We introduce Apeiron, a scalable and extensible framework for addressing *amorphous* user demands through autonomous, full-lifecycle application synthesis. Apeiron models the unstructured app development process as a heuristic optimization problem combining (i) a Computer-Use Agent (CUA) evaluator that simulates personas and demands, (ii) an *Activity Tracer* that grounds feedback in code-level interaction traces, and (iii) a *Locality Controller* that constrains changes during continuous integration and delivery (CI/CD). Furthermore, we introduce an innovative data generation approach using CUA-as-a-Judge to tackle data scarcity. Across 300 app scenarios, 2,400 personas, and 46,338 demands, Apeiron outperformed baselines by 10.7% in CUA ratings and 27.8% in user-demand task scores. The optimization process enhances task scores by 64.7%, and the tracer contributes a 25.1% gain. In CI/CD, Apeiron effectively restores 96.9% of the pre-shift mean CUA rating in one optimization step with <30% code changes in response to 30% demand shifts. Finally, a user study (N=18) shows that our CUA ratings strongly correlate with human judgment (Spearman’s 𝜌=0.685) and that users prefer Apeiron-synthesized apps over baselines.

Multimodal Transformers achieve superior performance in multimodal learning tasks. However, the quadratic complexity of the self-attention mechanism in Transformers limits their deployment in low-resource devices and makes their inference and training computationally expensive. We propose multimodal Sparse Phased Transformer (SPT) to alleviate the problem of self-attention complexity and memory footprint. SPT uses a sampling function to generate a sparse attention matrix and compress a long sequence to a shorter sequence of hidden states. SPT concurrently captures interactions between the hidden states of different modalities at every layer. To further improve the efficiency of our method, we use Layer-wise parameter sharing and Factorized Co-Attention that share parameters between Cross Attention Blocks, with minimal impact on task performance. We evaluate our model with three sentiment analysis datasets and achieve comparable or superior performance compared with the existing methods, with a 90% reduction in the number of parameters. We conclude that (SPT) along with parameter sharing can capture multimodal interactions with reduced model size and improved sample efficiency.