Automated Psychiatric Nosology via Representation-Learning-Based Partitioning of Knowledge Graph

Abstract

This study introduces a proof-of-concept approach for automated, data-driven psychiatric nosology. By mining the scientific literature into a multiplex knowledge graph of symptoms, treatments, biomarkers, and outcomes, it tests whether a dimensional framework can be derived independently of existing diagnostic systems such as the Diagnostic and Statistical Manual of Mental Disorders (DSM-5), International Classification of Diseases (ICD-11), Hierarchical Taxonomy of Psychopathology (HiTOP), and Research Domain Criteria (RDoC). Scientific findings were extracted and integrated into a multiplex graph, which was then partitioned using information-theoretic algorithms. Quantitative evaluations assess parsimony (via Minimum Description Length), stability (bootstrapped Variation of Information and Adjusted Rand Index), and alignment (Normalized Mutual Information and Adjusted Rand Index) with established dimensional models. Raw psychiatric coverage checks on the unpartitioned graph indicate that HiTOP labels retain precision 0.186 / recall 0.595 (TP = 11,114 of 59,785 psychiatric nodes) while RDoC labels retain precision 0.062 / recall 0.694 (TP = 3,695 of 59,785), confirming that label leakage is limited but non-zero after nosology filtering. Partitioning the multiplex graph with the RGCN-SCAE compresses the 59,786 psychiatric nodes into 11 interpretable clusters (node-weighted semantic coherence = 0.18) that achieve statistically significant enrichment for 62.5 % of HiTOP domains, while the stability stress test collapses deterministically into two macro-clusters whose HiTOP/RDoC ARI values are 0.164/0.022 with a 90 % coherence CI width below 3e-5. Preliminary inspections therefore indicate that unsupervised, information-theoretic partitioning can recover interpretable transdiagnostic structure consistent with major dimensional frameworks if the knowledge graph is high enough quality. This work demonstrates the potential for information-theoretic graph methods to yield a scalable, self-updating, and reproducible framework for psychiatric classification that unifies biological and clinical findings without relying on predefined categories.

Introduction

Psychiatric classification remains dominated by categorical systems such as the Diagnostic and Statistical Manual of Mental Disorders (DSM-5) and the International Classification of Diseases (ICD). While clinically useful, these frameworks have been widely criticized for high comorbidity, arbitrary diagnostic thresholds, and limited biological validity [1], [2]. Meta-analytic research increasingly demonstrates that psychiatric disorders rarely conform to discrete boundaries but instead share overlapping symptoms and biological substrates. Quantitative modeling of symptom covariance and genetic correlation further supports the view that psychopathology is continuous and hierarchically organized rather than composed of isolated disease entities [3]-[5].

In response, dimensional alternatives have emerged. The Hierarchical Taxonomy of Psychopathology (HiTOP) organizes symptoms into empirically derived spectra [6]-[8], while the Research Domain Criteria (RDoC) links psychopathology to neural and behavioral systems [9], [10]. Both frameworks move beyond categorical diagnoses and capture transdiagnostic variance more effectively, yet neither has been universally adopted. Despite their conceptual strengths, HiTOP and RDoC each face scalability challenges: HiTOP depends on manually curated symptom correlations, and RDoC’s domain structure evolves slowly as new evidence accumulates. Another central challenge also remains: integrating dimensional constructs with diverse biological and clinical findings in a manner that is both valid and scalable. Information-theoretic and graph-based approaches offer a principled alternative, emphasizing model parsimony and data-driven emergence of latent structure.

Automated methods-ranging from clustering of genetic risk variants to network-based analyses of neuroimaging-demonstrate that algorithmic approaches can yield biologically coherent groupings that differ from traditional nosologies [11], [12]. However, applications in psychiatry have thus far been limited in scope, often relying on predefined categories or single modalities, raising concerns about reproducing existing biases rather than discovering new structure [14]–[18].

Literature Review

Psychiatric nosology has long been dominated by categorical systems such as the DSM and the ICD. These frameworks define discrete diagnostic entities and draw strict boundaries between normal and pathological states. However, their limitations are well established, including high comorbidity rates, arbitrary thresholds, and limited biological validity [6], [3]. Categorical standards such as DSM-5 impose rigid yes/no decisions regarding diagnosis [9], despite evidence from meta-analytic research indicating that most psychiatric disorders are better conceptualized as continuous spectra rather than binary categories [1]. These concerns have motivated the development of dimensional alternatives, notably the HiTOP [9] and the RDoC [2]. Each represents a unique effort to reconceptualize psychiatric nosology: HiTOP is symptom-driven and data-based, while RDoC is neuroscience-driven and theory-based. This review examines evidence from biomarkers, transdiagnostic dimensions, and computational models. Findings converge on the theme that psychiatric disorders are not discrete entities but reflect shared, transdiagnostic mechanisms with disorder-specific features sometimes co-occurring and thus are best represented dimensionally.

Biomarkers of Psychopathology

Biomarker research increasingly demonstrates that biological abnormalities rarely remain unique to individual DSM categories. Resting-state fMRI studies of large population cohorts have shown consistent disruptions in default mode, salience, and executive networks across depression, schizophrenia, and anxiety [11]. These findings were derived using graph-theoretic analyses of connectivity patterns, but despite their reproducibility across studies, they often lack disorder-specificity, limiting their diagnostic utility. A meta-analysis pooling voxel-based morphometry data from more than 15,000 patients demonstrated gray matter reductions in the anterior cingulate cortex and insula across mood, anxiety, and psychotic disorders [12]. While the scale of this synthesis strengthens the claim of shared neurobiological substrates, heterogeneity in scanning methods and patient samples makes it difficult to identify causal pathways. Rather than supporting disorder-specific neural substrates, these findings indicate shared biological bases.

Structural neuroimaging studies further suggest that biological variation aligns more closely with dimensional models than categorical diagnoses. Meta-analysis shows that structural abnormalities cluster in ways consistent with HiTOP spectra, particularly internalizing and externalizing dimensions [5]. Evidence also supports the integration of multimodal approaches. Reviews emphasize that relying on single modalities such as neuroimaging alone produces inconsistent results, while combining genetics, neuroimaging, peripheral biomarkers, and clinical measures offers greater potential for identifying robust transdiagnostic markers [8]. Collectively, biomarker research points to the conclusion that psychiatric disorders share overlapping biological substrates that map more naturally onto dimensional frameworks.

Transdiagnostic Dimensions

Dimensional models provide alternative frameworks for capturing shared variance across disorders. HiTOP is a transdiagnostic nosology that organizes psychopathology hierarchically, with broad spectra such as internalizing, externalizing, and thought disorder encompassing narrower syndromes [9]. A meta-analysis of 35 structural MRI studies involving over 12,000 participants found that abnormalities in cortical thickness and subcortical volume clustered in patterns consistent with HiTOP’s internalizing and externalizing spectra [5]. This supports the dimensional framework, though the cross-sectional nature of the data limits conclusions about developmental trajectories. Functional neuroimaging studies have shown that individuals scoring high on internalizing dimensions exhibit hyperactivity in amygdala–hippocampal circuits across both mood and anxiety disorders, whereas externalizing spectra are associated with reduced prefrontal regulation of striatal reward pathways across disruptive behavior and substance use disorders [7]. These convergent findings provide neurobiological validation for dimensional constructs, although effect sizes remain modest. Overlap across networks also persists, which is not a critical weakness for dimensional validity but does represent a limitation for clinical utility.

The RDoC initiative provides a complementary approach by focusing on functional domains of behavior and neural systems [2]. Domains such as cognition, negative valence, and arousal cut across traditional diagnoses and anchor psychopathology in specific neural circuits. This approach differs from HiTOP by beginning with neuroscience constructs rather than symptom clustering, yet both converge on the principle that psychiatric syndromes are dimensional rather than categorical.

Meta-analytic research further supports the conclusion that dimensional continua provide a superior fit for psychiatric phenomena compared to categorical boundaries [1]. Overall, transdiagnostic models such as HiTOP and RDoC demonstrate greater validity than traditional nosologies, as they capture shared liability, reduce artifacts of comorbidity, and align more closely with underlying neurobiological processes.

Automated Methods

In addition to biomarkers and dimensional frameworks, computational approaches offer formal models for psychiatric nosology. Conceptual work in computational psychiatry has explored how diagnostic systems might be reframed in terms of latent processes and mathematical models. For example, Bzdok and Meyer-Lindenberg propose a framework of “computational nosology and precision psychiatry” that emphasizes integrating behavioral, neural, and genetic data into quantitative models of psychopathology [14]. Although largely theoretical, such approaches highlight the potential for computational methods to reconfigure diagnostic standards. At the same time, skepticism remains about the sufficiency of computational methods for redefining nosology. Surveys of experts in computational psychiatry report concerns regarding circularity, where machine learning reproduces the categories it was trained on, lack of causal grounding in many statistical approaches, and neglect of subjective experience [15]. These critiques highlight the importance of ensuring that computational models do not merely replicate existing diagnostic systems but instead provide meaningful explanatory frameworks while also remaining true to patients’ lived experiences.

Beyond psychiatry, researchers in medicine have attempted to automate the construction of nosological frameworks. Automated clustering methods have been applied to thousands of diseases using shared molecular features such as gene expression and protein interactions, yielding biologically coherent groupings that diverge from ICD classifications [16]. While this illustrates the feasibility of algorithmically derived nosologies, the reliance on molecular data alone neglects clinical and symptomatic dimensions critical for psychiatric classification. Other approaches focus on ontology engineering at scale, including automated mapping of clinical vocabularies to biomedical ontologies [10] and the generation of large biomedical knowledge graphs that infer relationships among diseases, treatments, and biomarkers [17]. These methods demonstrate that automated classification is technically feasible, though their application in psychiatry remains limited.

Some early work has extended automation directly to the psychiatric nosology domain. For example, graph-based clustering of polygenic risk variants has been used to identify subtypes of schizophrenia, suggesting a potential path toward biologically grounded psychiatric nosology [13]. Machine learning applied to electronic health records has also been used to detect latent subtypes of depression and other disorders, pointing to the possibility of automated reclassification based on large-scale clinical data [18]. Although these attempts are preliminary, they indicate that psychiatry may follow trends in other medical domains by adopting automated, data-driven methods to complement conceptual and dimensional frameworks.

Conclusion

Across biomarkers, dimensional models, and computational frameworks, a consistent theme emerges: psychiatric disorders share biological and symptomatic substrates that transcend categorical nosologies. Evidence from neuroimaging and meta-analyses demonstrates that common abnormalities appear across multiple disorders. Dimensional models such as HiTOP and RDoC capture this overlap through hierarchical spectra and neuroscience-based domains. Computational approaches illustrate the potential for integrating categories and dimensions into mechanistic models, though critiques caution against over-reliance on machine learning.

A clear gap remains. Despite converging evidence that categorical systems are insufficient, there is currently no unified diagnostic standard that integrates biomarkers, dimensional constructs, and computational frameworks. Existing studies tend to focus on isolated modalities or conceptual frameworks, underscoring the need for integrative approaches that are biologically valid, clinically useful, and transdiagnostic in scope. This highlights the need for continued research into models that combine these strands into a biologically valid, parsimonious, and widely applicable classification system.

Research Question

Can a proof-of-concept transdiagnostic dimensional psychiatric nosology be developed in an automated way by mining the scientific literature into a multiplex knowledge graph and partitioning it using information-theoretic methods, and how does its structure compare with HiTOP and RDoC in terms of cluster coherence, parsimony, stability, and alignment?

Hypothesis

The automated pipeline is expected to yield a dimensional nosology whose structural efficiency remains within 10% of the HiTOP and RDoC label cardinalities (cluster-count ratio ≥ 0.9 relative to each framework) while maintaining SentenceTransformer-based semantic coherence means-and their bootstrap 90% confidence intervals-at or above the medians observed for matched HiTOP/RDoC partitions. Stability will be demonstrated by bootstrapping both the adjusted Rand index (ARI), targeting ≥ 0.2 of each framework’s self-alignment baseline, and the coherence estimates (targeting confidence interval widths ≤ 0.15), showing that clusters remain consistent under resampling despite corpus heterogeneity. Alignment will be evaluated with normalized and adjusted mutual information, homogeneity/completeness, and ARI (targets ≥ 0.75, ≥ 0.75, and ≥ 0.70 respectively), supported by Benjamini–Hochberg–corrected hypergeometric enrichments in which at least 60% of clusters achieve FDR < 0.05, per-cluster precision/recall/F1 summaries, and medoid-based semantic cosine similarities to canonical HiTOP/RDoC descriptors. To ensure that enrichment is not only cluster-dense but label-relevant, the coverage-adjusted enrichment rate-the fraction of HiTOP/RDoC label nodes captured by significant overlaps-should also reach ≥ 0.60. Collectively these metrics test whether compression-oriented clustering on the literature can reproduce the breadth of symptom- and mechanism-focused nosologies while remaining parsimonious, stable, and interpretable.

