While this may seem of mostly theoretical interest, in this work, we show that it can be used in practice to the benefit of BNNs.

As proved by Feng et al. (2021), the binary cross-entropy loss We include more results on teacher model and teacher model + {DRO (Hashimoto et al., 2018) /ARL (Lahoti et al., 2020) / FairRF (Zhao et al., 2022) /our knowledge distillation} in Tab. Effect of our label smoothing can be observed by comparing between "Teacher (with hard label)" and "Teacher (with softmax/linear label)" in the 6 tables. Here the capacity is the same, the only difference is the label smoothing. Here the training method is the same, only difference is capacity. Table 8: Results on COMP AS dataset with sensitive attribute race .

Machine learning has been widely adopted in real-world scenarios that has great social influence, and fairness in automatic decision-making systems has become an arising concern.

The presence of training label noise is generally considered harmful.

Here we proved that (1) and (2) are equivalent; (1) and (3) are equivalent. Proposition 3. 14 Lemma 2. Given With the lemma above, we now present the proof of Proposition 3. B.1 Example Implementation We provide an example implementation of Algorithm 2 in Listing 1. 17 1 Based on exponentiation by squaring. Best results are in bold. Based on the observation, Wei et al. Our method identified a different source of gradient vanishing caused by the small coefficients for higher-order terms in DAG constraints.

These experiments include COP-Gen training in the latent space of pretrained Residual Flow and BigGAN.

Current methods like membership inference or active IP protection either work only in settings where the suspected text is known or do not provide reliable statistical guarantees. We discover that, on the contrary, it is possible to reliably determine if a language model was trained on synthetic data if that data is output by a watermarked LLM.