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REVIEW 5 major objections 5 minor 57 references

Homing through Reinforcement Learning

T0 review · 5 major / 5 minor · reviewed 2026-08-03 · deepseek-v4-flash

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Pith's one-line read In a 2D Q-learning homing model, mean homing time is reported to be non-monotonic in rotational diffusion with a crossover at D_r≈12, and the learned policy is claimed to beat a stochastic-resetting ABP baseline.

desk verdict The cost function makes the align action strictly dominant, so the RL is ε-greedy always-align; the central 'learning' claim is circular. read the letter →

arxiv 2602.08566 v2 pith:TH4MZN4X submitted 2026-02-09 cond-mat.soft cond-mat.stat-mech

Riya Singh , Pratikshya Jena , Anish Kumar , Shradha Mishra This is my paper
classification cond-mat.softcond-mat.stat-mech
keywords agenthominglearninghomeframeworktargetadaptiveagents
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper simulates a tiny agent in a circular arena. The agent has a heading direction and always knows which way home is. At each step it can either turn to point exactly at home or randomly jiggle its heading. A simple reinforcement-learning rule (Q-learning with a 2×2 table) updates action values using the change in distance to home as the cost. Since moving toward home always lowers the cost, the agent gradually learns to always turn homeward—a policy that is essentially written into the cost function.
Extended reading notes

Core claim

Abstract: 'For a single self-propelled agent moving with constant speed, we find that the mean homing time ⟨T_home⟩ exhibits a non-monotonic dependence on the rotational diffusion strength D_r, with an optimal noise level D_r*, revealing a subtle interplay between exploration and goal-directed correction.' If the paper is correct, a Q-learning agent with a radial-distance cost shows a noise-dependent homing time with a crossover at D_r*≈12, and the learned policy systematically outperforms an active Brownian particle baseline.

Load-bearing premise

The angular threshold function φ(r) = (π/2)(r/R0) + tan^{-1}(2.0/r) (Eq. 2) is posited by hand as the boundary between the two discrete states and is later reused as the resetting rule in the ABP baseline (Eq. 9). Every reported statistic—the binary state definition, the resetting frequency, the scaling regimes, and the RL-vs-ABP comparison—depends on this uncalibrated functional form. If φ(r) were replaced by a constant or any other radial dependence, the non-monotonicity, the two scaling regimes, and the claimed improvement over the ABP could disappear.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

5 major / 5 minor

Summary. The paper proposes a Q-learning framework for homing in a continuous 2D domain. A single self-propelled agent has a binary state based on an angular threshold φ(r) and two actions: align to home (a=1) or undergo stochastic reorientation (a=2). The cost is the change in radial distance to home. The authors report a non-monotonic mean homing time as a function of rotational diffusion strength Dr, with a claimed optimal noise level Dr*≈12, and state that the RL agent outperforms an Active Brownian Particle (ABP) baseline. They extend the model to two and many agents with soft repulsion, claiming that one agent becomes faster and that the fastest agent improves with group size. The central conclusion is that cost-driven learning, stochastic reorientation, and interactions enable adaptive navigation.

Significance. If the claims were correct, the paper would offer a simple RL description of homing that links individual and collective navigation, with testable predictions about resetting statistics and noise-dependent efficiency. The authors provide extensive simulation data and a clear model definition. However, the learning component is effectively trivialized by the cost function: action 1 yields the minimum possible cost in every state, so Q-learning converges to an always-align policy independent of Dr. The non-monotonicity and action-selection crossover then arise from the fixed ε-greedy exploration and the state-independent stochastic action, not from learned adaptive behavior. The ABP comparison is not made under identical conditions, and the multi-agent claims lack a no-interaction control. Because the central mechanism is not supported, the significance of the reported phenomena is substantially diminished.

