With the availability of diverse sensor modalities (i.e., RGB, Depth, Infrared) and the success of multi-modal learning, multi-modal face anti-spoofing (FAS) has emerged as a prominent research focus. The intuition behind it is that leveraging multiple modalities can uncover more intrinsic spoofing traces. However, this approach presents more risk of misalignment. We identify two main types of misalignment: (1) \textbf{Intra-domain modality misalignment}, where the importance of each modality varies across different attacks. For instance, certain modalities (e.g., Depth) may be non-defensive against specific attacks (e.g., 3D mask), indicating that each modality has unique strengths and weaknesses in countering particular attacks. Consequently, simple fusion strategies may fall short. (2) \textbf{Inter-domain modality misalignment}, where the introduction of additional modalities exacerbates domain shifts, potentially overshadowing the benefits of complementary fusion. To tackle (1), we propose a alignment module between modalities based on mutual information, which adaptively enhances favorable modalities while suppressing unfavorable ones. To address (2), we employ a dual alignment optimization method that aligns both sub-domain hyperplanes and modality angle margins, thereby mitigating domain gaps. Our method, dubbed \textbf{D}ual \textbf{A}lignment of \textbf{D}omain and \textbf{M}odality (DADM), achieves state-of-the-art performance in extensive experiments across four challenging protocols demonstrating its robustness in multi-modal domain generalization scenarios. The codes will be released soon.

The memoryless additive inverse Gaussian noise channel model describing communication based on the exchange of chemical molecules in a drifting liquid medium is investigated for the situation of simultaneously an average-delay and a peak-delay constraint. Analytical upper and lower bounds on its capacity in bits per molecule use are presented. These bounds are shown to be asymptotically tight, i.e., for the delay constraints tending to infinity with their ratio held constant (or for the drift velocity of the fluid tending to infinity), the asymptotic capacity is derived precisely. Moreover, characteristics of the capacity-achieving input distribution are derived that allow accurate numerical computation of capacity. The optimal input appears to be a mixed continuous and discrete distribution.