{"id":"eac5f07f-2ce5-4bdb-aa2b-6da72c7f2a78","arxiv_id":"2411.17932","paper_version":1,"verdict":"REJECT","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"high","formal_verification":"none","parameter_count":0,"one_line_summary":"A small MNIST classifier is far more sensitive to shifts of internal decision boundaries than to scaling or clipping of activations, supporting the author's claim that such networks use distance-like representations.","lead":"This paper tests whether neural networks measure distances instead of feature strengths by shifting, scaling, and clipping internal activations of a small MNIST model. The model collapses when decision boundaries shift but tolerates scaling, which the author reads as evidence for distance-based internal representations.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The 'distance' perturbation is an affine pre-activation shift that moves the decision threshold, so sensitivity to it does not specifically implicate learned distance metrics.","rationale":"The reader's rejection is well grounded. The experimental design's central contrast is not valid: the so-called distance perturbation shifts the decision boundary, while the intensity perturbations are not formally defined and therefore cannot serve as a clean control. The paper's own acknowledgment in Section 6.4 that no intensity metric exists undermines the claim that robustness to scaling and clipping supports distance use. My proposed control would settle whether the observed offset sensitivity is a generic property of affine pre-activation shifts or a signature of learned prototypes. Since this load-bearing assumption is untested, the central claim is not established, and the reader's REJECT verdict should stand.","tokens_in":8670,"tokens_out":5594,"duration_ms":52405,"concrete_test":"Train the same two-layer architecture (Linear(784) -> ReLU/Abs -> Linear(10)) on MNIST, but freeze the first linear layer at a random orthogonal initialization and train only the output layer. Apply the identical offset and scale perturbation sweeps from Section 4.1. If this control shows the same asymmetric sensitivity (accuracy drops with 1-3% offsets, robust to scaling up to 200%), then the original pattern is explained by the affine perturbation geometry rather than by learned distance-based representations.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim rests on the contrast between 'distance' and 'intensity' perturbations in Section 4.1. The distance perturbation is an affine map of the pre-activation: scale=(1-p)r, offset=pr. For ReLU with scale>0, this is equivalent to moving the threshold in the nonlinearity, changing which features are active; for Abs, it moves the fold point. The paper's own Section 6.1 confirms that offset perturbations modify the set of accepted features. A threshold or decision-boundary shift is exactly what any intensity-threshold classifier would be sensitive to, so observed sensitivity to it is not evidence for Mahalanobis-distance representations. The intensity perturbations are not an independent control because the paper concedes in Section 6.4 that there is no formal definition of an intensity feature, so the asymmetry between the two perturbation classes is not established. Without a control that isolates distance-to-prototype from boundary movement, the central result reduces to the observation that classifiers depend on their decision boundaries.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper presents perturbation experiments on a two-layer MLP with ReLU or absolute-value activations trained on MNIST. A custom perturbation layer applies scale, offset, and clipping to the first-layer pre-activations. The authors label offset shifts as 'distance-based' perturbations and scaling/clipping as 'intensity-based' perturbations, and report that accuracy is sensitive to offsets but robust to scaling/clipping. They conclude that the networks learn Mahalanobis-distance representations and that this validates the author's prior theoretical framework [Oursland, 2024].","tokens_in":8811,"tokens_out":6755,"duration_ms":58810,"significance":"If the conclusion were valid, it would be a notable challenge to the default intensity/threshold reading of activations and would give empirical traction to a Mahalanobis-distance account of linear layers. The paper is transparent about its implementation and provides code, training details, 20 repeated runs, and full result tables. However, the experiments as designed do not isolate distance-to-prototype computation from ordinary decision-boundary sensitivity, and the intensity control is not independently defined. The positive contribution is therefore an interesting perturbation setup and an observation about scaling invariance, not evidence for the paper's central claim.","major_comments":[{"comment":"The 'distance-based perturbation' is an additive offset applied to the pre-activation z = Wx + b before the nonlinearity (y = min(scale * x + offset, clip)). For fixed scale, this is exactly a change of the bias/threshold: z + offset = Wx + (b + offset). Section 6.1 and Figure 3 confirm that offset perturbations change the set of accepted features by moving the ReLU threshold or the Abs fold point. Any threshold-based or intensity-based classifier is sensitive to a movement of its decision boundary, so the observed accuracy