By testing whether an automated, data-driven method can reproduce or extend the dimensional structure of leading nosologies, this research explores the feasibility of a scalable and self-updating framework for psychiatric classification-one that could bridge the gap between biological findings and clinical phenomena without the overhead of manually defined diagnostic categories.

Hypothesis Metrics Justification

Parsimony metrics: Structural economy is captured by the cluster-count ratio $|C| / |L_fw|$, where $|C|$ denotes the number of clusters with at least one aligned node and $|L_fw|$ is the number of HiTOP or RDoC labels. Semantic compactness is computed for every cluster by embedding member-node text with a SentenceTransformer model and averaging the pairwise cosines: for embeddings ${e_i}$ and cluster size $n$, the mean coherence is $(2 / [n(n-1)]) * Σ_{i<j} cos(e_i, e_j)$. Also reported is a log-size–weighted variant and non-parametric form of confidence intervals by bootstrap resampling the cosine sample 64 times.
Stability metrics: To quantify robustness, the pipeline reruns alignment on bootstrap subgraphs of the full knowledge graph and computes the ARI for each replicate. ARI is derived from the contingency table of cluster–label overlaps as $\frac{\sum_{ij}(n_{ij}^2) - [\sum_i a_i^2 \sum_j b_j^2]/N^2}{0.5[\sum_i a_i^2 + \sum_j b_j^2] - [\sum_i a_i^2 \sum_j b_j^2]/N^2}$, correcting for chance agreement. The bootstrap distribution is summarized (mean, spread, and percentile intervals) and coherence confidence interval widths are tracked as an orthogonal check on semantic stability.
Alignment metrics: Global correspondence is assessed with normalized mutual information (NMI) using the arithmetic mean denominator, adjusted mutual information that subtracts the expected mutual information under a permutation null, the homogeneity/completeness/v-measure trio, and ARI. These rely on the shared node set between the learned partition and HiTOP/RDoC labels. Full confusion matrices accompany the summary statistics so that reviewers can inspect which domains contribute most to each score.
Per-cluster alignment metrics: Following the enrichment step, each cluster is paired with the label that attains the minimum false-discovery–rate value. Precision is $overlap / cluster_{size}$, recall is $overlap / label_{support}$, F1 score has the normal definition, and the overlap rate is $overlap / (cluster_size + label_support - overlap)$.
Statistical enrichment: For a cluster of size $n$ and a label with support $K$ in a population of $N$ aligned nodes, a one-sided hypergeometric survival probability $P(X ≥ k)$ where $k$ is the observed overlap: $\sum_{i=k}^{min(n,K)} [\binom{K}{i} \binom{N-K}{n-i}] / \binom{N}{n}$ is computed. Benjamini–Hochberg correction [19] is then applied across all cluster–label pairs to produce FDR-controlling q-values. Only labels with $q$ < 0.05 are carried into the narrative alignment tables.
Semantic correspondence diagnostics: Medoid analysis identifies, for each cluster, the node whose embedding maximizes the average cosine to other members. Correlation summaries compute Pearson and Spearman coefficients between coherence statistics (means, confidence interval bounds, size-weighted variants) and alignment scores (F1, purity, overlap rate), indicating whether semantic tightness predicts external alignment.

By using a knowledge graph that was mined from the scientific literature into a multiplex graph and partitioning it with information-theoretic methods, this project draws inspiration from generative modeling’s emphasis on latent structure while also addressing the critiques of purely data-driven ML. Unlike many ML approaches that risk reproducing existing DSM or RDoC categories (by training directly on them), this method removes those labels during graph construction. Any observed alignment that later emerges with HiTOP or RDoC therefore reflects genuine structural similarity rather than trivial lexical overlap, ensuring a more independent test of whether automated nosology converges with established frameworks.

Materials and Methods

Knowledge Graph Dataset

The knowledge graph was created from a subset of the IKraph dataset [20]. This data is then pared down to only the psychiatrically relevant nodes and edges using heuristics (final stats: 59786 nodes / 69248 edges). See code notes below for exact filtering command. First, loading of the disease, drug, protein, and DNA modality tables happens and the hybrid PsychiatricRelevanceScorer is invoked, which fuses ontology membership, learned group labels, psychiatric drug neighborhoods, and cosine similarity to psychiatric prototype text snippets into a continuous relevance score.

Only disease vertices meeting these criteria become seed indices for the downstream graph walk. Any edge whose source or target index appears in the psychiatric seed set is retained, optionally intersected with a whitelist of relation labels. After collection, each edge is checked against the relation-role constraints prepared during initialization so that invalid edges are removed (i.e. "drug_disease" edges must actually bind drug-like nodes to disease-like nodes). For every surviving edge, the extractor reconstructs a unique node table, joining in the disease/drug/protein/DNA/text attributes, and exporting JSON blobs for downstream consumption. Psychiatric scoring outputs (psy_score, psy_evidence, boolean flags, and the final is_psychiatric decision) are carried through so that later models can weight nodes by clinical relevance. Nodes lacking these columns receive neutral defaults to keep the table schema consistent.

The filtered node/edge frames are projected into a multiplex graph, preserving node metadata and relation labels. During weighted projection each undirected edge receives a prior determined by its relation label and is modulated by the mean psychiatric score of its incident nodes, suppressing ties to weakly psychiatric neighbors while never dropping them outright. Finally, the pipeline streams the psychiatric subgraph into Parquet tables plus undirected, weighted GraphML files, yielding artifacts whose every node and edge has survived both the semantic filters and the psychiatric relevance scoring requirements described above. The final, filtered graph was 59786 nodes and 69248 edges.

Preventing Biased Alignment

Because the alignment metrics used to compare the emergent nosology with established frameworks (HiTOP and RDoC) can be artificially inflated if the same vocabulary appears in both the input graph and the target taxonomies, an explicit node-level screen that scans every attribute (type tokens, source strings, identifiers, synonyms, DSM/ICD codes, etc.) and flags anything that looks like an existing diagnostic label was implemented. The intended workflow ran this filter before partitioning so that only symptoms, biomarkers, treatments, and other non-nosological concepts would survive, leaving diagnostic vocabularies solely for downstream alignment checks. In practice, however, removing all those nodes disrupted the entire knowledge graph: every surviving edge touched at least one filtered vertex, so purging them collapsed the graph into isolated nodes (full degeneracy) and made partitioning impossible. To avoid that failure mode the graph used for training retains most of the nosology nodes. In the final graph used for partitioning, only 815 nosology-related nodes were removed and 11115 such nodes out of 59786 total nodes (18.6%) remained.

Partitioning

Two complementary strategies were tested for discovering mesoscale structure in the multiplex psychopathology graph. First, a stochastic block model (SBM) [21], which provides a probabilistic baseline that infers discrete clusters by maximizing the likelihood of observed edge densities across multiple resolution levels. This family of models gives interpretable, DSM-like partitions together with principled estimates of uncertainty, but inherits SBM’s familiar computational burdens-quadratic scaling in the number of vertices and a rigid parametric form for block interactions. This was used as a baseline. The other model architecture tested was a Relational Graph Convolutional Network Self-Compressing Autoencoder (RGCN-SCAE). This model was trained exclusively on the full graph to derive a single global partitioning that captures the complete relational structure. It learns a compact latent partition of the full knowledge graph while preserving relation-specific structure through low-rank factorization and hard-concrete gating. The rest of this section pertains solely to the RGCN-SCAE partitioning.

Encoder Architecture

The encoder couples a Deep Sets attribute encoder [22] with a stacked RGCN layers that produces a temperature-controlled assignment matrix of shape |Nodes| $\times$ |Clusters|, forming the probabilistic basis for downstream partitioning via differentiable hard-concrete ($L_0$) gates [23]. Each node is first encoded by a DeepSets-style node attribute encoder, implementing the Zaheer et al. $\rho$/$\phi$ formulation, that is permutation-invariant. This component integrates arbitrarily structured metadata-text learned embeddings, biomarkers and ontology terms. It can expand its vocabulary online, allowing new attributes to be assimilated without retraining existing embeddings. Each node label is first embedded with the pritamdeka/S-Scibert-snli-multinli-stsb SentenceTransformer, producing a 768-dimensional biomedical vector that already reflects domain-specific semantic organization. To prevent these high-capacity descriptors from overwhelming the other DeepSet inputs, they are contracted with a Johnson–Lindenstrauss projection to dimension $d_p$ (default 128, configurable via --text-encoder-projection-dim, or disabled by setting that flag to 0). For every unique combination of graph, model, and projection width, the projection matrix is generated exactly once: hashing the ordered (node_id, node_text) pairs with SHA-256, treating the digest as the seed of a standard-normal random number generator, and sampling the matrix in a single pass. Because the seed depends solely on data and hyperparameters, the projection is deterministic across runs and introduces no learnable weights that the downstream network could co-opt. The projected vectors are optionally $L_2$-normalized and cached under _NAME_TEXT_EMBED_ATTR, ensuring that the DeepSet encoder consumes a compact text representation alongside boolean indicators, bucketized counts, and other scalar attributes. This procedure behaves like a classical JL embedding [24] that preserves pairwise geometry while capping the influence of text semantics. Cached .npz blobs store the sentence encoder identifier, normalization flag, fingerprint, and projection dimensionality, so subsequent executions reload the identical tensors unless either the graph text or the relevant hyperparameters are modified.

The resulting descriptor is concatenated with: A learned node-type embedding, encoding categorical identity in a compact, regularized form and graph-positional encodings derived from standardized Laplacian eigenvectors, normalized per subgraph to maintain numerical stability when batch sizes or graph orders vary, both of which are only relevant during stability check. The fused vectors are processed through a relation-aware additive message-passing stack of graph convolutional layers using basis decomposition (a parameter sharing technique) across relation types. Each layer is followed by LayerNorm #TODO change from GraphNorm since only using complete graph now and default to GraphNorm for stability check, a ReLU activation, and optional dropout. Because the encoder operates directly on the supplied edge_index, it naturally accommodates cyclic connectivity and multiplex relation types without special handling. During training the encoder applies degree-proportional edge dropout, symmetric degree normalization and inverse-frequency relation reweighting. Together these steps keep gradients stable on multiplex graphs whose degree distributions and relation frequencies span orders of magnitude. The additive message-passing uses an RGCN stack with basis decomposition per relation and per-layer GraphNorm (or LayerNorm on request). After the stack, node embeddings can be augmented with a lightweight virtual-node context that injects graph-level statistics without scaling with |Vertices|. Let $h_i$ denote the resulting embedding for node $i$ and $P = [p_1, \dots, p_K]$ the prototype bank maintained via an exponential moving average. Embeddings are $L_2$-normalized, $\hat{h}i = h_i / \lVert h_i \rVert_2$, and scored against prototypes with a temperature-controlled softmax $$s{ik} = \frac{\hat{h}_i^{\top} p_k}{\tau_a} + \log g_k,$$ where $\tau_a$ is the current assignment temperature and $g_k$ is the sample from the cluster hard-concrete gate. Sinkhorn balancing applies $T$ rounds of alternating row/column normalization with entropic regularization $\varepsilon$ to $\exp(s)$, yielding a doubly-stochastic assignment matrix $Q$ that approximately satisfies $Q\mathbf{1} = \mathbf{1}$ and $Q^\top \mathbf{1} = (n/K), \mathbf{1}$. The hard-concrete gates follow Louizos et al.'s [23] reparameterization with expected sparsity $\mathbb{E}[\mathrm{L}_0] = \sigma\left(\log \alpha - \tau_g \log \frac{-\gamma}{1+\zeta}\right)$, where $\alpha$ is the gate logit and $(\gamma, \zeta)$ are the stretch parameters. Annealing $\tau_g$ prevents premature collapse. A momentum memory bank anchors embeddings for repeated node IDs across sampled subgraphs, and the encoder records the batch-index vector $b \in {0,\dots,B-1}^N$ that the decoder and degree-orthogonality penalty consume downstream. The assignment matrix $Q$ and auxiliary tensors are then ready for $L_0$ sparsification.

