Eureka: Task-Conditioned Meta-Agent Orchestration for Scientific Discovery

We present Eureka, a task-conditioned Meta-Agent architecture that compiles long-horizon tasks into dynamic obligation graphs with explicit acceptance semantics. During execution, Eureka forms Macro-Agents with specialized state, memory, operators, tools, verifiers, and local topology via receding-horizon planning, architecture promotion, and minimal-sufficient compilation. When bottlenecks recur, cost-benefit-gated evolution updates the local architecture under constraints. Theoretically, we establish results on regret, planning invalidation, amortization, subtree interfaces, serializability, and verification. Experimentally, Eureka completes 170/170 recursive tasks and generates 3,948 certificates with no false acceptances. Active context compresses median input from 9,490 to 4,005 tokens; incremental processing avoids 65.38% recomputation across 12,000 tasks; 16,000 concurrent executions serialize consistently. The same Meta-Agent instantiates a Theory-Discovery Agent and a Math/Conjecture Agent. The former yields structural results in quantum-process and spacetime theory. The latter identifies bottlenecks in Riemann Hypothesis research and advances a positivity certificate for Suzuki's localized Weil quadratic form to 0 < a <= 69/200 = 0.345, reaching ~99.55% of (log 2)/2. These results suggest that scientific-agent capability depends not only on the base model but on whether an architecture can be formed to match the task's cognitive structure.

BMFA: Boundary-Minority Free-Energy Adaptive Screening

Vision Transformers process spatially redundant tokens efficiently only when coarse token summaries preserve the evidence required by exponential attention aggregation. We identify a boundary-minority underestimation failure in which a spatially small, high-response region contributes dominant Gibbs mass while remaining nearly invisible to a block mean. We formalize the failure through the discrepancy between normalized log-mean-exp free energy and mean summarization, prove that minority Gibbs mass can remain non-vanishing as its spatial support and mean contribution vanish, and characterize the limitations of finite-order moment corrections. Building on the resulting analysis, we introduce Boundary-Minority Free-Energy Adaptive Screening (BMFA), which constructs a hierarchical piecewise-constant approximation and recursively refines blocks according to a computable lower-bound increment of local free energy. Controlled synthetic tests, COCO and LVIS diagnostic probes, closed-loop DeiT-Tiny evaluations, and ImageNet-1K experiments establish a consistent evidence chain. BMFA reduces the mean synthetic underestimate from 2.582 to 0.261 at a 5.794% leaf ratio, lowers the COCO image-edge mean gap from 2.254 to 0.526, and preserves 71.520% ImageNet Top-1 accuracy at a 55.861% leaf ratio. The current prototype evaluates selection quality after full QK computation; the reported leaf ratio therefore characterizes representation granularity rather than verified sparse-kernel speedup.

Stage-Aware Adaptation and Distribution Calibration for Subject-Driven Personalized Text-to-Image Generation

Subject-driven personalized text-to-image generation requires a pretrained diffusion model to acquire a specific subject from a few reference images while preserving subject identity, following novel text prompts, and maintaining sample diversity. Existing optimization-based methods instantiate subject adaptation through full fine-tuning, textual embedding optimization, or low-rank parameter updates; PaRa further constrains personalization from the perspective of parameter rank reduction. However, a uniform low-rank constraint or a uniform adapter strength cannot explicitly distinguish the capacity requirements of different denoising stages. Moreover, inference-time candidate selection driven mainly by identity similarity may compress the selected samples in the visual representation space. We decompose the problem into two complementary components: SPaRa denotes training-side stage-aware low-rank adaptation, DCAL denotes inference-side distribution-calibrated candidate selection, and SPaRa-DCAL denotes the combined framework. Theoretical analysis shows that timestep-dependent scaling controls the effective perturbation magnitude of a low-rank adapter, while identity-biased candidate selection restricts the radius of selected features around the reference center under explicit conditions. Auditable experiments under the SDXL and DreamBooth 30-subject protocol show that DCAL improves 1-LPIPS, CLIP-I, DINO-I, and CLIP-T on a fixed LoRA candidate pool, while revealing a clear trade-off with CLIP/DINO pairwise diversity and pairwise LPIPS. These results indicate that personalized generation should be evaluated through identity consistency, text alignment, and representation diversity rather than identity metrics alone.