major comments (5)
  1. [Eq. (7) with Eqs. (4)-(6)] The cost function C(t+Δt)=|r(t+Δt)|−|r(t)| makes action 1 strictly dominant in both states for every Dr. For a=1, θ(t+Δt)=0 and |r(t+Δt)|=r(t)−v0Δt (except when overshooting near home), giving the minimum possible cost −v0Δt. For a=2, the expected radial displacement is v0Δt E[cos(θ+η)] < v0Δt, so the expected cost is larger (less negative) for any state and any symmetric noise. Hence argmin Q is action 1 in both states; Q-learning reduces to an ε-greedy always-align policy with probability 1−ε/2 on action 1. The reported crossover in action selection (Fig. 4f) and the non-monotonic ⟨T_home⟩(Dr) (Fig. 3) are therefore not evidence of learned state-dependent control; they reflect the fixed exploration probability and the noise in action 2. A control run of a non-learning agent that chooses action 1 with probability 1−ε/2 and action 2 with probability ε/2 at every step is missing.
  2. [Fig. 3 and Sec. III A] The paper repeatedly calls Dr*≈12 an 'optimal noise level,' but Fig. 3 shows that ⟨T_home⟩ has a maximum at this value, not a minimum. If homing efficiency is measured by speed of arrival, this is the worst noise level, not an optimal one. The labeling appears to confuse a maximum of ⟨T_home⟩ with an optimum of the explored parameter. This mislabel affects the abstract and the interpretation of the scaling regimes in Fig. 4(e).
  3. [Sec. III D, Eqs. (9)-(11)] The ABP baseline is not obtained under 'identical conditions' as claimed. The RL agent's stochastic action uses uniformly distributed noise ζ∈[−π/2,π/2] (Eq. 5), whereas the ABP uses Gaussian white noise η with δ-correlations (Eq. 11). Moreover, the ABP's resetting probability p(t) is a deterministic function of |θ| and φ(r), while the RL agent's effective policy is ε-greedy with fixed random exploration. Any improvement of RL over ABP could be due to these differences in noise type and reset rule rather than to learning. A fair baseline would use the same noise distribution and the same effective action probabilities as the converged RL policy.
  4. [Secs. III B and III C] The claim that repulsive interactions make one agent consistently faster and that the fastest agent improves with group size lacks a no-repulsion control. In any ensemble of N independent agents, the minimum homing time among N iid draws decreases with N by order statistics alone. To attribute the speed-up to repulsion or coordination, the authors must compare against N non-interacting agents with the same initial conditions and noise. Without this control, the multi-agent findings are not distinguishable from a trivial extremal-statistics effect.
  5. [Eq. (2) and robustness] The angular threshold φ(r) is a hand-posed function with no calibration or sensitivity analysis. Every reported quantity—the binary state, the resetting statistics, and the ABP reset probability—depends on this functional form. Because the RL policy is effectively fixed, the non-monotonicity likely arises from the interplay between φ(r) and the random action. The authors should show that their qualitative results are robust to alternative choices of φ(r) (e.g., constant, different radial dependence). Without this, the 'optimal' Dr and the scaling exponents are not established as robust phenomena.
minor comments (5)
  1. [General] The paper contains several typos and awkward phrases: e.g., 'the cost also acts as an effective signal' in the abstract, 'in multi-agents system' and 'the fastest agent becomes progressively faster' (grammar). The distinction between 'optimal' and 'maximum' should be corrected throughout.
  2. [Fig. 4(e)] The power-law exponents (β,α) = (1.0,0.5) and (2.0,1.0) are stated without reporting the fitting procedure, confidence intervals, or the range over which the fits are performed. The inset collapse should specify the normalization of f(x).
  3. [Eq. (5)] The noise term √(2DrΔt) ζ with ζ uniform on [−π/2,π/2] has variance (π²/12)·2DrΔt. The choice of uniform rather than Gaussian noise is not justified; the ABP comparison is further complicated by this difference.
  4. [Sec. II] The reflecting boundary condition at R0=35 is mentioned but not described in detail. How is reflection implemented? This could affect the statistics for large Dr where trajectories may hit the boundary.
  5. [References] The reference list includes several arXiv preprints and some incomplete citations. For example, Ref. [4] (Paramanick et al.) is cited but not discussed in the text beyond the introduction; the authors should clarify how their work builds on it.