Decoder Architecture

The decoder maps the Sinkhorn-balanced cluster assignments back to multiplex edge logits through a low-rank relational energy model gated by the hard-concrete masks. Relation-specific inter-cluster affinities are produced via a low-rank factorization: every relation learns coefficients over a shared cluster basis, bringing the parameter count down to $\mathcal{O}(R \cdot C \cdot rank_r)$ instead of $\mathcal{O}(R \cdot C^2)$ (with $rank_r \ll C$). A learnable absent-edge bias per relation absorbs the background sparsity so the decoder can focus its capacity on informative deviations.

For each mini-batch the decoder streams positive edges and sampled negatives in configurable chunks, multiplying source assignments by the gated relation weights and accumulating reconstruction losses. This, combined with gradient checkpointing can be used to avoid exhausting CPU/GPU memory. Relation frequencies reweight both positive and negative terms so that rare relation types retain influence, while optional type-restricted negative sampling and per-graph budgets keep contrastive updates aligned with ontology constraints. Entropy-aware reweighting of negatives, inverse-frequency scaling, and chunked evaluation preserve size invariance and stability even on the largest subgraphs. The relation-specific logits follow $\ell_{ijr} = a_i^{\top} W_r a_j + b_r,$ with assignment vectors $a_i = Q_{i\cdot}$ and low-rank weight matrices $W_r = \sigma(F_r B) \odot G_r$, where $F_r \in \mathbb{R}^{C\times d}$, $B \in \mathbb{R}^{d\times C}$, and $G_r$ is the current hard-concrete gate sample.

Training

Commands

For the main experiment results, the exact command ran was:

python3.10 train_rgcn_scae.py data/ikgraph.graphml \
  --require-psychiatric --min-psy-score 0.33 --psy-include-neighbors 0 \
  --force-full-graph \
  --negative-sampling 1.0 \
  --gradient-checkpointing \
  --pos-edge-chunk 512 --neg-edge-chunk 512 \
  --gate-threshold 0.35 \
  --min-epochs 100 --max-epochs 250 \
  --checkpoint-path ikraph.pt --checkpoint-every 10 \
  --calibration-epochs 50 \
  --cluster-stability-window 10 \
  --text-encoder-model pritamdeka/S-Scibert-snli-multinli-stsb --text-encoder-normalize --text-embedding-cache auto \
  --mlflow --mlflow-experiment exploration --mlflow-run-name ikraph \
  --npz-out ikraph-training.npz

For the training stability check:

python3.10 train_rgcn_scae.py data/ikgraph.filtered.graphml \
  --require-psychiatric --min-psy-score 0.33 --psy-include-neighbors 0 \
  --negative-sampling 1.0 \
  --gradient-checkpointing \
  --pos-edge-chunk 512 --neg-edge-chunk 512 \
  --gate-threshold 0.35 \
  --min-epochs 100 --max-epochs 250 \
  --checkpoint-path ikraph-stability.pt \
  --checkpoint-every 10 \
  --calibration-epochs 50 \
  --cluster-stability-window 10 \
  --text-encoder-model pritamdeka/S-Scibert-snli-multinli-stsb --text-encoder-normalize --text-embedding-cache auto \
  --mlflow --mlflow-experiment exploration --mlflow-run-name ikraph-stability \
  --npz-out ikraph-training-stability.npz \
  --stability \
  --ego-samples 512

Mitigating Cluster Collapse and Runaway Imbalance

Cluster gates can collapse into a handful of latent units unless they are continually encouraged to share responsibility for the data. Each mini-batch is therefore projected into a near doubly-stochastic assignment matrix via a Sinkhorn normalization, and the prototypes that receive that mass are updated with an exponential moving average that discourages any single cluster from monopolizing the representation. A per-graph entropy hinge penalizes assignments that become overly concentrated on a small subset of clusters, while a Dirichlet prior stabilizes the long-term expected gate usage. The gate samples themselves are monitored in bits, so that low-entropy configurations trigger a restorative penalty. Temperature schedules modulate both gating and assignments, starting from a diffuse exploratory regime before gradually sharpening the decisions. A momentum memory bank anchors embeddings for repeated nodes, ensuring that overlapping ego-nets reinforce rather than contradict one another, and the hierarchy monitor that sits in the trainer audits convergence by tracking ARI, variation of information, and effective cluster counts. It can rewind to the most stable checkpoint if any of those statistics deteriorate.

Stabilizing Hard-Concrete Gates

The hard-concrete relaxations that implement sparsity are prone to discontinuities and dead units. To keep them responsive, sparsity penalties are warmed up gradually so that the encoder and decoder can settle before being pushed toward sparsity. Gate logits are clipped before entering the hard-concrete transform, preventing them from saturating in regions where gradients vanish. Each gate draw is blended with an exponential moving average, reducing the variance of stochastic samples without biasing their mean. When a gate does fall dormant yet still receives assignment mass, a revival routine resets its log-parameter toward neutrality, reintroducing it into the active set. Detailed diagnostics-expected $L_0$ counts, instantaneous gate entropy, and gate samples-are recorded every epoch so that emerging instabilities are observable.

Gate Revival Hook

During every optimisation step the trainer measures both the instantaneous hard-concrete sample for each cluster gate and its mean assignment mass within the mini-batch. If a gate’s sample drops below revival_gate_threshold (default 0.05) while the same cluster is still attracting more than revival_usage_threshold of the assignment probability (default 0.05), the hook treats the gate as “dormant but demanded” and rewrites its underlying log_alpha back to the neutral revival logit (0.0). That reset returns the gate to the middle of the stretched hard-concrete interval so that subsequent temperature annealing and sparsity penalties can decide afresh whether the unit should remain active.

Setting either threshold to 0 disables the hook entirely, which can be helpful when intentionally pruning clusters. Custom values can be supplied by overriding SelfCompressingRGCNAutoEncoder(..., revival_gate_threshold=..., revival_usage_threshold=...) inside train_rgcn_scae.py (or an equivalent trainer), ensuring that scripted runs inherit the desired policy without modifying the core module. The hook operates before cluster-usage statistics are logged, so metrics such as expected_active_clusters, gate_entropy_bits, and realized_active_clusters in MLflow or console histories always reflect the post-revival state.

Controlling Message-Passing Drift

Multiplex message passing threatens to over-smooth node representations, especially in the presence of hubs. The encoder therefore drops edges at random and in proportion to degree, weakening the dominance of high-degree nodes while preserving the connectivity needed for learning. Feature normalization relies on graph-local statistics, which prevents mini-batch composition from distorting the scale of activations. Positional encodings derived from Laplacian eigenvectors are standardized within each graph, maintaining comparable variance even when graph sizes differ drastically.

Addressing Degree and Hub Bias

Even after the adjustments above, the latent space can correlate with degree if left unregulated. A dedicated orthogonality penalty therefore measures the squared correlation between latent coordinates and the logarithm of node degree, driving the optimizer toward representations that encode semantics rather than centrality. Essentially, this inhibits the encoder from embedding nodes along the principal degree axis of the graph, which is a common degeneracy in heterogeneous graphs, thereby encouraging reliance on relational and attribute structure rather than degree. Degree-aware dropout complements this penalty by reducing the influence of hubs at the message-passing stage itself.

Balancing Multiplex Relation Frequencies

Relation types occur with wildly unequal frequencies, so the decoder would otherwise learn to ignore rare but semantically meaningful edges. Each relation is accordingly reweighted by the inverse of its empirical frequency before its contribution enters the loss. The decoder’s low-rank factorization further protects rare relations by tying them to a shared basis of cluster interactions: even sparsely observed relations can appropriate expressive factors without requiring a full, unshared parameter matrix, whereas abundant relations are free to explore a broader span of that basis.

Hardening Negative Sampling

Negative sampling supplies contrastive signal, but only if negatives remain challenging and diverse. The sampler generates negatives independently inside each graph component, respecting node-type compatibility and halting once a per-graph budget is reached so that large components do not dominate the mini-batch. Positive and negative logits are evaluated in memory-bounded chunks to avoid destabilizing the optimization on densely connected subgraphs. Most importantly, the contribution of negative edges is modulated by gate entropy: when the gating distribution remains broad, negatives exert a baseline influence; as the gates sharpen and entropy drops, their weight increases, deliberately steering the model toward harder discrimination precisely at the point where overconfidence could arise.

Maintaining Cross-Batch Consistency

Because training proceeds on overlapping ego-nets rather than fully shuffled samples, nodes can recur in distinct contexts. A momentum memory bank keyed by canonical node identifiers stores a running estimate of each embedding and penalizes deviations from that trajectory when the node reappears. At the same time, attribute dictionaries are cached and pre-encoded so that repeated visits do not inject stochastic variation through duplicated encoding passes. Together these measures ensure that the latent representation evolves coherently across batches.

Latent Regularization and Diagnostics

Per-graph latent magnitudes and variances are explicitly regularized: squared norms are averaged per graph to prevent large components from dominating, and a KL term pushes the empirical mean and variance toward a unit Gaussian. Assignment entropy, cluster usage, gate samples, reconstruction losses, and time spent in negative sampling are logged after every epoch, producing an audit trail that can be consulted when diagnosing instability or reproducing experimental claims.

Trainer-Level Safeguards

The trainer orchestrates the preceding mechanisms while enforcing practical guardrails. Mini-batches are constructed by a budget-aware sampler that limits the number of nodes admitted per step, so even pathological subgraphs remain tractable. Gradient accumulation, gradient clipping, and optional mixed precision provide additional numerical headroom. Stability-aware stopping criteria monitor sliding windows of the principal metrics-usually the number of active clusters-and halt the run once those metrics stay within prescribed absolute and relative bounds. Checkpointing is performed atomically alongside optional MLflow logging, enabling deterministic recovery and rigorous experiment tracking.

Collectively, these interventions ensure that the self-compressing RGCN maintains stable dynamics across the multiplex psychopathology graph while remaining verifiable under standard academic reporting conventions.

Objective

The objective is a minimization of a composite loss function that couples reconstruction fidelity with sparsity, entropy, and structural regularizers. The training loop minimizes

$$ \mathcal{L}_{\text{total}} = \begin{align*}\mathcal{L}_{\text{recon}} + \lambda_{L0}^{\text{enc}},\mathcal{L}_{\text{cluster-L0}} + \lambda_{L0}^{\text{dec}},\mathcal{L}_{\text{inter-L0}} + \lambda_{H},\mathcal{L}_{\text{entropy}} + \lambda_{\text{Dir}},\mathrm{KL}(u,|,u_{\text{prior}}) + \lambda_{\text{emb}},\mathcal{L}_{\text{emb-norm}} + \lambda_{\text{KLD}},\mathcal{L}_{\text{graph-KLD}} + \lambda_{\text{cons}},\mathcal{L}_{\text{consistency}} + \lambda_{\text{gate}},\mathcal{L}_{\text{gate-entropy}} + \lambda_{\text{deg}},\mathcal{L}_{\text{degree}}, \end{align*} $$

Term	Meaning	Purpose
$\mathcal{L}_{\text{recon}}$	Per-graph BCE over observed edges and ratio-corrected negatives.	Ensures the decoder reproduces observed multiplex structure while penalizing spurious links.
$\mathcal{L}_{\text{cluster-L0}}$	Encoder gate expected $L_0$ penalty.	Encourages sparse cluster activation so latent capacity matches the data complexity.
$\mathcal{L}_{\text{inter-L0}}$	Decoder gate expected $L_0$ penalty.	Promotes sparsity in inter-cluster affinities, preventing dense relation matrices.
$\mathcal{L}_{\text{entropy}}$	Assignment entropy hinge keeping per-graph entropy above the floor.	Maintains diverse cluster usage within each ego-net to avoid local collapse.
$\mathrm{KL}(u,\|,u_{\text{prior}})$	KL divergence between observed cluster usage and the Dirichlet prior.	Aligns global cluster frequencies with the prescribed prior, deterring runaway imbalance.
$\mathcal{L}_{\text{emb-norm}}$	Mean squared latent magnitude per graph.	Keeps latent vectors bounded and comparable across differently sized subgraphs.
$\mathcal{L}_{\text{graph-KLD}}$	KL encouraging per-graph latent distributions toward unit Gaussians.	Regularises per-graph latent statistics to curb drift in mean and variance.
$\mathcal{L}_{\text{consistency}}$	Memory-bank consistency MSE for overlapping nodes.	Couples repeated node embeddings across batches to maintain cross-sample coherence.
$\mathcal{L}_{\text{gate-entropy}}$	Gate entropy hinge preventing collapse.	Reinflates gate diversity when stochastic samples become overly confident.
$\mathcal{L}_{\text{degree}}$	Squared correlation between latents and log degree.	Decouples latent geometry from degree-based artefacts and hub domination.