drop under offset does not discriminate between distance-based and intensity-based representations. The central contrast therefore rests on a perturbation that is not a diagnostic of distance metrics.","section":"Section 4.1, Eq. (1), Figure 1"},{"comment":"The paper concedes that there is no formal definition of an intensity feature: 'we cannot definitively disprove intensity-based interpretations due to the lack of a widely accepted definition of what constitutes an intensity feature' and 'we find no equivalent statistical measure for intensity.' Without such a definition, classifying scaling and clipping as intensity perturbations is not justified, and the claim that intensity features are 'maintained' or 'targeted' is untestable. The asymmetry between the two perturbation families is assumed rather than derived, which undermines the central comparison.","section":"Section 6.4"},{"comment":"The text states that intensity perturbations produced fluctuations that were 'not statistically significant (p > 0.05), as detailed in Table 2 and Table 3.' This is contradicted by the tables: Table 3 reports P-values on the order of 1e-16 for every cutoff level, and Table 2 reports P < 0.05 for scale = 1%, 5%, and 10%, with ReLU accuracy falling to 75.33% at scale = 1%. The claimed robustness to intensity perturbations is therefore not supported by the paper's own statistics.","section":"Section 5, Tables 2 and 3"},{"comment":"The experiment is framed as validation of [Oursland, 2024], and the same framework is used to label offset perturbations as 'distance-based' (Section 4.1) and to interpret the results (Sections 6.1 and 6.4). This is circular: the perturbation classification is derived from the theory being tested, and the outcome is then read as confirming that theory. An independent operationalization of 'distance-to-prototype' (for example, perturbing estimated prototype locations or covariance structures rather than adding a bias shift) would be needed to break the circularity.","section":"Sections 3, 4.1, 6.4, and 7"}],"minor_comments":[{"comment":"The text refers to 'McCulloch and Pitt' but the reference list correctly gives 'McCulloch and Pitts'; please correct the in-text name.","section":"Section 2"},{"comment":"The perturbation formula {scale = (1 - p) * r, offset = p * r} is inconsistent with the stated training-time identity scale = 1, offset = 0; please clarify how r is computed and how p = 0 yields the baseline operation.","section":"Section 4.1"},{"comment":"The qualitative description 'approximately 98% for ReLU and 99% for Abs' should be replaced by the precise baseline values from Table 1.","section":"Section 5"},{"comment":"The t-statistics and p-values are reported with very few significant digits and with negative t-statistics for two-sided tests; please state the null hypothesis and the test procedure (paired vs. independent, one-sided vs. two-sided) explicitly.","section":"Appendix A, Tables 2-4"},{"comment":"The term 'principal disponent' is introduced without definition, and the paragraph appears to assert the non-existence of the entity it names; please define or remove this term.","section":"Section 6.4"}],"recommendation":"reject","confidential_remarks":"This is a self-contained empirical study, but the central inference is not supported by the reported experiments. I recommend rejection rather than major revision because the perturbation contrast is not a valid diagnostic for distance-metric computation: the offset perturbation moves a decision boundary that any linear classifier depends on, and the intensity perturbations lack a formal definition. A revision that preserves the current experimental design cannot repair the inference; a new experimental approach would be required. The self-referential structure (validating the author's own prior framework with experiments designed using that framework) should also be weighed by the editor."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The thing to know: the paper's main experiment does not support its title. The \"distance-based\" perturbation in Section 4.1 is an affine shift of the pre-activation (scale=(1-p)r, offset=pr). For a ReLU or Abs unit that is exactly moving the threshold that decides which features pass through. Any classifier that depends on its decision boundary—which is any classifier—will be sensitive to that. So the observed sensitivity to offset does not specifically implicate Mahalanobis-style distance representations. The stress-test note is right, and I don't think the paper has a response to it. Credit where it's due: the perturbation protocol itself is new as far as the cited literature goes, and the measurements are concrete. The paper is clearly written, the authors acknowledge the lack of a formal intensity definition (Section 6.4), and they publicly shipped code and data. That is more than many interpretability papers do. The soft spots are substantial. The scaling invariance is plausibly just a softmax artifact, as the paper itself half-admits in Section 6.2. The intensity perturbations are not an independent control because there is no definition of \"intensity\"—the paper concedes this. Evaluating on the training set weakens the generality of the accuracy numbers, though for feature-usage analysis it is at least defensible. The appendix tables have internal oddities: the baseline rows