Circularity Check

3 steps flagged · score 7.0 of 10

Eq. (7) makes alignment action optimal by construction; the reported Dr-dependent policy and RL-vs-ABP advantage are consequences of the hand-set reward/reset structure, not of learned navigation.

  1. self definitional [Sec. II, Eqs. (5), (6), and (7)]
    "To evaluate the effectiveness of each action within this evolution, we define the cost function, C(t+Δt) guiding the learning process based on the change in radial distance resulting from the chosen action. The instantaneous cost at time t+Δt is defined as: C(t+Δt)=|r(t+Δt)|−|r(t)|, (7) ... θ(t+Δt)= { 0, a(t)=1, θ(t)+√(2DrΔt) ζ, a(t)=2 } (5) ... r(t+Δt)=r(t)+v0Δt n̂(t+Δt) (6)."

    With a=1, Eq. (6) moves the agent exactly along the home direction, so |r(t+Δt)|−|r(t)| = −v0Δt deterministically, the minimum possible cost. With a=2, the one-step cost is −v0Δt cos(θ+η), whose expectation is strictly greater than −v0Δt for any nonzero symmetric noise. Therefore argmin_a Q(s,a)=1 in both states, for every θ, φ(r), and Dr. The 'learned' policy is the identity of the cost function with the alignment action; the Q-learning result is fixed by construction, not discovered.

  2. other [Sec. III A, Fig. 4(f)]
    "This behavior demonstrates a clear crossover in action selection, wherein increasing D_r leads to a growing favor for action 1, accompanied by a reduced preference of selecting action 2. The RL agent learn through Q-matrix update as in Eq. 8, and mostly perform the action 1. Hence by increasing D_r further the first action wins over the second one as shown in Fig.4(f)."

    Given Eq. (7), the greedy action is action 1 for all Dr, so a converged Q-table gives state- and Dr-independent action probabilities: P(a=1)=1−ε/2=0.85, P(a=2)=ε/2=0.15. The reported Dr-dependent 'crossover' is therefore not a learned policy responding to noise; it is a consequence of the fixed ε=0.3 exploration schedule and of the particular angular noise injected into action 2, possibly during the Q-learning transient. Presenting this as 'adaptive noise compensation' turns a prescribed stochastic-process effect into a learned prediction.

1 more flagged steps
  1. renaming known result [Sec. III D, Eqs. (9)-(10) and Fig. 8]
    "p(t)= { 0, |θ|≤φ, (|θ|−φ)/(π−φ), φ<|θ|<π, 1, |θ|≥π } (9) ... θ(t+Δt)= { 0, with probability p(t), θ(t)+√(2DrΔt) η, with probability 1−p(t) } (10) ... By comparing the mean homing time ⟨T_home⟩ for ABP and RL across a range of rotational diffusion strengths D_r, the RL trajectories are found to be shorter and less noisy, leading to consistently ⟨T_home⟩_RL < ⟨T_home⟩_ABP."

    Under Eq. (7) the RL agent effectively performs the alignment action with fixed probability 1−ε/2=0.85, i.e. it is an active Brownian particle with a constant high resetting probability. The ABP baseline instead uses the hand-set state-dependent reset probability p(t) from Eq. (9), built on the same arbitrary φ(r). The claimed 'improvement due to learning' is therefore a comparison of two hand-chosen reset policies, both relying on the uncalibrated φ(r); the known stochastic-resetting benefit is renamed as an RL advantage rather than demonstrated by learning.

