{"id":"ce0d8f0d-8acd-4569-8299-f5ce77e6a27c","arxiv_id":"2503.05601","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":7,"one_line_summary":"By backpropagating through a mass-spring network, the authors co-design controller and body and observe that classification, memory, and nonlinearity are shared between brain and body.","lead":"This paper trains a simulated soft body, a network of springs and weights, together with its controller by sending error signals back through the physics. A smart generalist might care because it offers a concrete way to offload computation onto body mechanics and to create closed-loop robot controllers without pre-specified feedback signals.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The 'reciprocal relationships' claim in the MNIST task rests on a visual PCA comparison between brain outputs and body outputs with unmatched dimensionalities and no quantitative separation metric or fixed-body baseline; this leaves the central claim underdetermined.","rationale":"The paper has real strengths: a clear computational framework, public code, a concrete proof that a linear-spring MSDN can be nonlinear due to geometry, and a novel closed-loop training procedure. The reader's conditional verdict is reasonable. However, the single most load-bearing point for the abstract's 'reciprocal relationships' claim is the MNIST evidence. Because the body output is the training target and the brain output is an intermediate variable, a naive visual PCA comparison is biased toward showing cleaner clustering in the body. The paper does not report any quantitative measure of separation, nor does it compare against a control in which the body is untrained. This is an internal evidential gap, not a disagreement with consensus. If the quantitative test shows no significant body contribution, the main claim about reciprocity would be substantially weakened; if the test confirms the visual impression, the claim is supported. The closed-loop 'embedding' claim is less affected by this concern, but the 40% locomotion success and lack of statistical detail already justify the conditional verdict. I therefore recommend keeping the verdict at CONDITIONAL (unchanged), with the added requirement of the quantitative PCA/baseline analysis.","tokens_in":25502,"tokens_out":6515,"duration_ms":64377,"concrete_test":"Re-analyze the saved MNIST runs (code is public) by computing a class-separation metric, e.g., linear-readout one-vs-all accuracy or silhouette score, on the brain output and on the body output after projecting both to the same dimensionality, and compare these values to a control where the body parameters are frozen at initialization and only the brain is trained. If body-output separation does not significantly exceed brain-output separation and the fixed-body control under matched conditions, the reciprocal-role conclusion is not supported.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim that brain and body exhibit reciprocal functional roles is most directly supported by Fig. 2(c), where PCA of the brain output (initial mass-point positions, 2(N_mov-1) dimensions) and the body output (CMP trajectory) are visually compared. This comparison is not controlled: the two outputs have different dimensionalities, and PCA retains only the top two variance directions, so stronger label separation in the body plot can reflect the projection or the fact that the training loss directly shapes body trajectories to match label-specific targets, rather than a body-side contribution to classification. No quantitative separation index (e.g., silhouette score, linear readout accuracy) or comparison against a fixed/random-body baseline is provided. The label-map analyses are also qualitative and reported without error bars. Under these conditions, the paper's headline conclusion that classification was 'not completed solely in the brain' is not yet established even within the simulation. The closed-loop embedding result is a distinct contribution, but it does not rescue the reciprocal-division claim. Simulation fidelity, while a valid limitation, is secondary because the evidence is incomplete before real-world transfer is considered.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper introduces 'backpropagation through soft body' (BPTSB), a differentiable simulation framework that trains a neural-network or sine-wave-generator 'brain' jointly with a mass-spring-damper 'body' by gradient descent. Three task families are studied: MNIST classification with drawing behavior, time-series emulation using a custom 'expanded NARMA' target, and autonomous generation of Lissajous and locomotion behaviors with a feedback layer that replaces the trained open-loop sine-wave generator. The authors use PCA, label maps, and information processing capacity (IPC) to argue that recognition/control and memory/nonlinearity are distributed reciprocally between brain and body, and they report a closed-loop functional-transfer result.","tokens_in":25661,"tokens_out":4110,"duration_ms":37383,"significance":"If the reciprocal-role claim were established, the paper would be a useful contribution to morphological computation and differentiable co-design, because it attempts to localize information-processing function inside a trained embodied agent rather than treating the body as an actuation-only plant. The closed-loop feedback-layer construction is a distinctive, potentially practical result, and the geometric nonlinearity proof in