Henrik Bostrom

Ziyun Li, Huancheng Hu, Soon Hoe Lim et al.

Flow-based generative models can be viewed through a physics lens: sampling transports a particle from noise to data by integrating a learned velocity field, and each sample corresponds to a trajectory with its own dynamical effort. Motivated by classical mechanics, we introduce Kinetic Path Energy (KPE), an action-like, per-sample diagnostic that measures the accumulated kinetic effort along an ordinary differential equation (ODE) trajectory. Empirically, KPE exhibits two robust correspondences: {i} higher KPE predicts stronger semantic fidelity; {ii} high-KPE trajectories land in sparse representation regions. We further provide theoretical guarantees linking trajectory energy to data sparsity. Paradoxically, this correlation is non-monotonic. At sufficiently high energy, generation can degenerate into memorization. Leveraging the closed-form formula of empirical flow matching, we show that extreme energies drive trajectories toward near-copies of training examples. This yields a Goldilocks principle and motivates Kinetic Trajectory Shaping (KTS), a training-free two-phase inference strategy that boosts early motion and enforces a late-time soft landing, reducing memorization and improving generation quality across benchmark tasks.

Amir Hossein Akhavan Rahnama, Judith Butepage, Pierre Geurts et al.

Evaluating explanation techniques using human subjects is costly, time-consuming and can lead to subjectivity in the assessments. To evaluate the accuracy of local explanations, we require access to the true feature importance scores for a given instance. However, the prediction function of a model usually does not decompose into linear additive terms that indicate how much a feature contributes to the output. In this work, we suggest to instead focus on the log odds ratio (LOR) of the prediction function, which naturally decomposes into additive terms for logistic regression and naive Bayes. We demonstrate how we can benchmark different explanation techniques in terms of their similarity to the LOR scores based on our proposed approach. In the experiments, we compare prominent local explanation techniques and find that the performance of the techniques can depend on the underlying model, the dataset, which data point is explained, the normalization of the data and the similarity metric.