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parse/dev/EcGGFkNTxdJ/EcGGFkNTxdJ.md

@@ -621,7 +621,7 @@ where the last inequality follows from Equation (6). This proves that Algorithm
 Theorem 3. Supposing in Algorithm 1 any permutation of agents has a fixed non-zero probability to begin the update, a sequence $\left( \pi _ { k } \right) _ { k = 0 } ^ { \infty }$ of joint policies generated by the algorithm, in a cooperative Markov game, has a non-empty set of limit points, each of which is a Nash equilibrium.
 
 Proof. Step 1 (convergence). Firstly, it is clear that the sequence $( J ( \pi _ { k } ) ) _ { k = 0 } ^ { \infty }$ converges as, by Theorem 2, it is non-decreasing and bounded above by $\frac { R _ { \mathrm { m a x } } } { 1 - \gamma }$ . Let us denote the limit by $\bar { J }$ . For every $k$ , y enote the tuple of a, and we note that ording to whose order the agents perform the sequential updates,is a random process. Furthermore, we know that the sequence $i _ { 1 : n } ^ { k }$ $\breve { \left( i _ { 1 : n } ^ { k } \right) } _ { k \in \mathbb { N } }$   
-of policies $\left( \pi _ { k } \right)$ is bounded, so by Bolzano-Weierstrass Theorem, it has at least one convergent subsequence. Let $\bar { \pi }$ be any limit point of the sequence (note that the set of limit points is a random set), and πkj 
 j=0 be a subsequence converging to $\bar { \pi }$ (which is a random subsequence as well). By continuity of $J$ in $\pi$ (Corollary 1), we have
+of policies $\left( \pi _ { k } \right)$ is bounded, so by Bolzano-Weierstrass Theorem, it has at least one convergent subsequence. Let $\bar { \pi }$ be any limit point of the sequence (note that the set of limit points is a random set), and πkj 
 j=0 be a subsequence converging to $\bar { \pi }$ (which is a random subsequence as well). By continuity of $J$ in $\pi$ (Corollary 1), we have
 
 $$
 J ( \bar { \pmb { \pi } } ) = J ( \operatorname* { l i m } _ { j  \infty } \pmb { \pi } _ { k _ { j } } ) = \operatorname* { l i m } _ { j  \infty } J ( \pmb { \pi } _ { k _ { j } } ) = \bar { J } .

parse/dev/G2Q2Mh3avow/G2Q2Mh3avow.md

@@ -94,7 +94,7 @@ Tab. 3: On generating contextual image captions and descriptions (CIDEr) from Co
 
 Method. We also address video-to-text retrieval, a common video understanding task, by using both audio and visual data. We improve on a prior approach (Portillo-Quintero et al., 2021) which computes a CLIP-based video-and-text similarity measure for one-to-many nearest neighbor matching. Adding in audio information, our system transcribes audio with speech-to-text ALMs (Bapna et al., 2022) for automatic speech recognition (ASR e.g., via Google Cloud speech-to-text API (gcl)), then summarizes the transcripts with an LLM using the following prompt:
 
-We compute similarity scores of the generated summary to the set of captions with a masked LLM (e.g., with sentence similarity from RoBERTa (Liu et al., 2019b)), and use those scores to re-weight the CLIP-based ranking from Portillo-Quintero et al. (2021). For videos with sufficientlylong transcripts ${ \geq } 1 4 5$ characters), the matching score is: CLIP (caption) · CLIP (video0)
 $\times$ RoBERTa (caption) · RoBERTa (GPT-3(prompt, Speech2Text (audio0)))
, where $\cdot$ represents normalized dot product of embeddings, and $\times$ represents scalar multiplication. If there is no audio or the transcript is too short, we default to Portillo-Quintero et al. i.e., the dot product of CLIP text embeddings and averaged CLIP image embeddings of all video frames $C L I P ( \mathrm { c a p t i o n } ) \cdot C L I P ( \mathrm { v i d e o } ^ { \prime } )$ .
+We compute similarity scores of the generated summary to the set of captions with a masked LLM (e.g., with sentence similarity from RoBERTa (Liu et al., 2019b)), and use those scores to re-weight the CLIP-based ranking from Portillo-Quintero et al. (2021). For videos with sufficientlylong transcripts ${ \geq } 1 4 5$ characters), the matching score is: CLIP (caption) · CLIP (video0)
 $\times$ RoBERTa (caption) · RoBERTa (GPT-3(prompt, Speech2Text (audio0)))
, where $\cdot$ represents normalized dot product of embeddings, and $\times$ represents scalar multiplication. If there is no audio or the transcript is too short, we default to Portillo-Quintero et al. i.e., the dot product of CLIP text embeddings and averaged CLIP image embeddings of all video frames $C L I P ( \mathrm { c a p t i o n } ) \cdot C L I P ( \mathrm { v i d e o } ^ { \prime } )$ .
 
 Results. We evaluate on MSR-VTT (Xu et al., 2016), noted in other recent works (Gao et al., 2021; Cheng et al., 2021) as a popular benchmark for video-to-text retrieval. We compare our method with zero-shot methods, as well as finetuned methods specifically trained on MSR-VTT. Results show that our method outperforms zero-shot state-of-the-art (Tab.4). Since our system uses Portillo-Quintero et al. (2021) to process CLIP features but additionally incorporates LLM reasoning on speech-to-text transcripts,