{"id":"464bdaa1-3961-4f87-acf7-b151cc1fd25a","arxiv_id":"2510.24342","paper_version":3,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"Transformer models lie along a continuous arc in a new seven-dimensional Brain-like Space, where global-semantic models align with higher-order brain networks and local-reconstruction models align with sensory networks.","lead":"This paper introduces a unified map, called Brain-like Space, that compares how AI models organize information against seven human brain networks without making the models process the same inputs. It charts 151 Transformer models and finds a continuous arc from local-detail models to global-semantic models, including surprises such as DINOv2 being less brain-like than its predecessor DINO.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"RoPE models all share a borrowed GPT-2 or ViT-base positional embedding in Eq (2), so the reported convergence of RoPE LLMs/LMMs may be an artifact of the shared Pbase rather than of model organization.","rationale":"I read the central claim as: the constructed spatial attention graphs faithfully represent each model's intrinsic information organization, so that cosine similarities to seven brain networks reveal a meaningful brain-likeness ordering. The load-bearing condition is therefore that Eq (2) is a valid proxy for a Transformer's spatial topology. The weakest point is not only that content is ignored, but that for RoPE models the proxy is another model's positional embedding. This makes the strong convergence of RoPE LLMs—a key supporting result—potentially circular or, at minimum, dependent on an arbitrary choice. If the test shows invariance across Pbase choices, the concern is resolved; if not, the central claim for RoPE models (and for the RoPE fusion narrative in Sec 2.5) should be substantially weakened. I agree partially with the reader: their content-free concern captures the same broad assumption, but the borrowed Pbase is a sharper, more easily falsifiable version. I also considered the graph-size mismatch between 136-node brain graphs and 50/197-node model graphs as a secondary worry; it affects all models roughly equally and does not specifically target the RoPE convergence result, so I did not make it the primary attack.","tokens_in":20603,"tokens_out":4752,"duration_ms":43873,"concrete_test":"For one RoPE LLM (e.g., LLaMA-7B), recompute its 7D Brain-like coordinates under four Pbase choices: GPT-2 absolute embeddings (as in the paper), sinusoidal, random orthogonal, and ViT-base, each rescaled by Eq (3)-(4), plus a content-dependent variant using the model's actual RoPE attention averaged over a few hundred neutral sentences. If the centroid moves across a cluster boundary (e.g., C3 vs C4) or the RoPE family's mutual separation changes materially, the RoPE-convergence and deep-fusion results are not robust to the arbitrary choice of Pbase.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The paper's central claim—that 151 Transformers occupy a shared arc-shaped geometry reflecting their intrinsic organization—rests on Eq (2), where each spatial attention graph is built from positional embeddings only, with no input content. For RoPE-based models (8 of 10 LLMs and most LMMs), the paper does not even use the model's own RoPE: in Methods, 'Construction of Spatial Attention Graphs in Artificial Neural Network Models', absolute positional embeddings from GPT-2 or ViT-base are substituted as Pbase, linearly interpolated and rescaled by Eq (3)-(4). Because Pbase is identical for all RoPE language models, and separately for all RoPE vision encoders, the reported convergence of RoPE LLMs near C3/C4 and the 'deep fusion' effect of RoPE in Sec 2.5 may be artifacts of the shared borrowed Pbase rather than evidence about model organization. The content-free assumption itself is inherited from self-cited ref [47] and is not validated in this paper; Sec 3.6 lists limitations but does not flag the foreign-embedding substitution or test sensitivity to the choice of Pbase. If the position of RoPE models shifts with Pbase, the arc geometry for a large fraction of the 151 models is not a measure of the models' own topological organization.