Rensselaer Polytechnic Institute

As the training set grows, diffusion models move from memorizing training samples to generalizing, and between these phases an intermediate kind of attractor appears that matches no training image yet recurs in generated samples. Reading generation as retrieval in a dense associative memory predicts such spurious states once storage capacity is exceeded; on MNIST, FASHION-MNIST, CIFAR-10 and LSUN-CHURCH the spurious fraction rises and then falls at the memorization-to-generalization boundary, with basin volumes between those of memorized and generalized samples.

As the training set grows, diffusion models move from memorizing training samples to generalizing, and between these phases an intermediate kind of attractor appears that matches no training image yet recurs in generated samples. Reading generation as retrieval in a dense associative memory predicts such spurious states once storage capacity is exceeded; on MNIST, FASHION-MNIST, CIFAR-10 and LSUN-CHURCH the spurious fraction rises and then falls at the memorization-to-generalization boundary, with basin volumes between those of memorized and generalized samples.

TokenCast learns a composable cost triple for each execution segment of an LLM agent (call count, net input-length change, and a cost residual), uses an exact composition identity to fold the cost of earlier context being re-read by every later call into a cumulative estimate, and refreshes the forecast from newly observed execution evidence without additional LLM calls; on SWE-bench Verified the mean cumulative prediction time is 32.8 ms per run, mean absolute error reduction against the strongest comparator averages 14.5% over 96 evaluated combinations across 4 task suites and 6 agent models, and offline budget-control replay uses 21.3% fewer tokens on average than a fixed-budget policy at matched trace completion.

TokenCast learns a composable cost triple for each execution segment of an LLM agent (call count, net input-length change, and a cost residual), uses an exact composition identity to fold the cost of earlier context being re-read by every later call into a cumulative estimate, and refreshes the forecast from newly observed execution evidence without additional LLM calls; on SWE-bench Verified the mean cumulative prediction time is 32.8 ms per run, mean absolute error reduction against the strongest comparator averages 14.5% over 96 evaluated combinations across 4 task suites and 6 agent models, and offline budget-control replay uses 21.3% fewer tokens on average than a fixed-budget policy at matched trace completion.