE MEMORY ACROSS DECISIONS

  • Disjoint candidate sets make persistent and resampled choices match, but repeated token competition couples decisions; at δ = 0.4, persistent noise gives Pr[AB] = 0.20 versus 0.36 under resampling.The resulting persistent-noise plurality is incorrect in the example.Source: §B.4.2 · p. 19

B.4.3 GAUSSIAN PERTURBATIONS HAVE A LOCAL TEMPERATURE INTERPRETATION

  • Gaussian noise acts like temperature sampling for near-tied logits, but suppresses large-gap alternatives more strongly than softmax sampling.The local analogy is approximately T ≈ 0.83σ for two competing tokens.Source: §B.4.3 · p. 20

B.5 INTERNAL PERTURBATIONS ACT AS LOGIT PERTURBATIONS

  • First-order weight perturbations induce additive logit shifts through intervening Jacobians, with query/key paths attenuating them relative to other components.At the experimental scale, linearization reproduces 89.7% of perturbation-induced arg-max changes on fixed teacher-forced prefixes; this does not establish sequence-level equivalence.Source: §B.5 · pp. 20–21

C CROSS-SCALE NUMBERS AND ABLATIONS

Last-block perturbations match or exceed full-weight results on four 7B reasoning tasks, but trail on three other tasks. Single-component perturbations also work across architectures and scales, while selected perturbations show little evidence of a coherent dense basin.

Cross-scale comparisons

  • At 7B, last-block perturbations match or exceed full-weight results by 0.9–2.5 points on four reasoning tasks, but trail by 1.3–2.2 points on MBPP, ROCStories, and USPTO.On Qwen models, last-block results range from 3.8 points below full-weight on 0.5B MBPP to 3.0 points above it on 1.5B GSM8K.Source: C CROSS-SCALE NUMBERS AND ABLATIONS · p. 21
  • Across Qwen scales, the full-weight and logit-bias ensemble gain curves track each other, with gains growing as model size increases.The sweep omits 0.5B Countdown and USPTO because the base model cannot perform those tasks.Source: C CROSS-SCALE NUMBERS AND ABLATIONS · p. 22, Figure 6 · p. 23

Single-component perturbations

Training-reward distributions

  • Every component yields nonzero selection-reward variability, and on OLMo 92–98% of compute-matrix perturbation members improve over base on the selection set.At 1.5B, 3B, and 7B, compute-matrix components have 1.7–2.5-point reward spreads, while value projections have 2–4-point spreads.Source: C CROSS-SCALE NUMBERS AND ABLATIONS · p. 23, Table 6 · p. 25

Geometry of selected perturbations

  • Selected perturbation directions show no detectable clustering, and their best member improves held-out accuracy by only 2.4 points versus 11 points on the selection set.The selected-member midpoint is 69.8% versus 69.7% at the endpoints; selected members score 69.7% on held-out items versus 69.4% for random members.Source: C CROSS-SCALE NUMBERS AND ABLATIONS · pp. 23–24

C.1 MATCHED COMPARISON UNDER THE ORIGINAL PROTOCOL

Under the authors’ original protocol, logit PSV and full-weight PSV are statistically indistinguishable on most model–task pairs, with mixed task-specific differences.

Matched comparison

  • On 22 of 28 model–task pairs the methods are statistically indistinguishable; logit PSV is significantly better on three pairs and significantly worse on three.It is significantly better on Countdown at 1.5B and 3B and GSM8K at 1.5B, and significantly worse on ROCStories at 1.5B and 3B and USPTO at 7B.Source: §C.1 · p. 25
  • On USPTO, both methods score exactly 31.9% on every Qwen model, matching a constant majority-class predictor.For Qwen models, most selected logit members use the grid’s smallest scale, 0.25, so a finer grid could favor logit PSV slightly.Source: §C.1 · p. 25
  • The comparison uses the released code and data, selects the top 50 members using only 200 training examples, and evaluates with N=5000.TT-MV uses a majority vote over 50 samples at T=0.7.Source: §C.1 · p. 25

D.1 THE FULL K-SWEEP ACROSS METHODS

Across the ensemble-size sweeps, logit PSV closely tracks or exceeds full-weight PSV on reasoning tasks, while TT-MV falls behind mainly for weaker models.

Full K-sweep

  • Across four model scales and three reasoning tasks, accuracy generally rises with ensemble size K, with larger gains at larger scales.The sweep evaluates K values from 1 to 128 for Countdown, GSM8K, and MATH-500.Source: §D.1 · p. 25
  • Logit PSV closely tracks or exceeds full-weight PSV across the reasoning-task sweeps.The comparison includes full-weight PSV, logit PSV, and temperature-sampling TT-MV without reward-based selection.Source: §D.1 · p. 25
  • TT-MV falls behind primarily in the weak-model regime, including 0.5B and 1.5B Countdown, where reward-based selection is most useful.Figure 9 reports raw majority-vote accuracy against the greedy base, while Figure 10 presents gains over that base.Source: §D.1 · p. 25

D.2 ARE WEIGHT AND LOGIT PERTURBATIONS COMPLEMENTARY?

The paper tests whether combining weight and logit perturbations adds complementary gains. Across most model–task pairs, the combination does not outperform the stronger individual method or a logit-only stacking control.

Complementarity test

  • The comparison composes full-weight PSV with logit PSV and contrasts it with both the stronger individual method and a smaller-range logit-on-logit control.The control tests whether gains from combining weight and logit perturbations exceed gains from composing output-space perturbations alone.Source: §D.2 · pp. 25, 28
  • On nine of twelve model–task pairs, stacked weight-and-logit PSV matches or trails the better individual method, with no systematic advantage over stacking two logit perturbations.Only 7B MATH-500 improves over both comparisons: by 1.0 point over the better single method and 0.3 points over the logit-only control.Source: §D.2 · p. 28, Figure 12 · p. 29
  • Figure 12 shows most stacked-versus-individual and stacked-versus-control points on or below equal accuracy, with 7B MATH-500 above both comparisons.Other above-diagonal exceptions are 3B MATH-500 and 7B GSM8K versus the stronger individual method, and 7B and 3B Countdown versus the logit-only control.Source: §D.2 · p. 28, Figure 12 · p. 29

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