# Eager Masked Multiresolution Discovery

- ID: 2758
- Canonical URL: https://synthcore.org/idea/2758/eager-masked-multiresolution-discovery
- API JSON: https://synthcore.org/api/idea/2758.json
- API Markdown: https://synthcore.org/api/idea/2758.md
- Verification status: unverified
- Source: [arXiv:2608.27612](https://arxiv.org/abs/2608.27612)
- Category: architecture
- Solves: speedup, scalability, accuracy
- ML areas: moe-routing, graph-nn, cnn, inference-speedup
- Math tags: combinatorics, numerical-analysis, tensor-decomposition
- Ratings: usefulness 6/10; difficulty 4/10; novelty 5/10

## Idea description

Replace recursive adaptive coordinate traversal in a CPPN-based architecture generator with one static multiresolution candidate tensor and an active boolean mask. Evaluate all candidate coordinates in parallel, compute local CPPN-output variance over each parent cell's children, and retain only children whose parent is active and whose predicted variation exceeds a threshold. This preserves adaptive refinement while enabling population batching, JIT compilation, GPU vectorization, and memory-bounded streaming.

## Mathematical statement

The paper constructs the complete multiresolution grid $\mathcal{G}_D=\bigcup_{d=0}^{D}\mathrm{Grid}_d$, where $D$ is the maximum refinement depth and $d$ is a grid level. Each level contains normalized cell centers $((2i+1)/2^{d+1}-1,(2j+1)/2^{d+1}-1)$ for integer indices $i,j\in[0,2^{d+1})$. The total number of candidates is $N_{\mathrm{total}}=(4^{D+2}-4)/3$. The batched evaluation $\mathbf{W}=\mathrm{vmap}(\mathrm{CPPN})(s,T)$ evaluates a population of CPPNs with parameters or genomes $s$ at static coordinate tensor $T$. For each parent cell $p$, let $C(p)$ be its four children, let $y_{p,c}\in\mathbb{R}^{K}$ be the $K$ CPPN outputs at child $c$, and let $\bar y_p$ be their mean. The local variation score is $V_p=|C(p)|^{-1}\sum_{c\in C(p)}\|y_{p,c}-\bar y_p\|_2^2$. With $a_p\in\{0,1\}$ denoting whether parent $p$ is active and $\tau_d$ a threshold at depth $d$, define the child mask $a_{p,c}=a_p\mathbf{1}[V_p>\tau_d]$. The root is forced active. High output variation therefore triggers refinement, while locally constant CPPN outputs suppress unnecessary nodes.

## Key formulas

- $$\mathcal{G}_{D}=\bigcup_{d=0}^{D}\mathrm{Grid}_{d},\qquad \mathrm{Grid}_{d}=\left\{\left(\frac{2i+1}{2^{d+1}}-1,\frac{2j+1}{2^{d+1}}-1\right):i,j\in[0,2^{d+1})\right\}$$
- $$N_{\mathrm{total}}=\frac{4^{D+2}-4}{3},\qquad \mathbf{W}=\mathrm{vmap}(\mathrm{CPPN})(s,T)$$
- $$V_p=\frac{1}{|C(p)|}\sum_{c\in C(p)}\left\|y_{p,c}-\bar y_p\right\|_2^2,\qquad \bar y_p=\frac{1}{|C(p)|}\sum_{c\in C(p)}y_{p,c}$$
- $$a_{p,c}=a_p\,\mathbf{1}[V_p>\tau_d],\qquad \mathrm{output}=\mathrm{CPPN}(T)\odot a$$

## Implementation notes

Integrate this at the topology-discovery or sparse-coordinate-generation stage of a CPPN-based network, neural field, adaptive CNN, or sparse graph generator; leave the CPPN architecture unchanged for the first experiment. First precompute tensors `coords[d]` for levels `d=0,...,D`, together with integer tensors `parent_of_child[d]` and `children_of_parent[d]`. Coordinates should have shape `[N_d, 2]`; mappings should use int32. For a population of genomes, evaluate the CPPN with a compiled batched call having shape `[population, N_d, coordinate_features]`. Reshape each level's child outputs to `[population, N_parent, 4, K]`, calculate `mean_child`, then calculate `V = mean((child_output - mean_child)^2, dim=(child, output))`. Propagate `active[d+1] = active[d][parent_of_child[d]] & (V[d] > tau[d])`, forcing the root active. Apply the resulting mask to instantiate nodes, edges, sparse tokens, or neural-field samples. A practical threshold is `tau[d] = alpha * median(V[d])`; alternatively retain the top fixed fraction of parent cells to impose a compute budget. For large depths, evaluate coordinates in fixed-size chunks and write masks or CPPN outputs to host memory rather than materializing every activation on the GPU. The mathematical quantities to reproduce exactly are the coordinate grid, parent-child hierarchy, batched CPPN evaluation, variance score, and hierarchical mask; threshold schedule, chunk size, and CPPN-output decoding are tunable engineering choices. Start with XOR or a 2-D image-coordinate neural field, population 256, and depths 4–7. Compare against recursive traversal using identical CPPN parameters and thresholds. Record generation time, peak GPU memory, discovered-node count, and solve rate. Success means at least 5x lower topology-evaluation time at equal node count, no loss in solve rate, and stable scaling with population size without recompiling once per genome.

## Disclaimer

AI-generated research hypothesis, automatically tested. Not peer-reviewed.