MotivNet: Motif Networks & Facial Emotion Recognition

• MotivNet is a dual-purpose framework encompassing a motif-based network generation algorithm and a facial emotion recognition model, each advancing its respective field.
• The network algorithm incrementally selects edges to precisely control motif prevalence and global graph properties using combinatorial scoring and precomputed matrices.
• The facial emotion recognition system leverages a pretrained Sapiens backbone with a lightweight ML-decoder head to achieve state-of-the-art performance across multiple benchmarks.

MotivNet describes two unrelated but prominent frameworks in the contemporary literature: a network-generation algorithm to control motif abundance in directed graphs (Mäki-Marttunen, 2016), and a state-of-the-art facial emotion recognition (FER) model leveraging a foundation vision backbone (Medicharla et al., 30 Dec 2025). Each “MotivNet” is independently significant and widely cited within its domain; both advance their fields by systematically enabling either structural motif patterning or robust emotional recognition from images.

1. Motif-Based Network Algorithm (“MotivNet”): Principles and Mechanisms

The original MotivNet algorithm operates on directed, unweighted graphs defined by an adjacency matrix $M\in\{0,1\}^{N\times N}$ with $M_{ij}=1$ indicating a directed edge $i\to j$ and with no self-loops $(M_{ii}=0)$. The construction process is primarily controlled by a motif-weight vector $\tilde w\in\mathbb{R}^{N_\text{mot}}$, where $N_\text{mot}$ is the count of possible $k$-node directed motifs (isomorphism classes; e.g., $N_\text{mot}=16$ for $k=3$, $218$ for $k=4$).

MotifNet’s key innovation is in incrementally assembling the network by greedily selecting edges whose addition most increases (or decreases) the aggregate desired motif counts, as quantified via a precomputed scoring function. Pre-motifs (distinct subgraph configurations prior to each candidate edge insertion) are enumerated, and two core matrices,

• $$G\in\{-1,0,1\}^{N_\text{premot}\times N_\text{mot}}$$, encoding whether adding an edge creates ($+1$), destroys ($-1$), or leaves unchanged ($0$) each motif,
• $F\in\{0,1\}^{N_\text{mot}\times N_\text{mot}}$, upper triangular, encoding motif extension relations via edge addition,

enable rapid computation of motif scoring over all possible insertions. The effective weights used for scoring are adapted from $\tilde w$ by summing over paths of intermediate motifs—formally, $w = (I - F/N)^{-1}\tilde w$—to incentivize stepping-stone submotifs where direct creation is rare.

At each iteration, a target node $k$ with unmet in-degree is selected proportional to its in-degree gap, and among all candidate sources $i$, the edge $i\to k$ maximizing $\lambda_i$—a sum over all premotif types weighted by expected motif creation rates—is chosen.

This combinatorial approach can target arbitrary combinations of motifs and can precisely enforce prescribed in- or out-degree distributions. If an out-degree constraint is required, the same procedure may be applied on the transposed graph.

2. Algorithmic Workflow and Computational Characteristics

The MotivNet generation process for a graph of $N$ nodes, target in-degree distribution $p_\text{in}(d)$, and motif-weight vector $\tilde w$ proceeds as follows:

1. For each node $k$, sample in-degree $n_k\sim p_\text{in}$; maintain input deficits $u_k$.
2. While any $u_k>0$, probabilistically select a $k$ with nonzero $u_k$.
3. For each $i\ne k$ with $M_{i,k}=0$, compute $\lambda_i$ via enumeration of all premotifs formed by adding candidate $i\to k$.
4. Select $i^* = \arg\max_i \lambda_i$, break ties randomly, insert edge, decrement $u_k$.

For $k=3$ (3-node motifs), each edge addition requires $O(N^2)$ work, scaling to $O(E N^2)$ in total for $E=\sum n_k$ edges, practical for $N\lesssim 10^3$. For $k=4$, it scales as $O(E N^3)$.

Matrices $G$ and $F$ must be precomputed and stored, incurring $O(N_\text{premot}\times N_\text{mot})$ space, which is modest for $k=3$ but grows at $k=4$.

3. Motif Prevalence Control, Global Properties, and Empirical Performance

Control over motif prevalence is directly achieved by specification of $\tilde w$; elevated $\tilde w_m$ promotes motif $m$, while negative values suppress. The adapted scoring ensures that precursor configurations (lower-edge motifs leading to $m$ by a single insertion) receive incentive, facilitating efficient traversal of motif–space and avoiding local optima due to sparse direct motif creation.

MotivNet-generated graphs can be further tuned for global structural attributes observed in biological or technological networks:

• Small-worldness is measured via $S(M) = [C(M)/C_\text{rand}]/[L(M)/L_\text{rand}]$, with $C$ the mean clustering coefficient and $L$ the harmonic mean path length.
• Modularity $Q(M)$ captures community structure via excess intra-community edge density.