carry non-zero t-statistics and p-values, and Table 2 shows statistically significant drops at 1% and 5% scaling that the text glosses over. Those inconsistencies are minor individually but they do not build confidence. The \"principal disponent\" passage in Section 6.4 is speculative, but the author at least flags it as not real; it is a symptom of the framework being used to interpret its own experiment, not a fatal flaw on its own. The circularity burden is real: the experiment is designed and interpreted through Oursland 2024, and the conclusion says it \"validates\" that framework. That does not make the measurements false, but it means the interpretation is not independent. Who is this for? People working on interpretability and representation analysis might read it as a cautionary example of how easy it is to build an experiment around an implicit assumption. It is not a reliable empirical result as it stands. Serious referee? Yes, I would send it out. The question is important, the experiment is falsifiable, and the flaws are fixable in principle with proper controls—e.g., a perturbation that isolates distance-to-prototype from threshold movement, a deeper network, and a cleaner intensity control. But I would expect rejection or major revision in its current form.","headline":"A readable, honestly-written paper whose central claim fails: the \"distance\" perturbation is just a decision-boundary shift, so the headline result is not established.","tokens_in":799,"tokens_out":984,"would_cite":false,"duration_ms":24977,"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 argues that trained neural networks with ReLU and Absolute Value activations encode inputs as distances to learned decision boundaries rather than as feature strengths, and supports the claim with perturbation experiments on…","keywords":["neural network interpretability","distance metrics","Mahalanobis distance","perturbation analysis","ReLU activations","absolute value activations","MNIST","intensity vs distance representations"],"falsifier":"Compensate for an offset perturbation by adding the corresponding constant to the second linear layer's bias so the post-activation decision boundary stays fixed; if accuracy is fully restored, the collapse under offset is boundary movement rather than learned distance. A second test: find a trained ReLU or Abs network whose accuracy collapses under large scaling or clipping while surviving 1% offsets, which would break the claimed asymmetry.","tokens_in":8402,"feed_emoji":"📏","tokens_out":8768,"duration_ms":73575,"temperature":0.7,"pith_summary":"This paper argues that trained neural networks with ReLU and Absolute Value activations represent inputs by measuring distances to learned decision boundaries rather than by the strength or intensity of feature activation. The evidence comes from MNIST perturbation experiments: scaling activations from 10% to 1000% of their range or clipping high activations leaves accuracy essentially unchanged, while shifting pre-activation outputs by as little as 1–3% of the range collapses accuracy. The authors read these results as supporting the earlier theoretical claim that linear layers compute Mahalanobis distances, and as showing that the smallest activations, not the largest, carry the discriminative signal. The paper acknowledges that the absence of a formal definition of intensity makes its control perturbations imperfect, so the strongest reading is that distance sensitivity is real, while intensity resistance is less cleanly established.","feed_headline":"Neural networks learn distances, not feature strength","feed_subtitle":"Shifting a trained network's decision boundary by a few percent collapses accuracy; rescaling activations barely hurts","key_machinery":"The carrying mechanism is the perturbation layer inserted between the first linear layer and the activation function, which applies $y = \\min(\\text{scale} \\cdot x + \\text{offset}, \\text{clip})$ to each unit with three fixed parameters. Offset moves the pre-activation decision boundary by a percentage of the unit's output range; scale multiplies the activation magnitudes; clip caps them. Comparing accuracy across the three perturbations is the experiment's probe for whether the network depends on distance-to-boundary or on activation magnitude. The theoretical object behind the probe is the Mahalanobis distance, a data-covariance-aware distance measure, which the companion theory says a linear node's pre-activation projection computes.","core_discovery":"On its own terms, the paper's discovery is that ReLU and Absolute Value networks behave as distance-measuring machines: a linear node projects the input, and its activation records how far that projection sits from a learned boundary, so the smallest post-activation values mark the strongest match to the node's feature. Empirically, offset perturbations that move the boundary by 1–3% of the activation range degrade accuracy sharply, whereas scaling by up to 1000% and clipping down to 50% of the maximum leave performance nearly intact. The Absolute Value network is more sensitive because folding the feature space makes it select a single minimum-distance feature, while ReLU selects a set of accepted features and degrades more gradually. This pattern is presented as empirical validation of the Mahalanobis-distance interpretation of linear