Section V.A is clean and explicit. The availability of source code and supplementary videos strengthens reproducibility. However, the headline claim is currently supported mainly by qualitative comparisons and lacks the controlled baselines needed to rule out trivial explanations.","major_comments":[{"comment":"The claim that 'label classification was not completed solely in the brain' rests on a visual PCA comparison between the brain output (initial positions of 2(Nmov-1) movable masses) and the body output (a time-indexed CMP trajectory), which have different dimensionalities and are projected onto their top two principal components. Because the training loss directly supervises the CMP trajectory to match label-specific target drawings, stronger visual label separation in the body panel may simply reflect that the loss is defined on the trajectory, not a body-side computational contribution. Please add a quantitative separation index (silhouette score or linear-readout accuracy on both representations) and at least two controls: a fixed/random body with a trained brain, and a brain-only mapping from input to trajectory (or an untrained-body system), to support the division-of-roles conclusion.","section":"Section II.C, Fig. 2(c)"},{"comment":"The expanded NARMA target in Eq. (1) was designed so that second- and third-order nonlinear profiles are large relative to standard NARMA (SI V.C.2), and the IPC in Fig. 3(c) is then measured on the very same fitted system and compared with the target's IPC. As a result, the observation that the trained system acquires higher-order IPC partly reflects the target construction rather than an emergent reciprocal distribution of functions. Please add a control with standard NARMA2/NARMA10 targets, or with random static target profiles, and report IPC of the untrained body/brain as a baseline. Also, the statement that 'memory was generated by the body since the brain was an FNN' is true by architecture; what needs support is the stronger claim that the body specifically elevates nonlinearity into nonlinear memory.","section":"Section II.D and SI V.C.2"},{"comment":"The closed-loop locomotion success rate is reported as 8/20 agents (40%) with success defined by a speed ratio threshold of 0.7, and Fig. 4(c) shows return-rate curves without confidence intervals or statistical comparison to the open-loop condition. Because the closed-loop transfer claim is a central positive result, please report per-seed curves, standard errors, and a statistical test (e.g., a paired test on the 20 seeds) for the comparison between sinusoidal drive and closed-loop control.","section":"Section II.E and IV.G"},{"comment":"The Methods explicitly state that collisions between mass points and spring intersections are ignored, and the ground reaction force in Eq. (20) is a differentiable exponential that permits sinking into the ground. These idealizations are acceptable for a simulation study, but they should be discussed as threats to the real-robot transfer implied by 'embedding brain functionalities into bodies'; please either add a paragraph in the Discussion or temper the stated generality.","section":"Section IV.A"}],"minor_comments":[{"comment":"There are several typographical errors, including 'Coupl ing' in the title, 'folllowing' in Section IV.C, and 'Ttime-series' in Table III(b).","section":"Global"},{"comment":"The table reports 'errors of the best samples' without indicating how many seeds were run or the distribution; please state the number of initializations and show mean/standard deviation.","section":"Fig. 2(b)"},{"comment":"The label-map analysis is qualitative and not accompanied by error bars over seeds or input samples; the conclusions about robustness would be better supported by a quantitative summary, such as mean label-map size with variance.","section":"Section II.C and V.B.3"},{"comment":"The statement that 'the total capacity reached the rank of one in all cases' is unexplained; a brief justification or a reference for why the total IPC equals the rank would help readers interpret the IPC profiles.","section":"Section IV.E"},{"comment":"The definition of 'label map size' would benefit from a formal equation; the current description ('proportion of the original label area') is ambiguous about how the discretization of the displacement grid is handled.","section":"Section IV.D"},{"comment":"The SWG frequency is fixed at 2π, but the switching-timing formula in Eq. (46) uses 2π/ω; please ensure the notation is consistent and clarify whether ω denotes angular frequency in radians per unit time.","section":"Section II.E and V.D.2"}],"recommendation":"major_revision","confidential_remarks":"The paper's core method is sound and the closed-loop embedding is promising, but the main reciprocal-division claim requires additional control experiments and quantitative metrics. I do not see grounds for rejection; the requested baselines and statistical reporting are within the scope of a revision. There is also a scope-fit question: the journal may prefer that the 'reciprocal relationships' framing be either substantiated with the new controls or softened."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nThis is a careful simulation study with a genuinely useful diagnostic toolkit, but its headline claim about reciprocal brain–body division is softer than the abstract suggests. Worth refereeing, not a pass as-is.