full rationale

The central learning claim reduces to its own reward definition: with C(t+Δt)=|r(t+Δt)|−|r(t)|, action 1 (θ→0) is the unique minimizer of expected one-step cost in both states and for every Dr, so the Q-table's argmin is predetermined. The non-monotonic ⟨T_home⟩(Dr) and the Fig. 4(f) 'crossover' are then properties of the fixed ε-greedy exploration and the prescribed noise in action 2, not of an adaptive state-dependent policy; no non-learning control that simply chooses action 1 with probability 1−ε/2 is provided. The ABP comparison is also constructed in favor of RL because the ABP reset probability (Eq. 9) is state-dependent and can be zero, while the RL agent, through Eq. (7), resets with high fixed probability. Additionally, the hand-set φ(r) is reused as the state boundary (Eq. 3) and as the ABP resetting rule (Eq. 9), so neither the scaling regimes nor the RL-vs-ABP advantage are independent of this arbitrary input. The self-citations [54,55] concern only parameter choices and are not load-bearing, so the circularity is not a self-citation chain. The score is 7 rather than 8-10 because the homing-time statistics themselves are genuine simulation outputs; only the interpretation that they demonstrate learned navigation reduces by construction. The paper's 'optimal noise' D_r* is also a maximum, not a minimum, but that is a correctness issue rather than circularity.

Assumptions & free parameters 8 free parameters · 5 assumptions · 0 invented entities

The paper introduces no new physical entities, but it relies on several hand-chosen parameters and an ad hoc threshold function. The most consequential choices are the angular threshold φ(r), the exploration probability ε, the learning rate α, and the ABP resetting rule, all of which directly shape the reported non-monotonicity, scaling exponents, and the RL-vs-ABP comparison.

free parameters (8)
  • Angular threshold function φ(r) constants = 2.0 (home radius) in tan^{-1}(2.0/r); R0=35 in (π/2)(r/R0)
    Eq. 2: the state boundary and resetting rule are defined by a hand-picked functional form with no derivation from biology or first principles.
  • Exploration probability ε = 0.3
    Chosen to 'balance exploration and convergence' (Sec. II); SM Fig. 9 shows results vary with ε but no principled selection is given.
  • Learning rate α = 0.001
    Chosen for convergence stability; SM Fig. 9 shows variation with α without a systematic optimum.
  • Interaction spring constant κ = 70
    Supplementary Eq. A2: harmonic repulsion strength chosen ad hoc; no calibration against data.
  • Particle radius R_i / contact distance σ_ij = 0.35
    Supplementary Eq. A2: finite particle size chosen without justification.
  • Scaling exponents (β, α) = (1.0, 0.5) for D_r≤D_r*; (2.0, 1.0) for D_r>D_r*
    Fig. 4(e): fitted to collapse P(τ,D_r); not derived from the dynamics.
  • Noise distribution for action 2 = ζ uniform in [−π/2, π/2]
    Eq. 5: bounded uniform noise chosen for 'symmetry and moderation'; not the Gaussian noise expected from 'rotational diffusion'.
  • D_r* crossover value = ~12
    Emergent from the chosen parameters; not universal and depends on all other ad hoc choices.
assumptions (5)
  • standard math Q-learning with ε-greedy and a tabular Q-matrix converges to an optimal policy for the finite MDP
    Implicitly assumed; the learning rate is fixed and no convergence check is reported.
  • domain assumption Cost C(t+Δt)=|r(t+Δt)|−|r(t)| is the correct objective for homing
    Eq. 7: reduces the goal to radial distance minimization, so the optimal policy is trivially 'always align to home'.
  • ad hoc to paper Binary state discretization based on φ(r) captures the information needed for homing
    Eq. 3: discards the sign and magnitude of θ except through the threshold, and discards all distance information beyond the threshold.
  • ad hoc to paper Harmonic repulsive potential models biological avoidance behavior
    Supplementary Eq. A2: a spring-like potential is introduced with no calibration against real avoidance data.
  • ad hoc to paper ABP resetting probability p(t) in Eq. 9 is a fair baseline for stochastic resetting
    The ABP uses Gaussian noise and a probabilistic reset rule, while the RL agent uses bounded uniform noise and deterministic resets; the 'identical conditions' claim is false.

