NeuroCogMap: Multi-Modal Cognitive Mapping

• NeuroCogMap is a framework that formalizes structured compressions of high-dimensional states into interpretable maps across robotics, neuroimaging, hippocampal mapping, concept modeling, and LLM interpretability.
• It employs distinct methodologies—including graph sparsification, GLM and logistic regression, topological data analysis, successor representations, and sparse autoencoders—to target specific inferential goals.
• The approach demonstrates trade-offs between representation granularity and computational efficiency, achieving significant reductions in memory use and improved predictive accuracy in diverse applications.

NeuroCogMap is a label used across several research lines that formalize “cognitive maps” as structured internal representations rather than as a single canonical algorithm. In the arXiv literature, the name denotes a graph-based compact mapping system for long-term robot SLAM (Zeng et al., 2019), a methodology for bidirectional mapping between task-fMRI activation maps and cognitive ontologies (Schwartz et al., 2013), algebraic-topological reconstructions of hippocampal cognitive maps from CA1 activity together with synaptic-topological models of map formation (Sorokin et al., 2022, Dabaghian, 2018), a successor-representation model that builds conceptual maps from word embeddings (Stoewer et al., 2023), and a system-level framework that organizes sparse-autoencoder features in LLMs into functional parcels linked to capabilities, failure modes, and human cortical responses (Sun et al., 1 Jul 2026). The common denominator is the construction of compact, interpretable, or topologically meaningful mappings between internal states and behavioral, semantic, or spatial structure.

1. Scope and terminological usage

The literature does not use NeuroCogMap for a single standardized object. In some cases it is the explicit name of a framework, as in the robot-mapping system and the 2026 LLM-interpretability framework. In other cases, the label is used to organize a methodology around cognitive ontologies, hippocampal topology, or successor representations. A recurrent misconception is therefore to treat NeuroCogMap as one architecture with one mathematical core; the papers instead define distinct frameworks that operate on different state spaces, different observables, and different inferential targets.

Domain	Represented object	Core formalism
Robotics	Long-term environment map	Pose-graph SLAM with sparsification
Neuroimaging	Brain activity and cognitive terms	GLM and weighted logistic regression
Hippocampal topology	Place-cell coactivity and arena topology	Simplicial complexes and persistent homology
Concept modeling	Semantic relations among words	Successor representation
LLM interpretability	Internal functional organization	SAE parcels, clustering, and encoding models

These uses nevertheless converge on a shared representational motif: a map is treated as a structured compression of high-dimensional experience. In the robot case, compression is literal graph sparsification; in neuroimaging, it is ontology-constrained decoding and forward inference; in the hippocampal literature, it is topological recovery of $\beta_1$ and related invariants; in conceptual modeling, it is semantic organization under the successor matrix $M$; and in LLM analysis, it is a mesoscopic parceling of latent features into reproducible functional systems.

2. Compact cognitive mapping in robotics

In robotics, NeuroCogMap is a directed graph $\mathcal G=(V,E)$ whose vertices are poses $$v_i=(x_i,y_i,\theta_i)\in\mathbb{R}^2\times[-\pi,\pi)$$ and whose edges encode relative motion, with sequential edges derived from odometry and loop-closure edges derived from visual template matches (Zeng et al., 2019). Its defining contribution is to keep map growth bounded during long exploration by combining two biologically inspired sparsification mechanisms: neighborhood fields and scene integration.

Neighborhood fields implement sparse vertex insertion. The scalar field

$g(d,\theta)=(1+\alpha d)(1+\beta\theta)$

depends on odometric translation $d$, absolute orientation change $\theta$, and tunable gains $\alpha,\beta>0$. A new pose vertex is created only if

$g(d,\theta)>\delta.$

Equivalently, the thresholds $d_{\rm th}=(\delta-1)/\alpha$ and $M$0 imply that any motion with $M$1 or $M$2 forces a new vertex. If consecutive motions do not satisfy the threshold, intermediate vertices are discarded and sequential edges are composed. Additional pruning removes “short” edges $M$3 as noise artifacts.

Global map optimization is formulated as a robust non-linear least-squares problem,

$M$4

where $M$5 and the residual contains translational and angular consistency terms, with the final angle wrapped into $M$6. The robust kernel $M$7, exemplified by Huber loss, down-weights outlying loop closures. The implementation exploits Ceres Solver’s sparse Cholesky or QR factorization.