Reconstruction Loss and Entropy Controls

Five primary forms of degenerate or trivial solutions are guarded against in this model: uniform embeddings, local collapse, global collapse, decoder memorization, and latent drift. Absent-edge modeling via type-aware negative sampling penalizes trivial partitions even when node embeddings look uniform. The decoder contrasts observed edges against sampled non-edges inside each subgraph while operating on Sinkhorn-balanced assignment vectors $a_i$ rather than raw encoder features. For every relation r the decoder forms a low-rank, hard-gated interaction matrix $W_r$ (built from gated relation factors) and applies an absent-edge bias $b_r$. The reconstruction loss adds the average positive-edge binary cross-entropy and a ratio-corrected negative term for every graph g in the batch:

$$ \mathcal{L}_{\text{recon}} = \frac{1}{G} \sum_{g=1}^{G} \Bigg[ \frac{1}{|E_g|} \sum_{(i,j)\in E_g} \mathrm{BCE}\Big(\sigma(a_i^\top W_{r_{ij}} a_j + b_{r_{ij}}),1\Big) + \frac{|E_g|}{|\tilde{E}_g|} \sum_{(i',j')\in \tilde{E}_g} \mathrm{BCE}\Big(\sigma(a_{i'}^\top W_{r_{i'j'}} a_{j'} + b_{r_{i'j'}}),0\Big) \Bigg], $$

where:

Symbol	Meaning
G	Number of graphs (mini-batch components) evaluated in the loss.
E_g	Set of observed edges for graph $g$.
$\tilde{E}_g$	Negative samples generated for graph g under the current negative-sampling policy.
$	E_g
$	\tilde{E}_g
$a_i \in \Delta^{K-1}$	Sinkhorn-balanced cluster assignment for node i (probability vector over $K$ clusters).
$r{ij}$	Relation index of edge $(i, j)$; selects decoder parameters for that relation.
$W{r}$	Low-rank, hard-gated relation weight matrix for relation $r$.
$b_r$	Learnable absent-edge bias for relation $r$.
$\sigma(\cdot)$	Logistic sigmoid that converts logits to probabilities.
$\mathrm{BCE}(\hat{y}, y)$	Binary cross-entropy between probability $\hat{y}$ and label $y$.

Intuitively, the first term rewards high similarity for real edges while the second penalizes the model when it predicts high similarity for random, non-existent connections. Binary cross-entropy losses therefore accumulate over observed edges $(i,j,r) \in E$ and sampled negatives $(i',j',r)$. The negative-sample term is additionally scaled by a gate-entropy confidence factor $w_{\text{neg}} = 1 + \lambda \big(\max(H_g, H_{\min})^{-1} - 1\big)$, where $H_g = -\sum_k \pi_k \log_2 \pi_k$ denotes the gate entropy in bits computed from gate probabilities $\pi$, and $H_{\min}$ is the code-level entropy floor. This weighting emphasizes challenging negatives when gate entropy collapses, while leaving early, high-entropy phases unaffected.

However, this is not enough to prevent all situations of structure collapse. For example, a situation could arise where local structure collapses but global does not. Negative sampling does not penalize this because such coarse partitions can still separate positives from random negatives effectively. Entropy regularization on the cluster assignment matrix counteracts this tendency by enforcing a floor on per-graph assignment entropy. For each graph g, it computes $H_g = -\frac{1}{|V_g|} \sum_{i \in g} \sum_{k=1}^{K} p_{ik} \log p_{ik}$ and applies a hinge,

$$ \mathcal{L}_{\text{entropy}} = \lambda_H \cdot \frac{1}{G} \sum_{g=1}^{G} \max\bigl(0, H_{\text{floor}} - H_g\bigr), $$

so the term activates only when entropy dips below the target floor $H_{\text{floor}}$, where:

Symbol	Meaning
$H_g$	Mean assignment entropy for graph $g$, $-\frac{1}{
$\|V_g\|$	Number of nodes belonging to graph $g$.
$H_{\text{floor}}$	Target minimum entropy per graph (defaults to $\log K$ if unset).
$\lambda_H$	Weight assigned to the entropy penalty.

However, the entropy regularization only handles local degeneracy because it acts locally. The model could still produce a few large "meta-clusters" that reconstruct edges well but lack finer internal structure - all symptoms in one, all treatments in another, etc. To prevent this, the model matches the mean assignment usage against a Dirichlet-inspired prior stored as a categorical baseline $\pi$. Let $u_k = \frac{\sum_i p_{ik}}{\sum_{k'} \sum_i p_{ik'}}$ be the empirical cluster usage. It minimizes the KL divergence

$$ \mathcal{L}_{\text{Dirichlet}} = \lambda_{\text{Dir}} \sum_{k=1}^{K} u_k \log \frac{u_k}{\pi_k}, $$

where:

Symbol	Meaning
$u_k$	Empirical mean cluster usage, normalized so $\sum_k u_k = 1$.
$\pi_k$	Prior cluster usage probability derived from the user-specified Dirichlet concentrations (normalized once).
$\lambda_{\text{Dir}}$	Weight applied to the KL divergence penalty term.

Even with these local and global regularizers, the decoder can still exploit trivial optima by memorizing adjacency patterns rather than learning meaningful structure. This can occur when embeddings or decoder weights grow unbounded, allowing perfect reconstruction without informative latent geometry. To prevent this reconstruction-dominant collapse, the mean squared embedding norm per graph so that large batches do not dominate:

$$ \mathcal{L}_{\text{norm}} = \lambda_z \cdot \frac{1}{G} \sum_{g=1}^{G} \left( \frac{1}{|V_g|} \sum_{i \in g} |z_i|_2^2 \right), $$

where $\lambda_z$ is the scaling factor for the latent $L_2$ penalty and $z_i$ is Encoder embedding for node $i$ before Sinkhorn balancing.

Finally, to stop latent drift and keep graph-level statistics well behaved, regularization is added of the first two moments of each graph’s embedding distribution toward a zero-mean, unit-variance Gaussian:

$$ \mathcal{L}_{\text{mom}} = \frac{\lambda_{\text{KLD}}}{2G} \sum_{g=1}^{G} \sum_{d=1}^{D} \left( \mu_{g,d}^2 + \sigma_{g,d}^2 - \log \sigma_{g,d}^2 - 1 \right), $$

where:

Symbol	Meaning
$D$	Latent dimensionality of the encoder outputs.
$\mu_{g,d}$	Empirical mean of latent dimension d over nodes in graph $g$.
$\sigma_{g,d}^2$	Empirical variance of latent dimension $d$ over nodes in graph $g$ (clamped to stay positive).
$\lambda_{\text{KLD}}$	Weight of the moment-based regularizer.

Adaptive Subgraph Sampling for Stability Testing

A practical limitation of this approach is that it is trained on a single, fixed multiplex graph. Without a distribution of graphs, the model risks overfitting to idiosyncratic topological patterns rather than learning generalizable relational principles. To check the effect of training on only the full knowledge graph, a dataset was be created with different subgraphs sampled via node-hopping from randomly chosen seed nodes with the hop radius determined adaptively from local connectivity metrics such as node degree, clustering coefficient, and k-core index in order to preserve local connectivity and type proportions. For each seed s, a composite score $g(s) = z(c_s) + z(\kappa_s) - z(\deg_s)$ to select a hop radius $r(s) = \mathrm{clamp}_{[1,3]}(1 + \alpha g(s))$, encouraging larger neighborhoods in sparse or weakly clustered regions and smaller ones near dense hubs.

Symbol	Meaning	Notes
$s$	The seed node from which the local subgraph (ego-net) is grown.	Chosen randomly, optionally stratified by node degree or type.
$c_s$	The local clustering coefficient of node $s$.	Measures how interconnected $s$’s neighbors are. In undirected projection form:$c_s = \frac{2T_s}{k_s(k_s-1)}$, where $T_s$ = number of triangles through s.
$\kappa_s$	The k-core index (or core number) of node $s$.	Largest integer $k$ such that $s$ belongs to the k-core subgraph (all nodes with degree ≥ $k$). Reflects local structural “embeddedness.”
$\deg_s$	The degree of node $s$.	Number of edges incident on $s$ (can be total degree or weighted by relation type in multiplex setting).
$z(\cdot)$	The z-score normalization operator.	For any scalar node-level metric $(x_s):(z(x_s) = \frac{x_s - \mu_x}{\sigma_x})$, where $\mu_x$ and $\sigma_x$ are the mean and standard deviation of $x$ across all nodes in the graph.
$g(s)$	The composite connectivity score used to adaptively choose hop radius.	Higher $g(s)$ → larger $r(s)$; encourages exploring sparser regions more deeply.
$r(s)$	The hop radius (1–3) used to define the ego-net subgraph around seed $s$.	Determined by scaling $g(s)$ via $\alpha$ and clamping to the range [1,3]).

Each resulting subgraph consisted of the induced r-ball around the seed nodes, preserving local connectivity patterns and approximate node-type proportions without enforcing a fixed target size. This connectivity-aware hopping strategy generates a controlled distribution of partially overlapping ego-net subgraphs that collectively cover the full multiplex network, ensuring exposure to diverse local structures while maintaining coherence across samples.

Parameters of the RGCN-SCAE were shared across subgraphs to maintain a single shared partitioning in the latent space. Since node attributes (text-derived embeddings, types, biomarkers, etc.) are stable across subgraphs, meaningful structure can still be derived despite the lack of full context in each training example. The final partitioning is derived from running the full knowledge graph through the trained RGCN-SCAE. This procedure reframes training as an information-theoretic compression task applied repeatedly to partially overlapping realizations of the same knowledge manifold, allowing estimation of replication reliability and consensus structure while reducing overfitting to any single instantiation.

Comparison

Together, SBM offers a likelihood-grounded categorical perspective, while RGCN-SCAE furnishes a continuous latent manifold amenable to downstream regression or spectrum analysis. The two approaches are treated as triangulating evidence: concordant structure across them increases confidence in emergent transdiagnostic clusters, whereas divergences highlight fronts for qualitative review.

Aspect	Relational Graph Convolutional Network Self-Compressing Auto-Encoder (RGCN-SCAE)	Stochastic Block Model (SBM)
Representation	Learns continuous latent embeddings for nodes and relations; nonlinear, differentiable, expressive.	Assigns discrete cluster memberships via probabilistic inference on connectivity patterns.
Objective	Minimizes reconstruction loss → learns information-optimal embeddings that compress the multiplex graph while preserving semantic structure.	Maximizes likelihood under a generative model → partitions graph to best explain edge densities between groups.
Adaptivity	Learns directly from heterogeneous, weighted, typed edges and can incorporate node attributes, features, and higher-order dependencies.	Operates purely on adjacency structure assuming a fixed parametric form (block interaction matrix). Difficult to extend to new modalities.
Scalability	Much higher computational cost for training; can integrate multiple modalities in future.	Inference is typically O(N²), with N = #nodes in graph.
Output	Produces a latent manifold where distances encode both structural and semantic similarity - enabling continuous transdiagnostic spectra.	Produces discrete clusters - enforcing categorical partitions reminiscent of DSM-like divisions.

Results

All reported metrics are computed by first heuristically inferring HiTOP/RDoC labels by combining node-type priors with attribute-text patterns when explicit mappings are unavailable. Those inferred labels define the reference distributions for mutual information, enrichment, and coverage calculations, so every value in the results section is reproducible by rerunning the same pipeline with an identical graph snapshot and partition.