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper introduces 'Brain-like Space', a seven-dimensional space in which each attention head of a Transformer model is embedded by the cosine similarities between five graph-theoretic metrics of its spatial attention graph and those of seven canonical functional brain networks derived from resting-state fMRI. Analyzing 151 Transformer-based models with 62,480 attention head graphs, the authors report a continuous arc-shaped geometry with four clusters (C1–C4) reflecting increasing brain-likeness. They attribute the distribution to data augmentation, training objectives, distillation, and positional encoding schemes, and report that the brain-likeness score does not correlate significantly with ImageNet accuracy (r=0.266, p=0.156). The framework is proposed as a task-free, modality-agnostic measure of organizational similarity between artificial and biological systems.","tokens_in":20949,"tokens_out":6550,"duration_ms":53418,"significance":"If the framework withstood scrutiny, it would provide a novel, input-free and modality-agnostic tool for comparing Transformer architectures with human brain networks, and the scale of the empirical survey (151 models, 62,480 head graphs, 1042 subjects) is a clear strength. The paper makes code and data availability explicit, and its descriptive observations (e.g., the global-semantic vs. local-reconstruction dichotomy) are internally consistent. However, the central claims currently rest on an unvalidated content-free assumption about positional encoding, a borrowed-positional-embedding substitution for RoPE models, and circular analysis choices (PC1, thresholds, k); these issues must be addressed before the results can be interpreted as evidence about intrinsic model organization.","major_comments":[{"comment":"The spatial attention graph is constructed from positional embeddings and query/key matrices only, with no input content. The paper explicitly adopts the hypothesis from ref [47] that a model's intrinsic spatial interaction structure is primarily determined by its positional encoding scheme. This assumption is load-bearing: if content-dependent attention contributes substantially to the topology of real Transformer representations, the Brain-like Space measures a property of positional embeddings rather than of model organization. The manuscript does not validate this assumption (e.g., by comparing the content-free graphs with content-dependent attention maps on a subset of models), and Sec. 3.6 does not list it as a limitation. Please provide such a validation or reframe the claims accordingly.","section":"Methods, Eq. (2)"},{"comment":"For RoPE-based models, the paper substitutes a borrowed absolute positional embedding Pbase from GPT-2 or ViT-base, linearly interpolated and rescaled, instead of using the model's own RoPE. Because Pbase is identical for all RoPE language models (and separately for all RoPE vision encoders), the reported convergence of RoPE LLMs near C3/C4 in Sec. 2.5 and the 'deep fusion' effect of RoPE may be artifacts of the shared borrowed Pbase rather than evidence about the models' own organization. Please either use the actual RoPE (e.g., with a fixed probe input) or report a sensitivity analysis over different Pbase choices; without this, the positional-encoding conclusions are not supported.","section":"Methods, 'Construction of Spatial Attention Graphs' and Eqs. (3)-(4)"},{"comment":"The brain-likeness score is defined as the sum of projections onto PC1 of the Brain-like Space, and PC1 is fit to all 151 models' attention heads. Likewise, the matched-head thresholds (0.8, lowered to 0.6) and the k=4 clustering are selected using the same dataset. This creates a circularity: the 'gradual increase' from C1 to C4 and the model rankings are partly determined by the very data being scored. Please use leave-one-model-out or nested construction of PC1 and thresholds, or otherwise demonstrate that the ranking is stable when the axis is defined independently.","section":"Sec. 2.6, Eq. (14)"},{"comment":"The matched-head threshold is lowered from 0.8 to 0.6 specifically for DINOv2 and MAE, and the resulting matches are 'almost exclusively' VIS. A lowered post-hoc threshold does not provide evidence for a specific brain-network alignment; at the standard threshold these models have no matches. The claim of 'reduced alignment in DINOv2 compared to its predecessors' is therefore weaker than stated. Please report matches at a fixed threshold or justify the threshold change a priori.","section":"Sec. 2.3 and Fig. 2e"},{"comment":"The 'standardized vector' used in the cosine similarity is not defined. It is unclear whether standardization is z-scoring across the five graph metrics, across heads, or across brain networks, and this choice affects every similarity value and hence the entire Brain-like Space. Please specify the standardization procedure and justify its invariance properties.","section":"Methods, Eq. (12)"}],"minor_comments":[{"comment":"The arXiv title 'A Unified