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Cite this review

Pith. "Pith review of Homing through Reinforcement Learning." pith.science (2026). https://pith.science/paper/TH4MZN4X

@misc{pith2026260208566,
  author       = {Pith},
  title        = {Pith review of: Homing through Reinforcement Learning},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/TH4MZN4X}},
  note         = {Machine review of arXiv:2602.08566}
}
abstract

Homing and navigation are fundamental behaviors in biological systems that enable agents to reliably reach a target under uncertainty. We present a Reinforcement Learning (RL) framework to model adaptive homing in continuous two-dimensional domain. In this framework, the agent's state is given by its angular deviation from home, actions correspond to alignment or stochastic reorientation, and learning is driven by a radial-distance-based cost that penalizes motion away from the target, where the cost also acts as an effective signal guiding the agent towards the home. For a single self-propelled agent moving with constant speed, we find that the mean homing time $\langle T_{\mathrm{home}} \rangle$ exhibits a non-monotonic dependence on the rotational diffusion strength $D_r$, with an optimal noise level $D_r^\ast$, revealing a subtle interplay between exploration and goal-directed correction. Extending to two agents with soft repulsion, one agent consistently reaches home faster than the other, while in multi-agents system, repulsion ensures separation and the fastest agent becomes progressively faster as group size increases. Finally, we have compared the homing time obtained from the RL agent with that of an Active Brownian Particle (ABP) with resetting and a pure ABP (without resetting) under identical conditions. The RL-based agent consistently achieves shorter homing times with trajectories that are less noisy and more directed than both cases, while the pure ABP typically continues wandering near the target without reliable localization. Our results show that cost-driven learning, stochastic reorientation, and inter-agent interactions enable efficient adaptive navigation, linking individual and collective homing. This RL framework captures key biological features such as feedback-based route learning, randomness to escape unfavorable orientations, and mutual coordination.

Figures

Figures reproduced from arXiv: 2602.08566 by the authors.

Figure 1
Figure 1. FIG. 1: (a) (Color online) Schematic representation of the homing model showing the circular domain of radius [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2: (Color online) Flowchart illustrating the reinforcement learning (RL) framework used for homing. The al [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3: (Color online) Mean homing time, [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (10 more)
Figure 4
Figure 4. Figure 4: FIG. 4: (a) (Color online) Mean number of resettings [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5: (a) (Color online) Plot shows [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]
Figure 6
Figure 6. Figure 6: (a) that as the number of particles in the group increases, the homing time for the fastest particle de￾creases. This indicates that the fastest particle becomes increasingly faster in larger groups. For clearer visual￾ization of this effect, the difference in the homi…
Figure 7
Figure 7. Figure 7: FIG. 7: (Color online) Mean number of resetting events [PITH_FULL_IMAGE:figures/full_fig_p008_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8: (Color online) [PITH_FULL_IMAGE:figures/full_fig_p009_8.png]
Figure 9
Figure 9. Figure 9: FIG. 9: (Color online) The plots (a-c) show the variation of the mean homing time [PITH_FULL_IMAGE:figures/full_fig_p013_9.png]
Figure 10
Figure 10. Figure 10: FIG. 10: (Color online) Four panels (a-d) show [PITH_FULL_IMAGE:figures/full_fig_p014_10.png]
Figure 11
Figure 11. Figure 11: FIG. 11: (Color online) The left panel (a-d) shows the time evolution of the angular deviation [PITH_FULL_IMAGE:figures/full_fig_p015_11.png]
Figure 12
Figure 12. Figure 12: FIG. 12: (Color online) The plot shows the variation of the standard deviation of angular deviation, [PITH_FULL_IMAGE:figures/full_fig_p016_12.png]
Figure 13
Figure 13. Figure 13: FIG. 13: (Color online)Standard deviation of the angular deviation [PITH_FULL_IMAGE:figures/full_fig_p017_13.png]

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