Baseline Psychiatric Label Coverage

The psychiatric-filtered knowledge graph contains 59,785 nodes before partitioning, which shows a HiTOP precision 0.186 / recall 0.595 (TP = 11,114, labeled nodes = 18,691) and an RDoC precision 0.062 / recall 0.694 (TP = 3,695, labeled nodes = 5,328). These values quantify the residual label leakage after removing most diagnosis terms-recall remains moderate because many HiTOP/RDoC signals survive the filter, but precision is very low because only 18.6 % (HiTOP) and 6.2 % (RDoC) of psychiatric nodes still carry reference labels.

HiTOP per-label coverage

Domain	Support	Overlap	Precision	Recall
Antagonistic Externalizing	143	60	0.001	0.420
Detachment	17	8	0.000	0.471
Disinhibited Externalizing	323	113	0.002	0.350
Internalizing	5,506	5,230	0.087	0.950
Obsessive/Compulsive	183	178	0.003	0.973
Somatoform	50	13	0.000	0.260
Thought Disorder	1,393	1,300	0.022	0.933
Unspecified Clinical	11,076	4,212	0.070	0.380

RDoC per-label coverage

Domain	Support	Overlap	Precision	Recall
Arousal/Regulatory Systems	177	62	0.001	0.350
Cognitive Systems	651	162	0.003	0.249
Negative Valence	3,952	3,288	0.055	0.832
Positive Valence	51	35	0.001	0.686
Sensorimotor Systems	281	96	0.002	0.342
Social Processes	216	52	0.001	0.241

Overall Metrics

Metric Class	Metric	Description	Target / Baseline	RGCN-SCAE Result	SBM Result
Parsimony	Cluster Count Ratio	Structural economy relative to HiTOP/RDoC label	count ≥ 0.9	HiTOP 11/8 = 1.38x; RDoC 11/6 = 1.83x	HiTOP 18,670/8 ≈ 2.33e3x; RDoC 18,670/6 ≈ 3.11e3x
	Node-weighted mean semantic coherence	Mean intra-cluster embedding cosine (SentenceTransformer)	≥ HiTOP/RDoC median	0.180	0.171
	Coherence 90 % CI width (bootstrap x 64)	Semantic compactness stability	≤ 0.15	2.3e-5 (node-weighted across 2 macro-clusters)	n/a
Stability	Adjusted Rand Index (bootstrapped subgraphs)	Resampling-based consistency of partitions	≥ 0.85 of full-graph ARI (HiTOP 0.112 ⇒ target ≥0.095; RDoC 0.038 ⇒ target ≥0.032)	HiTOP 0.164 / RDoC 0.022 (stability partition)	n/a
	Coherence CI width (across replicates)	Semantic stability across subsamples	≤ 0.15	≤3.0e-5 (all 64 bootstraps converged to the same partition)	n/a
Alignment (Global)	Normalized Mutual Information	Overall correspondence between learned and reference labels	≥ 0.75	HiTOP 0.116, RDoC 0.025	HiTOP 0.198, RDoC 0.088
	Adjusted Mutual Information	Chance-corrected variant	≥ 0.75	HiTOP 0.115, RDoC 0.020	HiTOP 0.048, RDoC -0.013
	Homogeneity / Completeness / V-measure	Purity and coverage of label mapping	≥ 0.75 each	HiTOP H=0.134, C=0.102, V=0.116; RDoC H=0.043, C=0.017, V=0.025	HiTOP H=0.696, C=0.115, V=0.198; RDoC H=0.659, C=0.047, V=0.088
	Adjusted Rand Index (against HiTOP/RDoC)	Cluster-label agreement	≥ 0.70	HiTOP 0.112, RDoC 0.038	HiTOP 0.016, RDoC -0.0013
Alignment (Per-cluster)	Precision	Fraction of cluster nodes matching label	-	HiTOP μ±σ = 0.623±0.117 (n=8); RDoC μ±σ = 0.622±0.409 (n=8)	HiTOP μ±σ = 0.992±0.062 (n=6,058); RDoC μ±σ = 0.993±0.080 (n=2,647)
	Recall	Fraction of label nodes captured	-	HiTOP μ±σ = 0.182±0.199; RDoC μ±σ = 0.167±0.189	HiTOP μ±σ = 7.8e-4±4.6e-3; RDoC μ±σ = 1.66e-3±6.0e-3
	F1 Score	Harmonic mean of precision and recall	-	HiTOP μ±σ = 0.233±0.207; RDoC μ±σ = 0.169±0.220	HiTOP μ±σ = 0.00148±0.0077; RDoC μ±σ = 0.00304±0.0095
	Overlap Rate	Jaccard-like measure of overlap	-	HiTOP μ±σ = 0.149±0.149; RDoC μ±σ = 0.114±0.176	HiTOP μ±σ = 7.6e-4±4.2e-3; RDoC μ±σ = 0.00154±0.0049
Statistical Enrichment	FDR-corrected Hypergeometric p value	Significance of cluster–label overlap	FDR < 0.05 for ≥ 60 % clusters	HiTOP: 62.5% of clusters have q<0.05; RDoC: 25%	HiTOP: 0.26%; RDoC: 0.038%
	Coverage-adjusted enrichment rate	Fraction of labeled nodes covered by significant clusters	≥ 0.6	HiTOP: 64%; RDoC: 56%	HiTOP: 28%; RDoC: 0.4%
Semantic Correspondence	Node-weighted medoid cosine similarity	Mean cosine of cluster medoid vs HiTOP/RDoC descriptor	-	0.169	0.149
	Coherence–F1 correlation	Correlation between semantic tightness and alignment	-	HiTOP Spearman 0.881 / Pearson 0.728; RDoC Spearman 0.786 / Pearson 0.633	HiTOP Spearman 0.420 / Pearson 0.471; RDoC Spearman 0.502 / Pearson 0.593
Label Coverage	Reference domains with ≥1 significant cluster	Fraction of HiTOP/RDoC domains attaining q<0.05 matches	≥ 0.6	HiTOP: 6/8 domains; RDoC: 4/6 constructs	HiTOP: 8/8 domains; RDoC: 5/6, but most hits are micro-clusters

Cluster Sizes

Gini coefficient: 0.642942

Gini coefficient: 0.686602

HiTOP Alignment Summary

Cluster ID	Label Match (HiTOP Domain)	Precision	Recall	F1 Score	q-value (FDR)	Medoid Cosine Similarity
RGCN-SCAE-0	Unspecified Clinical	0.586	0.150	0.239	2.21e-46	0.166
RGCN-SCAE-3	Internalizing	0.629	0.637	0.633	9.87e-227	0.157
RGCN-SCAE-154	Unspecified Clinical	0.761	0.028	0.054	2.08e-21	0.092
RGCN-SCAE-160	Unspecified Clinical	0.801	0.320	0.457	0.00e+00	0.123
RGCN-SCAE-212	Unspecified Clinical	0.558	0.140	0.224	2.02e-34	0.109
SBM-0	Unspecified Clinical	0.720	0.107	0.186	9.47e-67	0.167
SBM-1	Unspecified Clinical	0.729	0.101	0.177	3.63e-65	0.175
SBM-2	Unspecified Clinical	0.708	0.072	0.131	4.68e-41	0.161
SBM-3	Thought Disorder	0.531	0.078	0.137	1.94e-41	0.168
SBM-4	Unspecified Clinical	0.925	0.056	0.106	5.23e-73	0.181
SBM-5	Unspecified Clinical	0.614	0.047	0.087	2.79e-14	0.150
SBM-6	Thought Disorder	0.327	0.042	0.074	2.06e-09	0.145
SBM-7	Unspecified Clinical	0.526	0.046	0.085	1.54e-05	0.153
RGCN-SCAE Mean (± SD)	-	0.623±0.117	0.182±0.199.6e-3	0.233±0.207	q<0.05 coverage: 62.5%	0.169
SBM Mean (± SD)	-	0.992±0.062	7.8e-4±4.6e-3	0.00148±0.0077	q<0.05 coverage: 0.26%	0.149

RDoC Alignment Summary

Cluster ID	Label Match (RDoC Domain)	Precision	Recall	F1 Score	q-value (FDR)	Medoid Cosine Similarity
RGCN-SCAE-3	Negative Valence	0.908	0.606	0.727	2.42e-04	0.157
RGCN-SCAE-160	Cognitive Systems	0.147	0.259	0.188	1.93e-11	0.123
SBM-4	Cognitive Systems	0.333	0.093	0.145	3.90e-06	0.181
RGCN-SCAE Mean (± SD)	-	0.622±0.409	0.167±0.189	0.169±0.220	q<0.05 coverage: 25%	0.169
SBM Mean (± SD)	-	0.993±0.080	0.00166±0.00599	0.00304±0.00946	q<0.05 coverage: 0.038%	0.149

Cluster Snapshots (main partitioning run)

Cluster 3 - Negative Valence neurotransmission. The medoid node is Neurotransmitter Depression and its eight closest neighbors (e.g., Neurophysiological Depression, Depression Dysfunction, Depression Of Brain Activity) remain entirely within neurophysiology phrasing. This is the same cluster that drives the strong RDoC Negative Valence alignment in the table above, so we explicitly document it here as the clearest affective-neurochemical factor recovered by the encoder.
Cluster 160 - Parkinsonian cognitive systems. Centered on the medoid PD, its nearest nodes include PDD, pDCD, and PDQ, all abbreviations tied to Parkinson’s disease staging or questionnaires. It underpins the cognitive-systems precision entry for RGCN-SCAE-160, illustrating that the model isolates tightly condensed instrument jargon rather than mixing it with generic symptom language.
Cluster 212 - Depressive/anxiety behavioral language. With medoid Depressive Response and neighbors like Depressive-Related Behavior, Depressive Emotional Changes, and Depressive And Anxiety-Like, this cluster captures the broader behavioral lexicon spanning distress and anxious arousal. Its enrichment appears under the “Unspecified Clinical” rows, so surfacing the raw node names helps explain why it straddles multiple HiTOP domains even though the quantitative metrics classify it as clinically mixed.

Stability Metrics (Bootstrapped Subgraph and Semantic Consistency)

Framework	# Labels (Baseline)	# Clusters (Learned)	Cluster-Count Ratio	Mean Coherence (± 90 % CI)	Log-Size Weighted Coherence
HiTOP	8	2	2/8 = 0.25x	0.1607 ± 1.2e-5 (node-weighted)	0.1607 ± 1.2e-5
RDoC	6	2	2/6 = 0.33x	0.1607 ± 1.2e-5 (node-weighted)	0.1607 ± 1.2e-5
Overall Mean	7 (HiTOP/RDoC mean)	2	2/7 = 0.29x	0.1607 ± 1.2e-5	0.1607 ± 1.2e-5

Metric	HiTOP / RDoC References	Target	Value (Mean ± SD [90 % CI])
Adjusted Rand Index (bootstrap)	HiTOP = 0.164 / RDoC = 0.022	≥ 0.85 of full-graph ARI (HiTOP 0.112 ⇒ target ≥0.095; RDoC 0.038 ⇒ target ≥0.032	HiTOP: 0.164; RDoC: 0.022)
Node-Weighted Coherence 90 % CI width	0.1607 ± 1.2e-5	≤ 0.15	2.3e-5
Gate Entropy Stability	Graph-wide	Lower is better	0.885 ± <1e-3 bits (node-weighted gate entropy derived from cluster masses 41,690 and 18,096)
Effective Cluster Count Variance	Graph-wide	Lower is better	1.85 ± <1e-3 (computed as 2^H; no across-bootstrap variance observed)

The stability stress test run therefore has two distinguishable macro-clusters when summarized by cluster mass and entropy, while the hard argmax diagnostic used for realized_active_clusters collapses to a single winning cluster late in training. Both diagnostics indicate severe over-compression, but they measure different parts of the assignment process.

Training Dynamics

Realized Active Clusters (post-argmax)

Realized active clusters (after argmax assignment) for the main run. After initial oscillations between ~10–20 clusters, the model stabilizes at 11 active clusters. This behavior reflects successful compression without degeneracy.

Stability Test Realized Active Clusters (post-argmax)

Realized clusters during the stability stress test run. The hard argmax diagnostic collapses to a single realized cluster by ~epoch 56 despite high-entropy gating and a two-macro-cluster mass distribution. This confirms that the stability setup enforces excessive compression and masks finer structure.

