We thank all reviewers for their constructive comments. We fixed the architecture g in our previous experiments to a two layer neural network. We discussed how to select the layer choice and its impact above. The computational cost is low since the pretrained model is fixed, and we only optimize for g and c. We didn't test on Imagenet since we can't visualize results for all 1000 classes.

PAC-Bayes is a useful framework for deriving generalization bounds which was introduced by McAllester ('98). This framework has the flexibility of deriving distribution-and algorithm-dependent bounds, which are often tighter than VCrelated uniform convergence bounds. In this manuscript we present a limitation for the PAC-Bayes framework. We demonstrate an easy learning task which is not amenable to a PAC-Bayes analysis. Specifically, we consider the task of linear classification in 1D; it is well-known that this task is learnable using just O(log(1/δ)/ɛ) examples. On the other hand, we show that this fact can not be proved using a PAC-Bayes analysis: for any algorithm that learns 1-dimensional linear classifiers there exists a (realizable) distribution for which the PAC-Bayes bound is arbitrarily large.

In this paper, we study the problem of fair sparse regression on a biased dataset where bias depends upon a hidden binary attribute. The presence of a hidden attribute adds an extra layer of complexity to the problem by combining sparse regression and clustering with unknown binary labels. The corresponding optimization problem is combinatorial, but we propose a novel relaxation of it as an invex optimization problem. To the best of our knowledge, this is the first invex relaxation for a combinatorial problem. We show that the inclusion of the debiasing/fairness constraint in our model has no adverse effect on the performance. Rather, it enables the recovery of the hidden attribute.

A central piece in enabling intelligent agentic behavior in foundation models is to make them capable of introspecting upon their behavior, reasoning, and correcting their mistakes as more computation or interaction is available. Even the strongest proprietary large language models (LLMs) do not quite exhibit the ability of continually improving their responses sequentially. In this paper, we develop RISE: Recursive IntroSpEction, an approach for fine-tuning LLMs to introduce this capability, despite prior work hypothesizing that this capability may not be possible to attain. Our approach prescribes an iterative fine-tuning procedure, which attempts to teach the model how to alter its response after having executed previously unsuccessful attempts to solve a hard test-time problem, with optionally additional environment feedback. RISE poses fine-tuning for a singleturn prompt as solving a multi-turn Markov decision process (MDP), where the initial state is the prompt. Inspired by principles in online imitation and offline reinforcement learning, we propose strategies for multi-turn data collection and training so as to imbue an LLM with the capability to recursively detect and correct its previous mistakes in subsequent iterations. Our experiments show that RISE enables Llama2, Llama3, and Mistral models to improve themselves with more turns on reasoning tasks, outperforming several single-turn strategies given an equal amount of inference-time computation. We also find that RISE scales well, often attaining larger benefits with more capable models, without disrupting one-turn abilities as a result of expressing more complex distributions.

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Let's first consider the minimum for ˆV, Next, we prove the second part of the theorem regarding f. Note that, unlike the original PPO which samples mini-batches of frames, we sample on a trajectory-by-trajectory basis. For example, assume the batch size is 256 and n = 128 for the backup horizon, then each batch contains 2 128-step trajectories. C.1 Computational resources All the experiments were performed on an internal cluster of NVIDIA A100 GPUs. Training a MinAtar agent in a single environment takes less than 30 minutes (wall-clock time).

The predominant approach in reinforcement learning is to assign credit to actions based on the expected return. However, we show that the return may depend on the policy in a way which could lead to excessive variance in value estimation and slow down learning. Instead, we show that the advantage function can be interpreted as causal effects and shares similar properties with causal representations. Based on this insight, we propose Direct Advantage Estimation (DAE), a novel method that can model the advantage function and estimate it directly from on-policy data while simultaneously minimizing the variance of the return without requiring the (action-)value function. We also relate our method to Temporal Difference methods by showing how value functions can be seamlessly integrated into DAE. The proposed method is easy to implement and can be readily adapted by modern actor-critic methods. We evaluate DAE empirically on three discrete control domains and show that it can outperform generalized advantage estimation (GAE), a strong baseline for advantage estimation, on a majority of the environments when applied to policy optimization.

Despite satisfactory results on "easy" cases of single image reflection separation, prior dual-stream methods still suffer from considerable performance degradation when facing complex ones, i.e., the transmission layer is densely entangled with the reflection having a wide distribution of spatial intensity. The main reasons come from the lack of concern on the feature correlation during interaction, and the limited receptive field. To remedy these deficiencies, this paper presents a Dual-Stream Interactive Transformer (DSIT) design. Specifically, we devise a dual-attention interactive structure that embraces a dual-stream self-attention and a layer-aware dual-stream cross-attention mechanism to simultaneously capture intra-layer and inter-layer feature correlations. Meanwhile, the introduction of attention mechanisms can also mitigate the receptive field limitation. We modulate single-stream pre-trained Transformer embeddings with dual-stream convolutional features through cross-architecture interactions to provide richer semantic priors, thereby further relieving the ill-posedness of the problem. Extensive experimental results reveal the merits of the proposed DSIT over other state-of-the-art alternatives. Our code is publicly available at https://github.com/mingcv/DSIT.