The supplemental material is organized as follow. According to [1, Lemma 10.4], we have (1 The conclusion follows by letting ɛ 0 in above inequality. It follows from Lemma 3.1 that for any ɛ > 0, there exists Lemma B.2. Assume that y The conclusion follows by letting ɛ 0 in above inequality. According to [1, Theorem 10.34], when f(x,) is convex and L Our experiments were conducted on a PC with Intel Core i9-10900KF CPU (3.70GHz), 128GB RAM, two NVIDIA GeForce RTX 3090 24GB GPUs, and the platform is 64-bit Ubuntu 18.04.5 For the non-convex BLO problem within the text, we follow the parameter settings in Table 1.

In recent years, Bi-Level Optimization (BLO) techniques have received extensive attentions from both learning and vision communities. A variety of BLO models in complex and practical tasks are of non-convex follower structure in nature (a.k.a., without Lower-Level Convexity, LLC for short). However, this challenging class of BLOs is lack of developments on both efficient solution strategies and solid theoretical guarantees. In this work, we propose a new algorithmic framework, named Initialization Auxiliary and Pessimistic Trajectory Truncated Gradient Method (IAPTT-GM), to partially address the above issues. In particular, by introducing an auxiliary as initialization to guide the optimization dynamics and designing a pessimistic trajectory truncation operation, we construct a reliable approximate version of the original BLO in the absence of LLC hypothesis. Our theoretical investigations establish the convergence of solutions returned by IAPTT-GM towards those of the original BLO without LLC. As an additional bonus, we also theoretically justify the quality of our IAPTT-GM embedded with Nesterov's accelerated dynamics under LLC. The experimental results confirm both the convergence of our algorithm without LLC, and the theoretical findings under LLC.

In this paper, we propose a novel approach, Generalized fMRI-to-image reconstruction by adaptively integrating Expanded Semantic manifold and Structural information (GESS), to address the semantic gap in the fMRI-to-image reconstruction problem. The improvement in fMRI-to-image reconstruction can lead to a better understanding of the human visual system and the neural representations of visual stimuli, thus significantly enhancing the potential applications of brain-computer interface (BCI) technologies. However, it is essential to consider the ethical implications of such advancements. As BCI technologies move closer to being able to "read the mind", privacy and consent concerns may arise. It will be crucial to develop policies and guidelines for the responsible use of these technologies and ensure that they are employed in a manner that respects individuals' rights and autonomy.

Although existing fMRI-to-image reconstruction methods could predict highquality images, they do not explicitly consider the semantic gap between training and testing data, resulting in reconstruction with unstable and uncertain semantics. This paper addresses the problem of generalized fMRI-to-image reconstruction by explicitly alleviates the semantic gap. Specifically, we leverage the pre-trained CLIP model to map the training data to a compact feature representation, which essentially extends the sparse semantics of training data to dense ones, thus alleviating the semantic gap of the instances nearby known concepts (i.e., inside the training super-classes). Inspired by the robust low-level representation in fMRI data, which could help alleviate the semantic gap for instances that far from the known concepts (i.e., outside the training super-classes), we leverage structural information as a general cue to guide image reconstruction. Further, we quantify the semantic uncertainty based on probability density estimation and achieve Generalized fMRI-to-image reconstruction by adaptively integrating Expanded Semantics and Structural information (GESS) within a diffusion process. Experimental results demonstrate that the proposed GESS model outperforms state-ofthe-art methods, and we propose a generalized scenario split strategy to evaluate the advantage of GESS in closing the semantic gap. Our codes are available at https://github.com/duolala1/GESS.

Human languages support both semantic categorization and local pragmatic interactions that require context-sensitive reasoning about meaning. While semantics and pragmatics are two fundamental aspects of language, they are typically studied independently and their co-evolution is largely under-explored. Here, we aim to bridge this gap by studying how a shared lexicon may emerge from local pragmatic interactions. To this end, we extend a recent information-theoretic framework for emergent communication in artificial agents, which integrates utility maximization, associated with pragmatics, with general communicative constraints that are believed to shape human semantic systems. Specifically, we show how to adapt this framework to train agents via unsupervised pragmatic interactions, and then evaluate their emergent lexical semantics. We test this approach in a rich visual domain of naturalistic images, and find that key human-like properties of the lexicon emerge when agents are guided by both context-specific utility and general communicative pressures, suggesting that both aspects are crucial for understanding how language may evolve in humans and in artificial agents.

Recent advancements in Vision-Language Models (VLMs) have enabled complex multimodal tasks by processing text and image data simultaneously, significantly enhancing the field of artificial intelligence.

Silicon-photonics-based optical neural network (ONN) is a promising hardware platform that could represent a paradigm shift in efficient AI with its CMOScompatibility, flexibility, ultra-low execution latency, and high energy efficiency. In-situ training on the online programmable photonic chips is appealing but still encounters challenging issues in on-chip implementability, scalability, and efficiency.

Our loss function is the integral of that gradient (only the gradient itself is needed for training).