\n\nWhat is actually new: the combination of label maps, per-mass-point IPC profiles, and the closed-loop feedback-layer transfer without target feedback signals. The nonlinearity proof for MSDNs in the SI is clean. Code is released. The SI classification-by-readout result (91% without body to ~96% with body) gives a quantitative anchor that the body matters, which the main text only gestures at with PCA.\n\nThe soft spots are real. The PCA comparison in Fig. 2(c) puts a 2(N_mov-1)-dimensional brain output against the 2D CMP trajectory, projects both to two PCA axes, and claims better label separation for the body. With unmatched dimensionalities and no silhouette score, linear readout, or fixed-body baseline, that comparison cannot carry the 'not completed solely in the brain' conclusion. The expanded NARMA target was authored specifically to contain more higher-order nonlinearity than standard NARMA, so the IPC finding that the system develops higher-order profiles is partly a consequence of the target choice, not an independent discovery. And since body parameters are co-trained with the brain, the body's contribution is somewhat by construction. Locomotion closed-loop success at 40% is modest, and the paper's own methods note the ground contact force allows sinking and collisions are ignored — a genuine limitation, though secondary to the missing baselines. The label maps are interesting but qualitative, with no error bars.\n\nThat said, the paper is honest about these issues: the Discussion says the performance level's validity was unclear, and the SI reports negative results (Schemes 1–3 for closed-loop training mostly failed). That candor counts.\n\nFor whom: embodied intelligence and soft robotics readers who want a co-design pipeline and a way to probe what the body computes. Not for someone wanting a cleanly demonstrated new principle. It deserves a serious referee; revisions should require quantitative separation indices, at least one fixed-body or brain-only baseline, error bars over seeds, and a tempered phrasing of the 'embedding brain functions into bodies' claim. I'd bring it to reading group to argue about the evidence bar, but I wouldn't want it cited as established fact.","headline":"A solid co-design pipeline with useful diagnostics, but the 'reciprocal relationships' claim rests on a qualitative PCA comparison and needs baselines before it can carry the paper's conclusions.","tokens_in":26260,"tokens_out":4277,"would_cite":false,"duration_ms":37111,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"This paper shows that when a simple neural controller and a soft body are trained together by backpropagation through physics, the pair distributes recognition, memory, and nonlinearity across both components instead of keeping a clean…","keywords":["co-design","morphological computation","physical reservoir computing","differentiable physics","mass-spring-damper network","closed-loop control","information processing capacity","soft robotics"],"falsifier":"Run the same three tasks in a physics simulator that includes mass-point collisions, spring self-intersection, and a non-sinking contact model, or on a physical soft robot, and check whether the body still sharpens MNIST label separation and whether feedback-layer closed-loop locomotion still succeeds at a similar rate.","tokens_in":13,"feed_emoji":"🧠","tokens_out":3613,"duration_ms":114158,"temperature":0.7,"pith_summary":"The paper asks where information processing actually happens in an agent whose brain and body are optimized together. Using backpropagation through a differentiable mass-spring-damper simulation, called backpropagation through soft body, the authors train several brain–body systems and then analyze which computations each part performs. They find that recognition is not finished by the brain alone: the body sharpens label separation, supplies memory that the feed-forward brain lacks, and adds nonlinearity through its geometry. They also show that after training a sine-wave generator to drive a body, a simple feedback layer can be fitted by ridge regression and replace the generator, sustaining Lissajous drawing and locomotion in a closed loop. The point is that brain and body exchange roles, and that optimized brain functions can be embedded into the body.","feed_headline":"Soft bodies do real computation when co-trained with brains","feed_subtitle":"Simulated agents split classification, memory, and motion between controller and body, then run closed-loop on body feedback alone.","key_machinery":"The machinery is a differentiable mass-spring-damper network embedded in a backpropagation loop. Each spring has trainable stiffness, damping, and rest length, and the brain's weights or sine-wave amplitudes and phases are updated by the same chain rule as the body, so gradients pass through the Velocity Verlet time integration. Nonlinearity arises from geometric terms such as spring angles even though the springs themselves are linear, and a fitted feedback layer closes the loop by mapping measured spring lengths to control signals.","core_discovery":"The central claim is that co-designed brain–body systems do not evolve a top-down division of labor; instead, information processing is distributed reciprocally. In the MNIST drawing task, the body improves class separation beyond what the brain's initial positions already produce. In time-series emulation, the body generates memory and higher-order nonlinearities, while a multilayer perceptron brain compensates for nonlinearity that the body alone cannot supply. In