A second efficiency mechanism clusters loop closures by time interval. Incoming loop edges are accumulated into a time-contiguous cluster if both $M$8 and $M$9; otherwise the current cluster is finalized and one batch optimization is launched. OpenMP is used to distribute Jacobian evaluation and factorization, and scene integration is then applied: if an optimized loop-closure pair satisfies

$\mathcal G=(V,E)$0

then $\mathcal G=(V,E)$1 is eliminated, its edges are rewired to $\mathcal G=(V,E)$2, and the revisited place no longer accumulates duplicate vertices.

Evaluation on the public iRat Australia dataset, with a monocular visual SLAM system in a rat-like maze, showed strong size reduction. Standard SLAM grew to 3,911 vertices and 5,182 edges; scene integration alone yielded 2,191 vertices and 2,152 edges; and neighborhood fields with $\mathcal G=(V,E)$3, $\mathcal G=(V,E)$4, plus integration, yielded 497 vertices and 602 edges. Vertex-count growth was approximately linear for the standard map but nearly flat after 200 s for the full stack. The compact map preserved all four major junctions and loop closures with less than 15% orientation offset versus overhead ground truth, and each batch optimization with fewer than 1,000 poses took on average 30 ms in real time on a quad-core laptop. Relative to standard pose-graph SLAM implementations such as g2o, GTSAM, or Ceres alone, the method reduced memory and computation by 80–90% in long-run scenarios, at the cost of a less fine-grained representation along very straight corridors.

3. Cognitive ontologies and bidirectional inference in neuroimaging

In imaging neuroscience, NeuroCogMap denotes a methodology for mapping cognitive ontologies to and from the brain by combining ontology labeling, dimensionality reduction, forward inference, and reverse inference across a heterogeneous corpus of task-fMRI studies (Schwartz et al., 2013). The ontology used is CogPO, which organizes task paradigms into stimulus modality, explicit stimulus, instructions, and overt response. Experimental conditions are annotated by subsets of ontology terms, yielding a binary annotation matrix $\mathcal G=(V,E)$5.

The data pipeline assembled 19 task-fMRI studies, approximately 486 subjects, 131 contrast-map types, and 3,826 total contrast maps. All studies were re-preprocessed through SPM with realignment, slice-timing correction, coregistration, normalization to MNI space, and smoothing. Each contrast map was represented as a voxel vector $\mathcal G=(V,E)$6 with $\mathcal G=(V,E)$7. To reduce dimensionality, the method first applied spatially constrained Ward agglomerative clustering to form approximately 15,000 contiguous parcels, then averaged voxel intensities within each parcel, and finally retained the top approximately 30% most discriminative parcels by one-way ANOVA F-test, producing feature vectors $\mathcal G=(V,E)$8 with $\mathcal G=(V,E)$9–$$v_i=(x_i,y_i,\theta_i)\in\mathbb{R}^2\times[-\pi,\pi)$$0.

Forward inference was expressed through a voxel-wise GLM across all studies,

$$v_i=(x_i,y_i,\theta_i)\in\mathbb{R}^2\times[-\pi,\pi)$$1

with FWER correction at 5% used to test $$v_i=(x_i,y_i,\theta_i)\in\mathbb{R}^2\times[-\pi,\pi)$$2 and produce term-specific forward-inference maps. Reverse inference treated each ontology term as a one-vs-rest classification problem and fit an $$v_i=(x_i,y_i,\theta_i)\in\mathbb{R}^2\times[-\pi,\pi)$$3-regularized logistic regression,

$$v_i=(x_i,y_i,\theta_i)\in\mathbb{R}^2\times[-\pi,\pi)$$4

with class-balanced sample weights

$$v_i=(x_i,y_i,\theta_i)\in\mathbb{R}^2\times[-\pi,\pi)$$5

and a bias adjustment

$$v_i=(x_i,y_i,\theta_i)\in\mathbb{R}^2\times[-\pi,\pi)$$6

Inference used convex optimization rather than MCMC or variational Bayes, with L-BFGS and regularization selected by 10-fold stratified shuffle-split nested inside each leave-one-study-out fold.

