{
 "artifacts": null,
 "category": "sampling",
 "description": "Use a fixed learned energy or score network but search over inference protocols with different mobility, temperature, and duration. Select the shortest protocol that reaches a target accuracy without exceeding a prescribed entropy-production budget, exploiting the paper's observation that computational accuracy does not uniquely determine the thermodynamic path.",
 "formulas_latex": [
  "$$dx_t=\\mu_t[-\\nabla_xU_\\phi(x_t,y)]dt+\\sqrt{2\\mu_t k_{\\rm B}T_t}\\,dW_t$$",
  "$$W_2^2(p_0,p_\\tau)\\leq D_{\\rm eff}\\,\\tau\\,\\Sigma,\\qquad D_{\\rm eff}=\\mu k_{\\rm B}T$$",
  "$$\\tau_{\\min}(\\Sigma_{\\max})=\\frac{W_2^2(p_0,p_\\tau)}{D_{\\rm eff}\\Sigma_{\\max}}$$",
  "$$\\min_{\\{\\mu_t,T_t\\},\\tau}\\tau\\quad\\text{subject to}\\quad \\operatorname{Acc}(p_\\tau)\\geq A_0,\\ \\widehat\\Sigma\\leq\\Sigma_{\\max},\\ \\tau\\geq\\frac{\\widehat W_2^2}{D_{\\rm eff}\\widehat\\Sigma}$$"
 ],
 "id": 2781,
 "implementation": "Apply this to a small diffusion classifier, stochastic energy-based classifier, or iterative latent-state network. Train one potential U_φ or score model and freeze it during inference. Expose mobility, temperature, and number of Euler-Maruyama steps as protocol parameters. For each candidate schedule, initialize x_0 identically and use x_{j+1}=x_j−μ_j h∇U_φ(x_j,y)+sqrt(2μ_j k_B T_j h)z_j. Run K samples per input or a large validation batch. At checkpoints estimate the distribution of states, compute sliced Wasserstein displacement between successive checkpoints, and estimate entropy production with σ̂_j=(1/K)Σ_k||x_{j+1}^{(k)}−x_j^{(k)}||²/(h μ_j k_B T_j). Reject schedules that fail validation accuracy or exceed Σ_max; among remaining schedules choose the smallest step count. The Langevin dynamics and speed-limit inequality are imported from the mechanism, while W_2, entropy production, and accuracy are measured empirically. Begin with a two-dimensional Gaussian-mixture problem, then test a small MLP score model on MNIST. Compare constant-temperature, annealed-temperature, high-mobility, and low-mobility protocols. The quantitative prediction is a Pareto frontier: decreasing runtime below Ŵ_2²/(D_effΣ_max) must either reduce accuracy or increase dissipation. Successful protocols should have q=τD_effΣ/Ŵ_2²≥1, with the empirical transition near q=1 within 20%.",
 "math_summary": "Let U_φ(x,y) be a learned task potential, μ_t the mobility, T_t the temperature, and f_φ(x,y)=−∇_xU_φ(x,y). The stochastic inference state follows dx_t=μ_t f_φ(x_t,y)dt+sqrt(2μ_t k_B T_t)dW_t. With diffusion coefficient D_eff=μ k_B T, the Wasserstein speed limit gives W_2(p_0,p_τ)^2≤D_eff τΣ. For a maximum permitted entropy production Σ_max, the minimum feasible duration is τ_min=W_2^2/(D_effΣ_max). The protocol-selection problem minimizes τ subject to endpoint accuracy at least A_0, estimated entropy production at most Σ_max, and the speed-limit inequality.",
 "math_tags": [
  "stochastic-processes",
  "optimal-transport",
  "control-theory",
  "dynamical-systems"
 ],
 "ml_areas": [
  "diffusion-sampling",
  "scheduler",
  "training-dynamics"
 ],
 "paper": {
  "arxiv_id": "2608.27938",
  "arxiv_url": "https://arxiv.org/abs/2608.27938",
  "summary_what_math_gives_to_ml": "The paper provides a transferable Wasserstein speed limit for stochastic computation: a probability distribution cannot travel a specified distance in finite time without sufficient integrated probability-current activity, equivalent to entropy production or dissipated heat. Its important engineering consequence is protocol freedom: the same task accuracy can be achieved with different combinations of runtime, noise, mobility, and dissipation. A neural-network implementation can monitor distributional motion during stochastic optimization or inference and adapt the step size, noise level, or number of iterations when the measured trajectory approaches the speed-limit boundary.",
  "title": "The thermodynamic freedom of a thermodynamic computer",
  "year": "2026"
 },
 "ratings": {
  "difficulty": 6,
  "novelty": 8,
  "usefulness": 6
 },
 "solves": [
  "speedup",
  "stability",
  "accuracy"
 ],
 "title": "Dissipation-Constrained Fast Inference",
 "url": "https://synthcore.org/idea/2781/dissipation-constrained-fast-inference",
 "verification": {
  "peer_reviewed": false,
  "status": "unverified",
  "status_label": "Unverified",
  "verdict_source": "deterministic test code (paired-seed permutation statistics)"
 }
}