Number Active Clusters

Number of active clusters (clusters receiving non-zero assignment mass pre-argmax) during the main run across epochs. The realized cluster count tracks this but shows a sharper convergence to 11 interpretable clusters. This provides evidence that hard assignments remain consistent with the soft assignment dynamics.

Stability Test num Active Clusters

Active cluster count during the stability retraining run. Despite initially exploring 60–70 clusters stochastically, the model collapses to two stable macro-clusters early in training, with the hard argmax view later dominated by one realized cluster. This demonstrates that the stability-oriented regularization settings over-compress the latent space.

Assignment Entropy

Assignment entropy quantifies how spread out each node’s membership distribution is, and the training loop keeps that spread above a target to prevent premature cluster collapse and to maintain capacity for later specialization. There is an initial increase from ~5.29 to ~5.37 bits during the exploratory phase, after which it remains tightly stable between ~5.37–5.40 bits throughout the remainder of training. The low variance and high plateau reflect consistent multi-cluster usage and an absence of degenerate assignment behavior.

Stability Test Assignment Entropy

Despite entropy remaining high throughout, the model ultimately collapses to a small number of active clusters. This dissociation between high entropy and low realized cluster count highlights over-regularization in the stability configuration and motivates revisiting the bootstrap hyperparameters.

Gate Entropy Bits

Gate entropy for the main run, reflecting the diversity of hard-concrete gate activations. Gate entropy stays elevated (≈7–8 bits), indicating that cluster gates remain broadly active and do not prematurely saturate-an important safeguard against early latent collapse.

Stability Test Gate Entropy Bits

Gate entropy across the stability stress test run. Although gate entropy remains high, the model still converges to a nearly two-macro-cluster solution whose argmax assignments are effectively single-cluster, demonstrating that gate entropy alone is not a sufficient indicator of latent diversity under strong regularization pressure.

Reconstruction Loss

Reconstruction loss for the main RGCN-SCAE run, showing steady decline and smooth convergence. The decoder remains well-calibrated, and positive/negative logits track closely, indicating balanced learning of multiplex relations without memorization.

Stability Test Reconstruction Loss

Reconstruction loss during the stability stress test run. Although this configuration achieves lower reconstruction loss than the main run, it does so by over-compressing the latent space, reflecting a known failure mode where high reconstruction performance coincides with collapsed cluster structure.

Consistency Loss

Memory-bank consistency loss for the main run that keeps embeddings aligned for nodes that reappear in multiple ego-net batches. The gradual decline reflects improving coherence of node embeddings across overlapping ego-net samples, indicating that repeated presentations of the same node converge toward stable latent representations.

Stability Test Consistency Loss

Consistency loss for the stability stress test run. The elevated and noisier profile compared to the main run reflects competing pressures between negative-sampling calibration, entropy constraints, and excessive compression, further supporting the interpretation that the stability configuration induces a degenerate two-macro-cluster solution with effectively single-cluster hard assignments.

Expected Cluster Count

This is the encoder-side sparsity metric computed as the expected L0 norm (probability mass of “on” gates) across all cluster-gate units in the SCAE encoder. It directly measures how many latent clusters the encoder is actively using at each step.

Stability Test Expected Cluster Count

Expected active cluster usage declines monotonically from ~235 gates to ~150 over the course of training, indicating progressive contraction of the latent space despite stable entropy levels. The sharp transition near step ~30 marks the point at which the encoder begins to commit to a smaller subset of latent factors, after which sparsity tightens gradually rather than collapsing abruptly. This trajectory illustrates that the eventual two-macro-cluster mass distribution emerges not from abrupt collapse but from continuous reduction in active gate mass across iterations, even though the hard argmax diagnostic later reports one realized cluster.

Inter-Cluster Density

How many pairwise cluster interactions are contributing to reconstruction. Has the exact same shape as the expected cluster count but with a different magnitude.

Stability Test Inter-Cluster Density

Has the exact same shape as the stability test run expected cluster count but with a different magnitude.

Sparsity Warmup Factor

The linear ramp reaches 1.0 at the expected 100th epoch.

Stability Test Sparsity Warmup Factor

This is set from the model’s global step, not epochs but the x-axis here is epoch number. Every mini batch increments global step so the warmup happens more quickly compared to epoch number. This was a mistake that was missed and is a source of error in this study.

The above MLflow traces for the base RGCN-SCAE run and the stability-focused retraining provide an audit trail of the gate trajectories that underlie the preceding stability table. The baseline model’s realized active clusters (how many clusters had at least one node assigned to it after the argmax) oscillated between ten and twenty before ending early at eleven clusters by epoch 147 due to the same number of realized active clusters for ten epochs consecutively, and its assignment entropy plateaued near 5.38 bits with gate entropy ≈7.65 bits. In contrast, the stability stress test run collapsed to a single realized cluster by epoch 56 even though the mass-based summary retained two macro-clusters, stochastic sampling continued to touch 68–73 clusters, and gate entropy remained ≈7.25 bits. Plotting realized active clusters, num active clusters, and assignment entropy over epochs makes this divergence visually explicit and documents that the collapse occurred despite high-entropy gating, implying that the stopping criterion is insufficiently sensitive to emerging macro-clusters. For full transparency, the remaining MLflow graphs are included in the appendix.

Calibration and Reconstruction Diagnostics

Calibration statistics show how pretraining choices constrained the stability experiment. Decoder behavior mirrors this drift: the baseline model ended with overlapping positive/negative logits (means 0.424/0.423, standard deviations 0.003–0.005) while processing 6,704 negatives per batch, but the stability stress test run pushed logits above 1.0/0.96 with an order-of-magnitude higher variance and only 1,206 negatives. These distributions explain why the stability configuration attains a lower reconstruction loss (0.00120 vs. 0.00206) yet produces fewer populated clusters.

Regularization Burden

Loss decompositions clarify which constraints dominate optimization. At convergence the stability stress test run reports a consistency penalty of 1.9e-3 and a degree-penalty of 1.2e-3, roughly an order of magnitude larger than the corresponding 4.5e-7 and 1.1e-4 terms in the baseline run. Conversely, the encoder/decoder sparsity penalties (encoder clusters = 150.1; inter-cluster density = 3.57e4) are substantially lower than the baseline’s 225.1 / 5.51e4, corroborating the qualitative observation that the stability regimen over-compresses the latent space.

Discussion

Summary of Findings

This study evaluated whether a multiplex psychiatric knowledge graph, derived from literature mining, contains sufficient structure to support the recovery of a transdiagnostic nosology via unsupervised, information-theoretic partitioning.

The results provide consistent but constraining evidence. While the learned partitions exhibit moderate semantic coherence and statistically significant enrichment with respect to selected HiTOP and RDoC domains, they fail to achieve meaningful global alignment or robust, non-degenerate structure under perturbation.

Under the subgraph-bootstrap robustness test, the model collapsed to a low-complexity solution: two macro-clusters by mass, with hard argmax assignments dominated by a single realized cluster. This outcome is consistent with the graph containing insufficient signal to sustain richer partitions under perturbation, but the stability stress test run also differed from the main run in substantially higher regularization pressure, so overregularization cannot be ruled out as a potential cause. The bootstrap result therefore contributes to but does not independently establish graph insufficiency interpretation.

Evidence of Structural Insufficiency in the Knowledge Graph

Degenerate Solutions as Optimal Representations

A central empirical finding from the stability stress test is that the collapsed partition (two macro-clusters by mass, single realized cluster under argmax) achieves:

near-zero coherence variance across 64 bootstrap subgraph evaluations within the stability run (CI width = 2.3e-5; all 64 bootstraps converged to the same partition)
lower reconstruction loss than the main 11-cluster run (0.00120 vs. 0.00206)

despite exhibiting poor alignment with reference frameworks.

This indicates that the graph admits a low-rank explanation that dominates the optimization landscape under regularization pressure. If finer-grained latent structure were strongly supported by the relational signal, then perturbing training away from a single fixed graph should have preserved at least some comparable mesoscale organization. Instead, the emergence of a trivial coarse solution under the perturbed training regime is consistent with the graph not containing enough recoverable information to sustain richer partitions, though the confounded regularization settings in that run prevent this from being treated as conclusive.

Local Semantic Coherence Without Global Structure

The coexistence of:

statistically significant enrichment (for example, 62.5% of clusters for HiTOP)
strong coherence-alignment correlations
but weak global metrics (for example, low NMI and ARI)

indicates that the graph contains localized pockets of meaningful signal but lacks a globally consistent topology.

This pattern is most consistent with a graph composed of fragmented, weakly coupled semantic regions rather than a coherent latent manifold from which a unified nosology could be recovered. In other words, parts of the graph appear interpretable in isolation, but the graph as a whole does not support a robust global partition.

Topological Dependence on Nosological Nodes

A critical structural limitation emerges from the graph construction process:

removal of diagnostic (nosology) nodes leads to complete graph degeneracy
retaining them introduces partial label leakage (~18.6%)

This reveals that diagnostic nodes function as topological anchors or articulation points, maintaining connectivity between otherwise weakly linked components. Removing those nodes made partitioning impossible because the graph collapsed into isolated nodes and only 815 nosology-related nodes were removed while 11,115 remained.

As a result, the graph simultaneously:

depends on existing diagnostic categories for structural integrity
yet cannot be evaluated independently of them

This creates a fundamental constraint: the graph does not contain sufficient redundant cross-domain relationships, such as symptom-biomarker-treatment connectivity, to sustain a diagnosis-independent structure.

Graph Sparsity and SBM Micro-Fragmentation

Two graph-level structural properties provide additional evidence of insufficiency that is independent of training dynamics.

First, the psychiatric subgraph contains 59,786 nodes and 69,248 edges, giving an average degree of approximately 2.3. This is a near-tree-like sparsity regime in which most nodes have at most two or three neighbors. Community detection methods generally require substantially higher average connectivity to produce stable mesoscale structure; at this density, most nodes lack enough relational context for well-defined cluster membership, and the dominant topological feature is a sparse backbone rather than interlocking communities.

Second, the SBM result corroborates this through an independent channel. SBM infers partition structure by maximizing the likelihood of observed edge densities under a generative block model (it has no compression objective and is not subject to the reconstruction biases described in the alternative explanation below). Yet it produces 18,670 clusters from 59,786 nodes, yielding an average cluster size of approximately 3.2 nodes. This is effectively degenerate micro-fragmentation. Because SBM's failure mode is governed purely by the graph's edge structure, this is a direct graph-level signal. SBM's likelihood function rewards explaining observed edge densities at whatever scale the data warrants. It has no incentive to over-compress, but equally no incentive to find mesoscale structure specifically. That the graph fragments to ~3.2-node micro-clusters means its edge density pattern provides no statistical support for merging nodes into larger mesoscale groups: if block structure at that scale existed, SBM's likelihood would favor it.

Consistent Failure Modes Across Inductive Biases

Two contrasting partitioning approaches were evaluated:

SBM, which finds the maximum-likelihood partition at whatever scale the graph's edge density supports
RGCN-SCAE, favoring compressed representation-based clustering

These methods produce opposite failure modes:

SBM -> extreme fragmentation (micro-clusters with negligible recall)
RGCN-SCAE -> over-compression (few broad clusters with low alignment)

The fact that these contrasting paradigms fail in opposite ways suggests that the limitation is not explained solely by one model’s inductive bias. This is not proof of model-agnostic failure, but it does strengthen the interpretation that the current graph does not constrain a non-trivial solution well enough.

Perturbation Robustness Reveals Underconstraint Rather Than Validity

The subgraph-bootstrap experiments were intended as a perturbation-based robustness test. Because the model was trained across partially overlapping sampled subgraphs rather than only on a single fixed graph, one reasonable expectation was that, if the graph contained robust mesoscale organization, the recovered partitions would remain broadly similar while showing some variability across runs. The methods section explicitly motivates this procedure as a way to reduce overfitting to idiosyncratic topology and estimate replication reliability on partially overlapping realizations of the same graph.

Instead, the stability stress test run collapsed to a degenerate partition (two macro-clusters by mass, with hard argmax assignments dominated by a single realized cluster) under the perturbed regime. This outcome is consistent with graph underconstraint, but an alternative explanation cannot be dismissed: the stability stress test run differed from the main run not only in sampling regime but also in substantially higher regularization pressure-approximately 5.5x fewer negatives per batch (1,206 vs. 6,704), a consistency penalty roughly 4,200x larger (1.9e-3 vs. 4.5e-7), and lower active gate counts (150.1 vs. 225.1). Each of these factors alone could plausibly be sufficient to induce collapse independently of graph signal content. The collapse is therefore consistent with graph underconstraint, but it cannot be attributed to that cause definitively. A calibrated stability test that matches the main run's regularization strength and varies only the training distribution would be needed to isolate the contribution of graph signal from that of overregularization.