Evaluation used leave-one-study-out cross-validation so that test maps were always drawn from a held-out study. Precision and recall were compared against K-nearest-neighbor and Naive Bayes baselines. The weighted logistic models substantially outperformed both baselines in precision–recall across all terms. Rare terms in the long tail benefited most from the weighted logistic loss, which improved recall on under-represented classes without sacrificing global precision. The learned reverse-inference $$v_i=(x_i,y_i,\theta_i)\in\mathbb{R}^2\times[-\pi,\pi)$$7 maps coincided with known functional specializations, including fusiform face area for “faces,” auditory cortex for “words,” and frontal eye fields for “saccades.” The resulting framework therefore established a bidirectional statistical link between activation patterns and cognitive content, with the ontology serving both as an annotation language and as a structural prior that prevents trivial study-specific decoding.

4. Topological and synaptic formulations of hippocampal cognitive maps

In the hippocampal literature, NeuroCogMap is associated with algebraic-topological reconstructions of environmental structure from CA1 population activity and with models that connect synaptic reliability to the emergence or failure of spatial maps (Sorokin et al., 2022, Dabaghian, 2018). The underlying theoretical setting is that place-cell coactivity encodes the topology of the animal’s environment, and that simplicial complexes, homology groups, and Betti numbers provide a formal language for recovering this topology.

One formulation begins from the topological definitions of simplicial complexes $$v_i=(x_i,y_i,\theta_i)\in\mathbb{R}^2\times[-\pi,\pi)$$8, chain groups $$v_i=(x_i,y_i,\theta_i)\in\mathbb{R}^2\times[-\pi,\pi)$$9, boundary maps $g(d,\theta)=(1+\alpha d)(1+\beta\theta)$0, homology groups $g(d,\theta)=(1+\alpha d)(1+\beta\theta)$1, and Betti numbers $g(d,\theta)=(1+\alpha d)(1+\beta\theta)$2, with $g(d,\theta)=(1+\alpha d)(1+\beta\theta)$3 counting connected components and $g(d,\theta)=(1+\alpha d)(1+\beta\theta)$4 counting loops. Under the Nerve theorem, if a cover $g(d,\theta)=(1+\alpha d)(1+\beta\theta)$5 of the space has contractible finite intersections, then the nerve complex

$g(d,\theta)=(1+\alpha d)(1+\beta\theta)$6

is homotopy-equivalent to the space. In the hippocampal case, place fields are treated as approximately convex subsets of $g(d,\theta)=(1+\alpha d)(1+\beta\theta)$7, so the nerve can recover the number of holes in the arena. Dowker duality further relates a time-series complex on neurons to a point-cloud complex on time indices built from a binary activity matrix.

The experimental implementation recorded four adult male C57Bl/6J mice exploring circular O-shaped arenas with 0, 1, 2, or 3 non-transient obstacles, so that the true $g(d,\theta)=(1+\alpha d)(1+\beta\theta)$8 values were 0, 1, 2, and 3. CA1 activity was measured with GCaMP6s and an Inscopix nVista HD miniscope at 20 fps, and behavior was tracked by overhead camera at 20 fps. Preprocessing used motion correction and background flattening in CaImAn and neuron detection via CNMF-E. Candidate cells were validated by spike intensity threshold, round radial shape, transient duration at most 2 s, and merging of spatially overlapping candidates with identical traces. The typical yield was approximately 500 real cells versus approximately 50 “fake” candidates.

Place-cell identification normalized traces to $g(d,\theta)=(1+\alpha d)(1+\beta\theta)$9 and binarized activity by a threshold $d$0, heuristically $d$1. Significance was then assessed by both mutual information,

$d$2

and spatial information,

$d$3

Only cells significant by both scores, for example in the top 20th percentile, were retained, and stationary frames were dropped to remove non-spatial neurons and flatten occupancy. This reduced the cell set by approximately 50%.

Two reconstruction strategies were then evaluated. The first was the Dowker or nerve-style time-series complex

$d$4

followed by persistent homology of $d$5 and $d$6. The second was a point-cloud approach using the time series $d$7, with either Vietoris–Rips complexes

$d$8

or persistent homology after Isomap embedding. Among dimension-reduction methods, Isomap with $d$9–15 yielded the most consistent recovery of topological loops; PCA gave a crude but visible hole; t-SNE and UMAP were not robust; and Mapper often overcounted loops unless tuned carefully. Quantitatively, the nerve-theorem method recovered $\theta$0 exactly in 9/10 trials, Isomap plus persistent homology in 8/10, and PCA-based visual counting in 7/10.