Geometric Space for Topological Alignment Between Transformer-Based Models and Human Brain Networks' differs from the first-page title 'A Unified Geometric Space Bridging AI Models and the Human Brain'; please align them.","section":"Title"},{"comment":"The same symbol W is used on both sides of the definition; please use a different symbol for the normalized edge weights to avoid confusion.","section":"Eq. (1)"},{"comment":"The notation '~A(l) ij' is not defined, and '10 −5' for epsilon and delta should be written as '10^{-5}'.","section":"Eq. (5)"},{"comment":"The k-means clustering input is not specified: please state whether clustering is performed on the seven-dimensional vectors or on the PC scores, and describe the feature space used for the silhouette analysis.","section":"Sec. 2.1"},{"comment":"The p-value for the ImageNet correlation is reported as 0.156 in the abstract and 0.1555 in Sec. 2.6; please standardize the rounding.","section":"Sec. 2.6 and Abstract"},{"comment":"The criteria for selecting the 30 representative vision models are not given; please describe the selection procedure or state that it is a convenience sample.","section":"Sec. 2.6"}],"recommendation":"major_revision","confidential_remarks":"The paper's strong claims outrun the evidence as presented. The reliance on a self-cited hypothesis (ref [47]) for the core graph construction, and the post-hoc threshold adjustments for DINOv2/MAE, are the main concerns. I recommend that the editor require the specific validations and sensitivity analyses listed in the major comments before considering the paper for publication."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: this is a substantial empirical effort with a genuine new idea—comparing model attention topology to intrinsic brain networks without stimulus-bound alignment. The scale is impressive: 151 models, 62k head graphs, public code, and the descriptive findings (arc-shaped geometry, DINOv2 drop, DeiT scaling inversion, null correlation with ImageNet) are not in the cited literature. I'd rather see this paper refereed than desk-rejected.\n\nThe soft spot is load-bearing. The spatial attention graph is built only from positional embeddings and learned Q/K matrices, with no input content (Eq 2). That's fine as an explicit modeling choice if it's tested, but the paper adopts it from ref [47] (same group) and does not validate it here. The stress-test concern is real and concrete: for all RoPE LLMs and LMMs, they substitute GPT-2 or ViT-base absolute embeddings as P_base, interpolated and rescaled, rather than using the model's own RoPE. So the reported convergence of RoPE models near C3/C4, and the \"deep fusion\" story in Sec 2.5, may be an artifact of a shared borrowed P_base. That covers most of the language and multimodal models in the study. A sensitivity check with at least one alternative P_base, or better, with actual content-dependent attention maps on a sample of inputs, would quickly show whether the geometry holds. It's surprising the limitations section doesn't mention this.\n\nThere's also a self-referential flavor to the brain-likeness score: PC1 is estimated from the same head set being scored, and the 0.8/0.6 matching thresholds and k=4 are chosen from the same data. No permutation nulls or confidence intervals are reported. These are fixable with a bit more care, but they make the headline numbers less trustworthy than the prose suggests.\n\nOverall: the paper is a worthwhile descriptive contribution to brain-AI alignment, and the authors have been unusually generous with code and data. The empirical phenomena are probably real as properties of the method; whether they're properties of the models themselves is not yet established. I'd send it to peer review, but condition acceptance on a serious re-analysis of the RoPE models and proper statistical baselines. If the authors can't do that, I'd treat the specific RoPE findings as preliminary.","headline":"Large, well-intentioned mapping effort, but the RoPE model results are built on borrowed positional embeddings and the content-free assumption is untested, so the headline arc geometry is provisional.","tokens_in":21461,"tokens_out":2903,"would_cite":false,"duration_ms":24779,"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":"A seven-dimensional Brain-like Space maps 151 Transformer models by attention-head topology to seven resting-state brain networks.","keywords":["Brain-like Space","Transformer attention topology","functional brain networks","brain-AI alignment","graph-theoretic similarity","positional encoding","self-supervised vision models","resting-state