nodes.","pith_inferences":["An offset before ReLU or Abs is mathematically equivalent to changing the first layer's bias, so offset sensitivity alone does not separate the distance-metric hypothesis from the generic fact that linear classifiers depend on their decision boundaries; a cleaner control would keep the boundary fixed while varying distances.","A testable extension: train the same architecture on synthetic data with known covariance structure and check whether the first-layer weight vectors align with the inverse covariance matrix implied by the Mahalanobis distance.","If the distance-based reading is right, pruning and quantization schemes that discard small activations may be removing the most decision-relevant signal, so low-magnitude activations near boundaries should be protected rather than discarded.","The scaling invariance could be tested against the LogSoftmax explanation by replacing the cross-entropy head with a linear head and repeating the scale perturbation; if invariance disappears, normalization is the cause, and if it persists, distance-based computation is."],"forward_implications":["Activation magnitude should not be read as feature strength; saliency and feature-visualization methods that emphasize large activations may be highlighting the values the classifier cares least about.","Adversarial vulnerability is a natural consequence, since tiny input changes that shift pre-activation projections by a few percent can move the network's selected features across decision boundaries.","Absolute Value networks rely on a single precise distance measurement, so they should be expected to degrade faster under small boundary shifts than ReLU networks, which can fall back on alternative accepted features.","Interpretability and robustness work should be redirected toward the geometry of decision boundaries and small-magnitude activations rather than toward suppressing or amplifying large activations."],"supporting_citations":[{"why":"Holds the theoretical claim under test: linear nodes with absolute-value activations compute Mahalanobis distances, which this paper aims to validate empirically.","marker":"[Oursland, 2024]"},{"why":"Defines the generalized distance measure that the paper's distance-metric interpretation is built on.","marker":"[Mahalanobis, 1936]"},{"why":"Supplies the MNIST dataset and digit-classification task for all training and perturbation experiments.","marker":"[LeCun et al., 1998]"},{"why":"Introduces the perturbation-analysis approach and the observation that small input changes can flip predictions, which the offset experiments build on.","marker":"[Szegedy et al., 2013]"},{"why":"Frames adversarial examples through decision boundaries near data, the same mechanism the paper invokes to explain offset sensitivity.","marker":"[Goodfellow et al., 2014]"},{"why":"Provides the threshold-activation neuron model that the paper identifies as the origin of the intensity interpretation it challenges.","marker":"[McCulloch and Pitts, 1943]"},{"why":"Roots the perceptron's activation-as-strength reading, the intensity view the experiments argue against.","marker":"[Rosenblatt, 1958]"},{"why":"Supplies the formal definition of distance metrics used to distinguish distance-based from intensity-based features.","marker":"[Deza and Deza, 2009]"}],"fun_headline_variants":["Neural nets: distance sensors, not intensity gauges","Tiny distance tweaks crash networks, huge scaling safe","ReLU networks measure distance, not activation strength","Activation codes distance: scaling to 1000% won't hurt"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that an offset added before ReLU or Abs is a distance-only perturbation that leaves intensity features intact, but that offset is exactly a change to the first layer's bias—a decision-boundary shift any linear classifier depends on—and the paper offers no formal definition of intensity to rule out a symmetric control.","fun_headline_variants_meta":{"raw":{"variants":["Neural nets: distance sensors, not intensity gauges","Tiny distance tweaks crash networks, huge scaling safe","ReLU networks measure distance, not activation strength","Activation codes distance: scaling to 1000% won't hurt"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00024,"raw_usage":{"total_tokens":1420,"prompt_tokens":750,"completion_tokens":670,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":366,"completion_tokens_details":{"reasoning_tokens":602}},"tokens_in":366,"tokens_out":670,"duration_ms":6353,"temperature":1.0,"reasoning_tokens":602,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T11:41:17.468262+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compensate for an offset perturbation by adding the corresponding constant to the second linear layer's bias so the post-activation decision boundary stays fixed; if accuracy is fully restored, the collapse under offset is boundary movement rather than learned distance. A second test: find a trained ReLU or Abs network whose accuracy collapses under large scaling or clipping while surviving 1% offsets, which would break the claimed asymmetry.","supporting_citations":[{"cited_title":"Encyclopedia of distances","cited_arxiv_id":null,"evidence_quote":"Supplies the formal definition of distance metrics used to distinguish distance-based from intensity-based features."}],"review_version":1}