A complementary model incorporated synaptic unreliability into the coactivity complex. With a readout window $\theta$1 ms, the instantaneous coactivity complex $\theta$2 contains precisely those cell tuples that co-fire in $\theta$3. Synaptic transmission probabilities $\theta$4 are drawn from a log-normal distribution with mode $\theta$5, and a simplex enters the effective complex only if all requisite transmissions and the readout response succeed. The learning time is then defined by

$\theta$6

Numerically,

$\theta$7

with $\theta$8–$\theta$9 in typical runs. Below $\alpha,\beta>0$0, no finite time suffices to recover the correct Betti signature. Weakening synaptic transmission sharply increases learning time, prolongs the death times of spurious cycles, and shrinks the learning region in the space of firing rate $\alpha,\beta>0$1, place-field size $\alpha,\beta>0$2, and cell count $\alpha,\beta>0$3. Compensation is possible through increased firing, larger place fields, or larger ensembles, with empirical scalings $\alpha,\beta>0$4 with $\alpha,\beta>0$5, $\alpha,\beta>0$6 with $\alpha,\beta>0$7, and $\alpha,\beta>0$8 with $\alpha,\beta>0$9.

5. Conceptual cognitive maps from successor representations

A distinct NeuroCogMap formulation models conceptual maps by training neural networks to approximate successor-representation rows from word embeddings (Stoewer et al., 2023). The architecture accepts a pre-computed spaCy embedding vector, applies a dropout layer with $g(d,\theta)>\delta.$0, passes the result through a single fully connected hidden layer with a nonlinear activation, and outputs a 60-dimensional softmax vector, one unit for each memory state in the training vocabulary.

The mathematical core is the successor representation

$g(d,\theta)>\delta.$1

with value function

$g(d,\theta)>\delta.$2

Here the transition matrix $g(d,\theta)>\delta.$3 (denoted $g(d,\theta)>\delta.$4 in the paper) is derived from pairwise cosine similarities between word embeddings,

$g(d,\theta)>\delta.$5

The discount factor $g(d,\theta)>\delta.$6 sets the representational scale: small $g(d,\theta)>\delta.$7 favors local associations, whereas $g(d,\theta)>\delta.$8 yields broader, more global structure.

The experimental setup used 60 training words, divided into 20 animals, 20 vehicles, and 20 furniture items, plus 30 validation words with 10 held-out words per category. Two independent networks were trained, one with $g(d,\theta)>\delta.$9 and one with $d_{\rm th}=(\delta-1)/\alpha$0, using learning rate $d_{\rm th}=(\delta-1)/\alpha$1, 500 epochs, and batch size 20. Visualization was performed with classical MDS rather than t-SNE, because t-SNE was judged sensitive to hyperparameters and prone to distorting global geometry. Cluster quality was measured by the Generalized Discrimination Value (GDV), which is negative for tight, well-separated clusters.

The reported geometry depends strongly on scale. For $d_{\rm th}=(\delta-1)/\alpha$2, the combined GDV over all points was $d_{\rm th}=(\delta-1)/\alpha$3, with $d_{\rm th}=(\delta-1)/\alpha$4 on training and $d_{\rm th}=(\delta-1)/\alpha$5 on validation; the corresponding MDS projection showed three emergent clusters, one for each semantic category, and validation words fell into their respective groups. For $d_{\rm th}=(\delta-1)/\alpha$6, the combined GDV was $d_{\rm th}=(\delta-1)/\alpha$7, with $d_{\rm th}=(\delta-1)/\alpha$8 on training and $d_{\rm th}=(\delta-1)/\alpha$9 on validation; the projection showed a more uniform spread with more overlap among held-out words. The framework therefore treats a conceptual map not as a symbolic taxonomy but as a learned predictive geometry over semantic transitions, with scale controlled directly by $M$00.

6. Functional organization of LLMs

In the 2026 framework, NeuroCogMap is a cognitive-neuroscience-inspired system for organizing LLM internals into functional parcels and linking them to interpretable functions, cognitive capabilities, a four-level hierarchy, model failures, and human cortical responses (Sun et al., 1 Jul 2026). A functional parcel is defined as a non-spatial group of sparse-autoencoder feature directions whose task-evoked activation profiles are selective and reproducible across inputs, semantically coherent within the group, and interpretable as a unitary functional computation.