fMRI"],"falsifier":"Rebuild the space using content-dependent attention matrices obtained by feeding real tokens through the same 151 models, keeping the same five graph metrics and seven network targets; if the reported arc and four clusters do not reproduce, the positional-only graph is not capturing the organization the paper claims to measure.","tokens_in":20436,"feed_emoji":"🧠","tokens_out":9153,"duration_ms":77363,"temperature":0.7,"pith_summary":"The paper tries to establish that the internal organization of any Transformer-based model can be placed on a single geometric axis shared with the human brain, without running any input through the model. It does this by comparing the graph topology of each attention head with seven canonical resting-state brain networks and arranging the 151 models in a seven-dimensional \"Brain-like Space.\" The reported result is an arc-shaped distribution: models trained for global semantic abstraction, and language-dominant models, sit near higher-order cognitive networks, while models trained to reconstruct local detail sit near sensory networks. If the claim holds, it would give researchers a task-free, modality-agnostic way to ask whether an artificial system organizes information the way a brain does, and to compare vision, language, and multimodal models on the same terms.","feed_headline":"151 Transformers line up on one brain-likeness arc","feed_subtitle":"Graph-theoretic comparison with seven brain networks separates global-semantic from local-detail models—no input needed.","key_machinery":"The load-bearing construction is the spatial attention graph, defined without any input content as the softmax of position-based query-key products in Eq. (2), with the absolute positional embedding matrix and learned query and key matrices as the only inputs; for rotary-encoding models the paper borrows absolute embeddings and rescales them to match weight statistics. Each graph is described by five graph-theoretic metrics, and the cosine similarity of that five-dimensional signature to the signatures of the seven canonical functional brain networks becomes one coordinate. The seven coordinates place every attention head as a point in the Brain-like Space, on which PCA and k-means reveal the arc and four clusters.","core_discovery":"On the paper's own terms, every attention head of every Transformer model is embedded as a point in a seven-dimensional space whose coordinates are cosine similarities between a five-metric graph signature (clustering, modularity, degree spread, shortest paths, global efficiency) and the corresponding signatures of seven functional brain networks extracted from resting-state fMRI of 1,042 participants. Across 62,480 attention heads from 151 models, the points form a continuous arc that the authors divide into four clusters of increasing brain-likeness. Language-dominant models concentrate in the most brain-like cluster; vision models split by pretraining, with global-semantic variants (DINO, DINOv3, BEiT, AugReg-trained ViTs) near the cognitive end and local-reconstructive variants (MAE, DeiT3, DINOv2) near the sensory end. Multimodal models with rotary positional encoding fuse their vision and language components toward the cognitive end, while learnable-position models separate them. Fine-tuning and instruction tuning change the positions only slightly, and brain-likeness scores are not significantly correlated with ImageNet Top-1 accuracy (r = 0.266, p = 0.156).","pith_inferences":["A natural extension, not stated by the paper, is to use the space as an architecture-level diagnostic: if randomly initialized Transformers already occupy meaningful positions, the arc is set by architecture and positional encoding rather than learning.","The same construction could be applied to non-attention architectures by substituting their spatial interaction graphs; if CNNs' fixed receptive fields land near the sensory end, the global-sensory dichotomy would look like a property of architecture rather than training alone.","Because the alignment score tracks training objectives but not ImageNet accuracy, it could serve as a cheap, task-free monitor for drift toward local-detail processing during fine-tuning or distillation.","The non-significant accuracy correlation does not establish a causal trade-off between brain-likeness and performance; it only shows the two measures can vary independently in the sampled vision models."],"forward_implications":["Any Transformer-based model can be scored for brain-likeness without processing any input, so vision, language, and multimodal models become directly