Discriminative Random Walks (DRWs) are a simple yet powerful tool for semi-supervised node classification, but their theoretical foundations remain fragmentary. We revisit DRWs through the lens of information geometry, treating the family of class-specific hitting-time laws on an absorbing Markov chain as a statistical manifold. Starting from a log-linear edge-weight model, we derive closed-form expressions for the hitting-time probability mass function, its full moment hierarchy, and the observed Fisher information. The Fisher matrix of each seed node turns out to be rank-one, taking the quotient by its null space yields a low-dimensional, globally flat manifold that captures all identifiable directions of the model. Leveraging the geometry, we introduce a sensitivity score for unlabeled nodes that bounds, and in one-dimensional cases attains, the maximal first-order change in DRW betweenness under unit Fisher perturbations. The score can lead to principled strategies for active label acquisition, edge re-weighting, and explanation.

Tosupportthis, we compute the cosine similarity between representations from augmented and original samples, i.e., CS = Ex D,t T[sim(g f(t(x)),g f(x))]. For linear evaluation benchmarks, we randomly choose validation samples in the training split for each dataset when the validation split is not officially provided. Note that the pretraining setups are the same as they officiallyusedforImageNet pretraining described in[2,5,30]. When incorporating our AugSelf into the methods, we use λ=1.0andAAugSelf ={crop,color},unlessotherwisestated. Other hyperparameters are the same as the ImageNet100 setup describedinSectionF.1.

Furthermore, AugSelf can easily be incorporated into recent state-of-the-art representation learning methods with a negligible additional training cost.

However, existing methods assume a reliable and unbiased forecasting environment, which isnot always available inthe wild. Inthis work, we investigate the vulnerability ofspatiotemporal trafficforecasting models andpropose apractical adversarial spatiotemporal attack framework.

These assumptions are not strong and can be satisfied in most of environments includes MuJoCo, Atarigamesandsoon. Let f be an Lebesgue integrable function, P and Q are two probability distributions, |f| C,then EP(x)f(x) EQ(x)f(x) CDTV(P,Q) (5) Proof. Suppose there are two actions a1, a2 under state s, and let Q1(s,a1) = u, Q1(s,a2) = v. In this way, we can derive the upper bound of Ea π2Q1(s,a) Ea π1Q1(s,a)asabove. Since both sides of the above equation have the same minimum (here the minima are given by Qk = Q), we can replace the objective in Problem 2 with the upper bound in Eq. (10) and solve therelaxedoptimizationproblem.

Therefore, a series of attempts Chung et al. [2020], Wu et al. [2020], Wang et al. [2020c], Gordon et al. [2020a], Tang et al. [2019], Aguilar et al. [2019] have been made to review the techniques for effective