Optimization over $\tilde w$ to maximize $S(M)$ or $Q(M)$ (e.g., using genetic algorithms on small $N$) produces weight vectors that generalize to higher $N$ while increasing small-world or modular properties well beyond standard Erdős–Rényi or directed Watts–Strogatz models.

Empirically, MotivNet achieves maximal over-representation of the targeted motif in both 3- and 4-node cases compared to random and iterative probabilistic rewiring methods, at substantially reduced computational cost (e.g., $N=100$, $k=3$ in $0.6$–$12$ seconds) (Mäki-Marttunen, 2016).

4. Practical Implementation Guidelines

For effective MotivNet deployment:

• Precompute and persist matrices $G$ and $F$.
• Select or adapt $p_\text{in}$ to match real or synthetic application requirements (e.g., delta, binomial, power-law distributions).
• Carefully implement the scoring routine (inner loop) to optimize speed (C/C++ or optimized MATLAB recommended for $N\sim 200$, $k=4$).
• Use optimizer-based search for $\tilde w$ if targeting nontrivial global features (small-worldness or modularity).
• Validate by direct motif enumeration and global metrics, benchmarking against random or canonical null models.

These principles permit extension to networks with node types (e.g., excitatory/inhibitory) or integration with alternative generative paradigms (e.g., preferential attachment).

5. MotivNet as a Facial Emotion Recognition Framework

An independent development under the name MotivNet establishes a robust, generalizable FER system utilizing the Meta Sapiens backbone (Medicharla et al., 30 Dec 2025). MotivNet repurposes Sapiens—a ViT-based, Masked Autoencoder pretrained on 300M human images with 308 facial landmarks—by discarding the pose/keypoint decoder and attaching a lightweight ML-Decoder head. This head implements cross-attention from fixed, non-learnable group queries (one per emotion class) to the encoder output tokens, followed by group-wise MLPs and average pooling to produce class logits.

Fine-tuning is performed on AffectNet (seven emotion classes), with uniform sampling of 3,803 per class and standard cross-entropy loss. Performance is evaluated with Weighted Average Recall (WAR) and Top-$k$ accuracy, achieving:

• WAR: JAFFE $58.57\%$, CK+ $80.00\%$, FER-2013 $53.87\%$, AffectNet $62.52\%$.
• Top-2 Accuracies: up to $96.67\%$ (CK+). MotivNet matches or exceeds cross-domain SOTA on most benchmarks and is within 10 percentage points of single-domain SOTA on Top-2 accuracy.

Architectural deviation from Sapiens is minimal ($<2\%$ of parameters introduced by the new head) and the fine-tuning data distribution closely matches Sapiens’s pretraining set, as measured by Jensen–Shannon divergence of feature histograms, fulfilling three formal “Sapiens downstream task” criteria: (1) benchmark performance, (2) model similarity, and (3) data similarity.

6. Generalization, Robustness, and Operational Considerations in FER

MotivNet’s generalization derives from Sapiens’ MAE pretraining, large-scale facial data, and the use of cross-attention via ML-Decoder. It maintains balanced recall across both laboratory and wild datasets, with robustness attributable to large-scale human image pretraining, per-class balanced sampling, and adaptive selection of local facial features.

Inference on an A100 GPU processes images at ~15 ms/image (batch 32), and distillation or quantization can enable edge deployment with modest losses. Adequate performance is sustained with 3–5K per-class training instances. FER remains sensitive to face detection/pre-crop quality and lighting; shifts in input distribution can be partially mitigated using color-jitter augmentation at inference. Adapters ($<500$ samples/class) may be attached for out-of-domain generalization (e.g., avatars).

MotivNet thus establishes a new standard for cross-domain, in-the-wild FER, leveraging foundation model pretraining, minimal architectural adaptation, and empirical validation across several public benchmarks.

7. Summary and Domain Distinctions

The designation “MotivNet” denotes both a motif-oriented network generation algorithm for directed graphs (Mäki-Marttunen, 2016) and a robust, Sapiens-based FER system (Medicharla et al., 30 Dec 2025). Both are characterized by technical rigor in design, transparent parameterization, and well-justified benchmarks. In network science, MotivNet/MBN is notable for precisely shaping local and global features via combinatorial control of motif distributions. In computer vision, MotivNet for FER leverages foundation model pretraining to realize strong, out-of-domain emotional classification without complex domain adaptation workflows. Despite their naming convergence, these frameworks address unrelated scientific challenges, yet both illustrate the contemporary emphasis on transferability, interpretability, and domain-general solutions in computational modeling.