# Dissipation-Constrained Fast Inference

- ID: 2781
- Canonical URL: https://synthcore.org/idea/2781/dissipation-constrained-fast-inference
- API JSON: https://synthcore.org/api/idea/2781.json
- API Markdown: https://synthcore.org/api/idea/2781.md
- Verification status: unverified
- Source: [arXiv:2608.27938](https://arxiv.org/abs/2608.27938)
- Category: sampling
- Solves: speedup, stability, accuracy
- ML areas: diffusion-sampling, scheduler, training-dynamics
- Math tags: stochastic-processes, optimal-transport, control-theory, dynamical-systems
- Ratings: usefulness 6/10; difficulty 6/10; novelty 8/10

## Idea 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.

## Mathematical statement

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.

## Key formulas

- $$dx_t=\mu_t[-\nabla_xU_\phi(x_t,y)]dt+\sqrt{2\mu_t k_{\rm B}T_t}\,dW_t$$
- $$W_2^2(p_0,p_\tau)\leq D_{\rm eff}\,\tau\,\Sigma,\qquad D_{\rm eff}=\mu k_{\rm B}T$$
- $$\tau_{\min}(\Sigma_{\max})=\frac{W_2^2(p_0,p_\tau)}{D_{\rm eff}\Sigma_{\max}}$$
- $$\min_{\{\mu_t,T_t\},\tau}\tau\quad\text{subject to}\quad \operatorname{Acc}(p_\tau)\geq A_0,\ \widehat\Sigma\leq\Sigma_{\max},\ \tau\geq\frac{\widehat W_2^2}{D_{\rm eff}\widehat\Sigma}$$

## Implementation notes

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%.

## Disclaimer

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 Not peer-reviewed.