comparable on a single organizational axis.","Training objectives that push global semantic abstraction—self-distillation with semantic consistency, masked token prediction, Mixup-based augmentation—move vision models toward higher-order cognitive networks, while pixel-reconstruction and CNN-distillation objectives push them toward sensory networks.","RoPE-based multimodal models show deep fusion of vision and language components in the space, whereas models with learnable positional encodings show a division of labor, with vision components shifting to less brain-like clusters.","Brain-likeness is not a proxy for ImageNet performance: the reported correlation is weak and non-significant (r = 0.266, p = 0.156), so organizational similarity and downstream task accuracy can part ways.","Fine-tuning and instruction tuning leave a model's brain-like organization largely unchanged, suggesting that the organization is set during pretraining."],"supporting_citations":[{"why":"Supplies the load-bearing hypothesis that intrinsic spatial interaction structure is primarily determined by positional encoding, which the paper adopts in Eq. (2).","marker":"[47]"},{"why":"Defines the AugReg data augmentation strategy whose global-disruption effects drive vision models toward higher-order networks.","marker":"[14]"},{"why":"Defines the 3-Augment strategy used by DeiT3, the low-alignment comparison case.","marker":"[15]"},{"why":"Defines DINO self-distillation with semantic consistency, used as the semantic-abstraction example.","marker":"[20]"},{"why":"Defines BEiT masked token prediction, supporting the semantic-abstraction training-objective result.","marker":"[21]"},{"why":"Source of DINOv2's patch-level contrastive loss and high-resolution final stage, used to explain reduced brain-likeness.","marker":"[23]"},{"why":"Defines MAE pixel-reconstruction objective, the detail-reconstruction extreme with no high-threshold matches.","marker":"[24]"},{"why":"Provides the seven-network functional atlas used to define the Brain-like Space axes.","marker":"[44]"},{"why":"Supplies the resting-state fMRI dataset that yields the group-level functional connectivity matrix.","marker":"[40]"},{"why":"Supplies the second resting-state fMRI dataset used alongside the first for the group-level connectivity estimate.","marker":"[41]"}],"fun_headline_variants":["Transformer heads trace an arc of brain-likeness","Brain-mapping reveals a spectrum of model alignment","One arc links 151 AI models to human brain networks","Task-free map shows models on a brain-likeness curve","No accuracy payoff: brain-likeness arc defies ImageNet"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"An attention graph is drawn only from position information and learned query and key weights, with no actual input content, based on the assumption that a model's spatial interaction structure is set by its positional encoding; if content-dependent attention dominates real Transformers, the space measures positional schemes instead of model organization.","fun_headline_variants_meta":{"raw":{"variants":["Transformer heads trace an arc of brain-likeness","Brain-mapping reveals a spectrum of model alignment","One arc links 151 AI models to human brain networks","Task-free map shows models on a brain-likeness curve","No accuracy payoff: brain-likeness arc defies ImageNet"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000284,"raw_usage":{"total_tokens":1682,"prompt_tokens":961,"completion_tokens":721,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":577,"completion_tokens_details":{"reasoning_tokens":640}},"tokens_in":577,"tokens_out":721,"duration_ms":6463,"temperature":1.0,"reasoning_tokens":640,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T15:41:39.340430+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Rebuild the space using content-dependent attention matrices obtained by feeding real tokens through the same 151 models, keeping the same five graph metrics and seven network targets; if the reported arc and four clusters do not reproduce, the positional-only graph is not capturing the organization the paper claims to measure.","supporting_citations":[{"cited_title":"In: Eu ropean Conference on Computer Vision, pp","cited_arxiv_id":null,"evidence_quote":"Defines the 3-Augment strategy used by DeiT3, the low-alignment comparison case."},{"cited_title":": Increasing diversity in connectomics with the chinese human connectome project","cited_arxiv_id":null,"evidence_quote":"Supplies the second resting-state fMRI dataset used alongside the first for the group-level connectivity estimate."}],"review_version":1}