The pipeline begins by attaching an SAE to each transformer layer $M$01 and extracting sparse activations

$M$02

with reconstruction through decoder directions $M$03. Activations are averaged over tokens in the answer span. Features are screened by nonzero-activation rate, using thresholds 0.03 for Gemma2 and 0.01 for Llama-3.1, and by variance threshold $M$04. A selectivity index

$M$05

is computed, and only the top 50%–80% most selective features are retained. After concatenation across layers into $M$06, columns are $M$07-normalized and truncated SVD is used to retain at least 80% of variance.

Parcel discovery uses a k-means-style clustering in the reduced feature space with an added layer-coherence penalty. For feature $M$08 from layer $M$09 and parcel $M$10 with centroid $M$11 and layer distribution $M$12, the assignment cost is

$M$13

The number of parcels is selected by sweeping $M$14 from 10 to 300 and combining a gap statistic, LLM-assisted functional-description quality, and non-redundancy into

$M$15

For Gemma2-2B, this criterion peaked at $M$16 parcels.

Parcels are then annotated from top-activating examples, activation-weighted keywords, and dataset distributions. A human audit of 60 parcels reported that 93.3% passed independent-rater checks for faithfulness and specificity. Capabilities are linked to parcels by combining task-evoked activation, steering effects, and semantic similarity. For dataset $M$17 and parcel $M$18,

$M$19

and a fused activation–intervention score is

$M$20

Capability scores $M$21 over datasets are combined with textual similarity $M$22 to define a signed parcel–capability mapping

$M$23

Positive values indicate supporting relations and negative values suppressive ones. The resulting capabilities are organized into four operational layers: L1 perception and attentional gating, L2 representation and knowledge integration, L3 abstraction and meta-cognitive control, and L4 situated application and social interaction. The hierarchy was supported by higher within-layer semantic similarity than between-layer similarity, with paired t-tests giving $M$24, and by prerequisite effects in a synthetic two-hop reasoning benchmark, with Welch t-tests giving $M$25.

A central claim of the framework is the separation of representational systems from behavioral-control systems. For normative and pathological response sets, parcel-level and capability-level activations and connectivities are contrasted through signatures such as

$M$26

together with analogous connectivity contrasts $M$27 and $M$28. Hallucination and bias produce larger parcel and capability deviations in belief-related parcels, whereas refusal failure and sycophancy concentrate in control-related parcels. A 12-dimensional detection feature set combines positive and negative parcel/capability activation indicators, connectivity mismatches relative to normative means, and prototype-alignment terms. These feed a logistic-regression classifier with $M$29 regularization and class-balanced weighting, evaluated by AUROC under stratified 5-fold cross-validation. The paper states that this detector consistently outperformed baselines including token entropy, perplexity, self-consistency, hidden probing, early-logits SVM, SmoothLLM, and attention-based detectors.

The same internal signatures are used for targeted intervention. The three most positive and three most negative parcels are selected, and steering coefficients are set by

$M$30

with generation-time injection scaled by $M$31. The reported outcome was substantial improvement in factual accuracy for hallucination, fairness accuracy for bias, refusal accuracy for refusal failure, and reduction in sycophancy rate.

NeuroCogMap was also evaluated as a bridge to human neuroscience. On the LeBel story-listening fMRI dataset with Schaefer100 parcels and Yeo7 networks, a ridge-encoding model fit parcelwise responses as

$M$32

with $M$33 selected by inner cross-validation over $M$34 to $M$35. NeuroCogMap parcel activations achieved mean prediction $M$36, outperforming WordRate ($M$37), Word2Vec ($M$38), BERT ($M$39), Language-Context ($M$40), and Language-Standard ($M$41), with gains concentrated in Default, Frontoparietal Control, and Salience/Vent Attention networks. In a separate two-step fMRI task, the same framework achieved mean $M$42 across ROIs, exceeding Word2Vec ($M$43), BERT ($M$44), Language-Context ($M$45), and Language-Standard ($M$46). Across five Psych-101 experiments, participant-level NeuroCogMap activations predicted Gemma2-2B fit quality with Pearson $M$47 from 0.21 to 0.60. The framework also guided an extension of a Dual-systems Model, producing lower AIC than both the baseline and a behaviour-only model in Two Step Task One (262.45 versus 268.77 and 268.73) and Two Step Task Two (465.95 versus 478.29 and 473.53).

Taken together, these results define the most system-level use of the NeuroCogMap label: a mesoscopic atlas of internal LLM function that is simultaneously descriptive, interventional, and comparative across artificial and biological cognition.