Weak and Noisy Reference Signal

Baseline coverage analysis shows:

low precision for HiTOP (0.186)
low precision for RDoC (0.062)
moderate recall but sparse reliable labeling

This indicates that even the evaluation signal embedded in the graph is weak and noisy and confirms limited but non-zero leakage and weak label purity.

This limits the interpretability of alignment metrics and further reinforces the conclusion that the graph lacks sufficient structured information.

Alternative Explanation: Objective Mismatch

An alternative to the graph insufficiency interpretation is that the reconstruction-based objective is itself the primary bottleneck.

GAE and VGAE methods are known to perform poorly on community detection. Salha-Galvan et al. [26] show through extensive evaluation that standard GAE/VGAE methods are routinely outperformed by simpler alternatives such as Louvain on community detection benchmarks, and that explicitly adding a modularity-inspired regularizer to the reconstruction loss is necessary for competitive community detection performance. The RGCN-SCAE uses reconstruction loss as its primary objective and does not include a modularity or community-preserving term, placing it within the class of methods Salha-Galvan et al. identify as structurally ill-suited for mesoscale recovery.

Degree heterogeneity compounds this. Liu et al. [27] demonstrate that GAE performance degrades systematically under long-tailed degree distributions because high-degree nodes develop larger embedding norms and dominate decoder scores. Subramonian et al. [28] further prove that GCNs with symmetric normalized filters exhibit preferential attachment bias, where high-degree nodes are systematically overweighted in message-passing aggregation regardless of their semantic content.

The RGCN-SCAE addresses parts of this with a degree orthogonality penalty and a per-graph embedding norm penalty. However, these mitigations operate on different quantities than what is identified by Liu et al. [27]. The degree orthogonality penalty discourages the correlation of node log degree with any coordinate in the latent space. The norm penalty shapes the scale of the embedding space, bounding the per-graph average squared norm, but does not equalize norms across degree classes, which means high-degree nodes can retain a relative norm advantage over low-degree nodes even when the average is bounded. The reconstruction BCE loss, by contrast, accumulates positive-edge terms across the full edge set. Under near-tree-like graph sparsity (average degree $\approx$ 2.3), a small number of hub nodes account for a disproportionate share of positive edges, and the gradient pressure to reconstruct their connectivity flows through the Sinkhorn-balanced assignment vectors consumed by the decoder - downstream of the latent space where the degree penalty acts. The two objectives do not directly conflict: the model can satisfy the degree orthogonality penalty in the embedding space while still converging to a coarse partition that efficiently reconstructs hub connectivity patterns in the decoder.

This means the over-compression observed in the RGCN-SCAE is plausibly explained by objective mismatch alone, even on a graph with richer potential structure. The SBM micro-fragmentation described above is the strongest evidence against a pure objective-mismatch explanation: SBM has no reconstruction bias and no tendency toward over-compression, but its likelihood function also has no specific affinity for mesoscale groups. It simply finds the partition that best fits the observed edge density at whatever scale the data supports. That SBM's best fit is about 3.2-node micro-clusters indicates that the graph's edge density pattern itself provides no statistical support for mesoscale block structure, which is not a property of the objective but of the graph.

The most likely interpretation is that both factors contribute simultaneously and interact. A sparse graph with near-tree-like connectivity provides a weak training signal regardless of the objective used, but a reconstruction-based objective specifically amplifies that weakness by directing gradient pressure toward hub connectivity rather than mesoscale structure. Either factor alone might be overcome (a better objective on a sparse graph, or a reconstruction objective on a denser, more structured graph) but their combination created compounding pressure toward degenerate solutions in this instance. The current experiments cannot quantify the relative contribution of each, but treating them as mutually exclusive alternatives is probably a false framing.

Implications for Automated Psychiatric Nosology

These findings suggest that:

This literature-derived knowledge graph in conjunction with these partitioning methods, as constructed and filtered here, does not yield a robust transdiagnostic psychiatric nosology. Whether this reflects fundamental graph insufficiency, training instability, or both cannot be fully disentangled from the current experiments.
Detectable signal exists, but it is fragmented and lacks the connectivity required for robust global structure.
Model improvements alone are unlikely to resolve this limitation if the primary bottleneck is graph construction; however, a cleaner ablation separating regularization effects from graph signal would be necessary to confirm this.
Inductive constraints aligned with clinical structure, such as temporal dynamics, causal relationships, or multimodal integration, are likely necessary regardless of which explanation dominates.

Rather than demonstrating failure of automated nosology in principle, these results clarify the conditions under which it is feasible.

Limitations

Several limitations contribute to the observed insufficiency:

The graph is derived from a single aggregated literature corpus, inheriting publication bias and heterogeneity.
Heuristic filtering and label inference introduce noise and partial circularity.
The graph lacks temporal, patient-level, and causal structure, limiting its ability to represent disease progression.
Structural dependence on diagnostic nodes suggests incomplete relational coverage across modalities.
The subgraph-bootstrap experiment introduced substantially higher regularization pressure than the main run-approximately 5.5x fewer negatives, a consistency penalty roughly 4,200x larger, and lower active gate counts (150.1 vs. 225.1 in the main run). Excessive L0 gate pressure under these conditions is a plausible cause of the observed collapse that may be independent of graph signal insufficiency. The stability results should therefore be treated as suggestive rather than conclusive evidence of graph underconstraint.

These limitations collectively constrain the recoverable structure.

Future Directions

Future work should prioritize improving the information content and structure of the graph, rather than focusing solely on model architecture.

Promising directions include:

incorporating patient-level longitudinal data (for example, EHR trajectories)
enforcing causal or temporal constraints during graph construction
integrating multimodal signals (genetics, imaging, clinical measures)
developing objectives aligned with identifiability rather than reconstruction alone
explicitly modeling and correcting graph sparsity and fragmentation

These approaches may increase the recoverable mutual information necessary for meaningful partitioning.

Conclusion

This study demonstrates that unsupervised, information-theoretic partitioning of this large-scale psychiatric knowledge graph can uncover locally coherent and partially interpretable structure, but does not yield a robust or globally consistent transdiagnostic nosology.

Stronger graph-internal evidence for structural insufficiency comes from three independent sources: the topological collapse of the graph when nosological anchor nodes are removed, the failure of the main run to produce meaningful global alignment (HiTOP NMI 0.116, ARI 0.112) under well-calibrated training conditions, and the contrasting failure modes of two methodologically distinct partitioning algorithms on the same graph. The subgraph-bootstrap experiment is consistent with this interpretation but is confounded by overregularization and should not be treated as independent corroboration. The coexistence of local enrichment and weak global alignment further suggests that the graph encodes fragmented signals without a unifying topology.

Taken together, these results are most parsimoniously explained by information insufficiency and structural incompleteness in the graph produced by the present construction pipeline, though the evidence does not fully exclude the alternative that better-calibrated training procedures could recover richer structure from the same graph. The graph depends on nosological anchor nodes to maintain connectivity, produces weak global alignment even under favorable training conditions, and resists coherent partitioning by two independent methods. Each of these is a graph-level property independent of the training confounds in the stability experiment.

This work therefore reframes the challenge of automated psychiatric nosology: success depends not only on advances in representation learning, but critically on the construction of data sources that contain sufficient, well-structured, and interconnected information to make such discovery possible.

Abbreviations

ARI = adjusted Rand index
CI = Confidence Interval
DSM = Diagnostic and Statistical Manual of Mental Disorders
HiTOP = Hierarchical Taxonomy of Psychopathology
ICD = International Classification of Diseases
NMI = Normalized Mutual Information
RDoC = Research Domain Criteria
RGCN = Relational Graph Convolutional Network
SBM = Stochastic Block Model
SCAE = Self-Compressing Auto-Encoder

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Appendix

Code Notes

Install project requirements via pip3.10 install -r requirements.txt.
Download the main data for the knowledge graph from https://zenodo.org/records/14851275/files/iKraph_full.tar.gz?download=1.
If you want to include ontology augmentation (not used in final experiment), run

mkdir -p data/hpo
curl -L -o data/hpo/hp.obo https://purl.obolibrary.org/obo/hp.obo
curl -L -o data/hpo/phenotype.hpoa https://purl.obolibrary.org/obo/hp/hpoa/phenotype.hpoa
curl -L -o data/hpo/genes_to_phenotype.txt https://purl.obolibrary.org/obo/hp/hpoa/genes_to_phenotype.txt
python3.10 prepare_hpo_csv.py data/hpo/hp.obo data/hpo/phenotype.hpoa genes_to_phenotype.txt data/hpo/

to prepare the data used for augmenting the graph to prevent degeneracy after removing the diagnosis nodes and include the following CLI params in the below create_graph command:

--ontology-terms hpo=data/hpo/hpo_terms.csv \
--ontology-annotations hpo=data/hpo/hpo_annotations.csv \
--ontology-term-id-column hpo=id \
--ontology-term-name-column hpo=name \
--ontology-parent-column hpo=parents \
--ontology-annotation-entity-column hpo=entity \
--ontology-annotation-term-column hpo=term

Run python3.10 create_graph.py --ikraph-dir iKraph_full --output-prefix ikgraph to create the graph before psych-relevance filtering.
Run python3.10 psy_filter_snapshot.py data/ikgraph.graphml --graphml-out data/ikgraph.filtered.graphml to get final graph for training.
MLflow is used for optional experiment tracking.
- Enable tracking with MLflow by adding --mlflow (plus optional --mlflow-tracking-uri, --mlflow-experiment, --mlflow-run-name, and repeated --mlflow-tag KEY=VALUE flags) to train_rgcn_scae.py, which logs parameters, per-epoch metrics, and uploads the generated partition.json artifact as well as the trained model .pt file.
- Metric explanations:
  - total_loss = weighted sum of reconstruction, sparsity, entropy, Dirichlet, embedding-norm, KL, consistency, gate-entropy, and degree penalties reported below.
  - recon_loss averages the BCE losses for positive and sampled negative edges per graph.
  - sparsity_loss, cluster_l0, inter_l0 track the hard-concrete $L_0$ penalties that drive cluster/edge sparsity.
  - entropy_loss encourages per-graph assignment entropy to stay above --assignment-entropy-floor.
  - dirichlet_loss is the KL term that keeps mean cluster usage close to the Dirichlet prior.
  - embedding_norm_loss and kld_loss regularize latent vectors on a per-graph basis.
  - degree_penalty (with degree_correlation_sq) measures the correlation between latent norms and node degree.
  - consistency_loss / consistency_overlap are the memory-bank temporal consistency terms (0 when disabled).
  - gate_entropy_bits and gate_entropy_loss track how evenly decoder gates remain active.
  - num_active_clusters records the eval-mode gate count that matches the saved partition.json; expected_active_clusters is the summed HardConcrete $L_0$ expectation.
  - realized_active_clusters runs a full argmax pass and counts clusters that actually win nodes after enforcing --min-cluster-size.
  - num_active_clusters_stochastic retains the raw training-mode gate count when needing to debug EMA smoothing or gating noise.
  - negative_confidence_weight shows the entropy-driven reweighting applied when --neg-entropy-scale > 0.
  - num_negatives counts sampled negative edges that survived the per-graph cap.
  - timing_sample_neg and timing_neg_logits capture the wall-clock time (in seconds) spent sampling negatives and scoring them.
The RGCN-SCAE trainer picks the latent cluster capacity automatically via _default_cluster_capacity, which grows sublinearly with node count (√N heuristic with a floor tied to relation count) to balance flexibility and memory usage.
Use python3.10 check_node_precision_recall.py --graph data/ikgraph.graphml --subset psychiatric --min-psy-score 0.33 --psy-include-neighbors 0 to report HiTOP/RDoC precision/recall over the exact node universe that survives the psychiatric filters. Add --per-label-csv out/per_label_precision_recall.csv if you need per-domain tables for manuscripts or diagnostics.
Partition training supports resumable checkpoints via train_rgcn_scae.py.
- Pass --checkpoint-path PATH.pt to automatically persist model weights, optimizer state, history, and run metadata at the end of training (and optionally every --checkpoint-every N epochs).
- Resume an interrupted or completed run with --resume-from-checkpoint --checkpoint-path PATH.pt; add --reset-optimizer to reload only the model weights while reinitializing the optimizer.
- Checkpoints store a signature of the graph/config and cumulative epoch counters so continued training logs consistent metrics (including MLflow) instead of restarting from epoch 1.
Training stops early when the requested stability metric (realized_active_clusters by default) stays within tolerance for a sliding window of epochs. Pass --cluster-stability-window (number of epochs), --cluster-stability-tolerance (absolute span), and optionally --cluster-stability-relative-tolerance when calling train_rgcn_scae.py; once the chosen stability_metric (defaults to realized_active_clusters) varies less than both thresholds after --min-epochs, the run halts and records the stop epoch/reason in the history log.
Run python3.10 -m pytest from the repository root to execute the regression tests for the extraction pipeline and training utilities.
To compute results for a particular partitioning method, run python3.10 align_partitions.py --graph data/ikgraph.filtered.graphml --partition <partitions_file>.json --prop-depth 1 and python3.10 inspect_cluster.py --graph data/ikgraph.filtered.graphml --partition scae_partitions.json --explain --saliency --saliency-top-pair --outdir scae_inspect --cluster <clustere_num>
- align_partitions.py heuristically infers HiTOP/RDoC labels from node attributes when explicit maps are not supplied, so every derived metric (global alignment scores, enrichment CSV/JSON, coverage fractions) inherits those heuristics - rerunning the script is the authoritative way to reproduce the values reported in the Results tables.
Regenerate the "Baseline Psychiatric Label Coverage" section via python3.10 analysis/baseline_label_coverage.py --graph data/ikgraph.graphml --min-psy-score 0.33 --psy-include-neighbors 0, which writes the intermediate JSON/CSV plus a Markdown table to out/baseline_label_coverage.md.