locomotion and limit-cycle tasks, a trained sine-wave generator's command can be transferred to a feedback layer, yielding closed-loop autonomous behavior whose response to perturbations is comparable to the open-loop drive.","pith_inferences":["A testable extension is to run the same tasks in a simulator with mass-point collisions, spring self-intersection, and a non-sinking ground contact; if the complementary division of labor persists, it is likely a generic property of soft-body co-design rather than an artifact of the simplified model.","The label-map result that sensitivity concentrates at mass points directly connected to the output suggests a design heuristic: place sensors or actuation where memory and nonlinearity are needed, rather than distributing them uniformly.","The 40% closed-loop locomotion success rate points to the brain-to-body transfer procedure itself as the bottleneck, and the simultaneous training schemes tested here rarely improved on regression, suggesting the feedback layer needs a genuinely co-trained optimization scheme."],"forward_implications":["If the division-of-labor finding holds, performance comparisons of controllers should account for the body's share of computation; a weaker controller plus a well-tuned body can match a stronger controller.","A feed-forward brain with no internal memory can still produce memory-dependent outputs because the soft body stores past inputs in its transient dynamics.","Closed-loop control can be obtained without pre-specified feedback targets: optimize an open-loop generator first, then regress a feedback layer onto its outputs.","Body geometry, such as multiple-circle versus double-circle connectivity and the number of movable masses, measurably changes nonlinear capacity and memory, so topology choice is a design lever.","Behavioral switching can be embedded through constant external inputs such as a simulated wind, and the system shows untrained bifurcation structure beyond the learned regimes."],"supporting_citations":[{"why":"Supplies the gradient-based mass-spring network co-design approach that backpropagation through soft body extends.","marker":"[40]"},{"why":"Provides the sine-wave-driven mass-spring locomotion setup and the spring-length modulation scheme used for the closed-loop tasks.","marker":"[45]"},{"why":"Supplies the MNIST dataset used for the classification and drawing experiments.","marker":"[47]"},{"why":"Provides the information processing capacity measure used to attribute memory and nonlinearity to the brain and body.","marker":"[48]"},{"why":"Supplies the Velocity Verlet integrator used for the differentiable physical simulation.","marker":"[70]"},{"why":"Provides the physical reservoir computing perspective that motivates embedding brain functionality into the body.","marker":"[10]"}],"fun_headline_variants":["Co-designed soft bodies do real computation","Soft body and brain share the computational load","Brains and bodies co-evolve to split information processing","Co-training embeds brain functions into soft bodies","Bodies compute, brains compensate: reciprocal co-design"],"cache_read_input_tokens":28416,"weakest_assumption_plain":"The results depend on the fidelity of the mass-spring-damper simulation: collisions between mass points and spring intersections are ignored, and the locomotion ground force is a differentiable exponential that lets objects sink, so a real soft body might not show the same division of labor.","fun_headline_variants_meta":{"raw":{"variants":["Co-designed soft bodies do real computation","Soft body and brain share the computational load","Brains and bodies co-evolve to split information processing","Co-training embeds brain functions into soft bodies","Bodies compute, brains compensate: reciprocal co-design"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000189,"raw_usage":{"total_tokens":1268,"prompt_tokens":812,"completion_tokens":456,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":428,"completion_tokens_details":{"reasoning_tokens":384}},"tokens_in":428,"tokens_out":456,"duration_ms":4483,"temperature":1.0,"reasoning_tokens":384,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T15:22:39.357626+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run the same three tasks in a physics simulator that includes mass-point collisions, spring self-intersection, and a non-sinking contact model, or on a physical soft robot, and check whether the body still sharpens MNIST label separation and whether feedback-layer closed-loop locomotion still succeeds at a similar rate.","supporting_citations":[{"cited_title":"Sakurai, M","cited_arxiv_id":null,"evidence_quote":"Supplies the gradient-based mass-spring network co-design approach that backpropagation through soft body extends."},{"cited_title":"Caluwaerts, J","cited_arxiv_id":null,"evidence_quote":"Provides the sine-wave-driven mass-spring locomotion setup and the spring-length modulation scheme used for the closed-loop tasks."},{"cited_title":"Bhovad and S","cited_arxiv_id":null,"evidence_quote":"Supplies the MNIST dataset used for the classification and drawing experiments."},{"cited_title":"Wang and S","cited_arxiv_id":null,"evidence_quote":"Provides the information processing capacity measure used to attribute memory and nonlinearity to the brain and body."},{"cited_title":"Wagner and D","cited_arxiv_id":null,"evidence_quote":"Supplies the Velocity Verlet integrator used for the differentiable physical simulation."}],"review_version":1}