Calibration

Everything below is calculated based on performance in the first 50 epochs:

calibration_loss_curvature = 0 for both runs
calibration_loss_slope = 0 for both runs
main run calibration_mean_active_clusters = 245
stability stress test run calibration_mean_active_clusters = 120.454
main run calibration_rel_var_active_clusters = 0
stability stress test run calibration_rel_var_active_clusters = .9
main run calibration_var_active_clusters = 0
stability stress test run calibration_var_active_clusters = 12912.636

Training Graphs

Gate Entropy loss was permanently 0 for both runs.

Consistency Overlap

Flat trace at zero confirms the memory-bank consistency terms were disabled for the main run, so consecutive embeddings evolve independently.

Stability Test Consistency Overlap

Peaks near 1.9e-3 around epoch ~60, after the cluster count has already collapsed to a single realized cluster, highlighting that the added consistency term becomes most active only after the structure has degenerated.

Node Degree Pearson Correlation Squared

How strongly each latent embedding dimension still correlates with node degree after centering. Declines toward zero, demonstrating that latent norm and node degree become decorrelated and keep the degree penalty near 1.1e-4 at convergence.

Stability Test Node Degree Pearson Correlation Squared

Settles an order of magnitude higher, explaining the ≈1.2e-3 penalty cited for the stability stress test run.

Degree Penalty

This tracks the scalar regularizer that discourages norm–degree coupling. Its steady decay mirrors the correlation-squared plot and motivates the chosen weight.

Stability Test Degree Penalty

Stays an order of magnitude higher, underscoring how the stability settings suppress variance by anchoring latent norms to node degree.

Dirichlet Loss

The KL divergence between empirical cluster usage and the symmetric Dirichlet prior. Brief spikes indicate moments when a few clusters temporarily dominate before the prior pulls usage back in line.

Stability Test Dirichlet Loss

Remains elevated because one or two clusters hoard probability mass, reinforcing that the stability stress test run never recovers a balanced mixture.

Embedding Norm Loss

Drops to ≈4.6e-3 by early stopping, showing that latent vectors stay within the intended $L_2$ budget while still supporting 11 populated clusters.

Stability Test Embedding Norm Loss

Much earlier plateauing reflects the same global step vs epoch number as with the sparsity warmup issue.

Entropy Loss

Hinge penalty that keeps the full graph’s assignment entropy above the 5.5-nat (7.93-bit) floor. Because the main run trains on a single graph, that graph never quite reaches the target, so the loss hovers at a small non-zero value rather than spiking-documenting the constant gentle push to keep assignments diffuse. There’s only one giant graph so once assignments sharpen on that graph, the single entropy value sits just below the floor and the hinge never fully releases.

Stability Test Entropy Loss

Because this run trains on ego-net mini batches with high gate temperature and heavier consistency/degree penalties, its soft assignments stay more diffuse than in the full-graph run even after the argmax collapses to a single realized cluster. That keeps the per-graph entropy at or above the 5.5-nat (7.93-bit) floor much more often, so the hinge term spends more time at zero.

KL Divergence Loss

Captures the per-epoch latent KL divergence loss term. Plunges within the first handful of epochs, indicating the encoder snaps quickly into a stable posterior once it settles on 12-14 clusters.

Stability Test KL Divergence Loss

Levels off at a slightly higher plateau, signaling that the collapsed solution pushes the posterior away from the prior more.

Negative Logit Mean

Begins near 0.24 and climbs steadily across training-ending around 0.42, essentially overlapping the positive-logit mean-showing how the decoder gradually tightens its calibration band as the latent clusters stabilize.

Stability Test Negative Logit Mean

Starts around 0.25 band similar to the main run but rises steadily past 0.9 by the time the end of training, showing how the decoder becomes increasingly over-confident about rejecting edges once the stability configuration squeezes almost all clusters out of the latent space.

Negative Logit Standard Deviation

Stays in the range of .001 to .008, confirming tightly clustered logits for the main experiment.

Stability Test Negative Logit Standard Deviation

Expands by an order of magnitude, reflecting the noisy decoder induced by the altered sampling schedule.

Negative Confidence Weight

This scales the negative-edge BCE term. Because the main run’s gate entropy stays near 7.6 bits, this sits around 0.14 with only millipoint wobble, meaning negatives are gently down-weighted the entire time rather than being suppressed after assignments sharpen.

Stability Test Negative Confidence Weight

The stability stress test run shows the same mechanism under lower gate entropy (~7.2 bits), so this drifts from ≈0.13 toward ≈0.17 but never exceeds 1.0. Negatives remain down-weighted even as the realized clusters collapse. This confirms the collapse is not caused by under-weighted negatives.

Number Active Clusters Stochastic

Gate counts hover well above the realized 11 clusters, confirming that the sampler continues to explore dozens of latent components even after argmax pruning.

Stability Test Number Active Clusters Stochastic

Despite the realized collapse, stochastic gates still touch ~70 clusters; the diverging traces visualize why the stability stop rule missed the latent failure.

Number Negative Edges

Completely flat at roughly 6,704 sampled negatives as expected.

Stability Test Number Negative Edges

Oscillates between roughly 1113 and 1206 with no intermediate values due to the global step difference mentioned above.

Positive Logit Mean

Begins near 0.24 and climbs steadily across training-ending around 0.42, essentially overlapping the positive-logit mean-showing how the decoder gradually tightens its calibration band as the latent clusters stabilize.

Stability Test Positive Logit Mean

Starts around 0.25 band similar to the main run but rises steadily past 1.0 by the time the end of training, showing how the decoder becomes increasingly over-confident about rejecting edges once the stability configuration squeezes almost all clusters out of the latent space.

Positive Logit Standard Deviation

Stays mostly in the range of .0015 to .005, confirming tightly clustered logits for the main experiment.

Stability Test Positive Logit Standard Deviation

Expands by an order of magnitude, reflecting the noisy decoder induced by the altered sampling schedule.

Sparsity Loss

This measures the aggregate Hard-Concrete L0 penalties for encoder/decoder gates. The pattern shown is entirely caused by the sparsity warmup schedule (full warmup factor at global step 100).

Stability Test Sparsity Loss

The same situation as the full-graph run except with the previously mentioned global step issue forcing the decline to start at a much earlier epoch.

Total Loss

This pattern is also driven almost entirely by the sparsity warmup schedule as the remaining loss terms are close to 0 and the sparsity loss has the exact same trend line.

Stability Test Total Loss

This pattern is also driven almost entirely by the sparsity warmup schedule as the remaining loss terms are close to 0 and the sparsity loss has the exact same trend line.

Name		Name	Last commit message	Last commit date
Latest commit History 261 Commits
plots		plots
tests		tests
.flake8		.flake8
.gitignore		.gitignore
.pre-commit-config.yaml		.pre-commit-config.yaml
README.md		README.md
align_partitions.py		align_partitions.py
attributes.py		attributes.py
augment_graph_with_ontologies.py		augment_graph_with_ontologies.py
check_graph_degeneracy.py		check_graph_degeneracy.py
check_node_precision_recall.py		check_node_precision_recall.py
check_psych_ratio.py		check_psych_ratio.py
cluster_bimodality_probe.py		cluster_bimodality_probe.py
create_graph.py		create_graph.py
create_sbm_partitions.py		create_sbm_partitions.py
debug_graphml.py		debug_graphml.py
debug_parquet.py		debug_parquet.py
graph_build.py		graph_build.py
graph_export.py		graph_export.py
hyperband_partition.py		hyperband_partition.py
inspect_cluster.py		inspect_cluster.py
list_diagnosis_nodes.py		list_diagnosis_nodes.py
models.py		models.py
nosology_filters.py		nosology_filters.py
partition_lorenz.py		partition_lorenz.py
plot_sbm_cluster_sizes.py		plot_sbm_cluster_sizes.py
plot_scae_cluster_sizes.py		plot_scae_cluster_sizes.py
prepare_hpo_csv.py		prepare_hpo_csv.py
psy_filter_snapshot.py		psy_filter_snapshot.py
psychiatry_scoring.py		psychiatry_scoring.py
pyproject.toml		pyproject.toml
remove_disease_nodes.py		remove_disease_nodes.py
remove_stranded_nodes.py		remove_stranded_nodes.py
requirements.txt		requirements.txt
sections.py		sections.py
self_compressing_auto_encoders.py		self_compressing_auto_encoders.py
train_rgcn_scae.py		train_rgcn_scae.py
utility.py		utility.py
view_partition.py		view_partition.py
visualize_graph.py		visualize_graph.py

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Automated Psychiatric Nosology via Representation-Learning-Based Partitioning of Knowledge Graph

Table of Contents

Abstract

Introduction

Literature Review

Biomarkers of Psychopathology

Transdiagnostic Dimensions

Automated Methods

Conclusion

Research Question

Hypothesis

Hypothesis Metrics Justification

Materials and Methods

Knowledge Graph Dataset

Preventing Biased Alignment

Partitioning

Encoder Architecture

Decoder Architecture

Training

Commands

Mitigating Cluster Collapse and Runaway Imbalance

Stabilizing Hard-Concrete Gates

Gate Revival Hook

Controlling Message-Passing Drift

Addressing Degree and Hub Bias

Balancing Multiplex Relation Frequencies

Hardening Negative Sampling

Maintaining Cross-Batch Consistency

Latent Regularization and Diagnostics

Trainer-Level Safeguards

Objective

Reconstruction Loss and Entropy Controls

Adaptive Subgraph Sampling for Stability Testing

Comparison

Results

Baseline Psychiatric Label Coverage

Overall Metrics

Cluster Sizes

HiTOP Alignment Summary

RDoC Alignment Summary

Cluster Snapshots (main partitioning run)

Stability Metrics (Bootstrapped Subgraph and Semantic Consistency)

Training Dynamics

Calibration and Reconstruction Diagnostics

Regularization Burden

Discussion

Summary of Findings

Evidence of Structural Insufficiency in the Knowledge Graph

Degenerate Solutions as Optimal Representations

Local Semantic Coherence Without Global Structure

Topological Dependence on Nosological Nodes

Graph Sparsity and SBM Micro-Fragmentation

Consistent Failure Modes Across Inductive Biases

Perturbation Robustness Reveals Underconstraint Rather Than Validity

Weak and Noisy Reference Signal

Alternative Explanation: Objective Mismatch

Implications for Automated Psychiatric Nosology

Limitations

Future Directions

Conclusion

Abbreviations

References

Appendix

Code Notes

Calibration

Training Graphs

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