Local Linear Convergence of ISTA and FISTA on the LASSO Problem

We establish local linear convergence bounds for the ISTA and FISTA iterations on the model LASSO problem. We show that FISTA can be viewed as an accelerated ISTA process. Using a spectral analysis, we show that, when close enough to the solution, both iterations converge linearly, but FISTA slows down compared to ISTA, making it advantageous to switch to ISTA toward the end of the iteration processs. We illustrate the results with some synthetic numerical examples

Intentional commitment as a spontaneous presentation of self

Commitment is a defining feature of human rationality. This study explores a social origin of spontaneous intentional commitment, assuming commitment in individual decision-making arises from an internalized self-presentation, transferring the audience of commitment from a real partner to an inner eye perspective. To test this "social inner eye" hypothesis, we exposed participants to different social contexts while maintaining the individual nature of the task. Across three experiments, we found that (a) individuals consistently showed stronger commitment when acting in front of others, (b) different social contexts had different impacts on the process of commitment formation, with the mere outside observer accelerating commitment, while a parallel player delays it, (c) participants spontaneously coordinated their intentions to avoid conflicts when playing with another parallel player, despite no coordination was required. Taken together, we demonstrated how social context influences the strength, content, and timing of individual commitment. These findings align with the perspective that individual commitment has a social origin. They also contribute to an understanding of why commitment is universally valued across cultures and is seen as a virtue rather than a weakness in human decision-making

The development of commitment: Attention for intention

The ability to take action according to a partially defined plan allows humans to resolve a distant future, even when steps are missing between the present and that future. Adhering to this partial plan requires an intentional commitment that curbs distracting desires conflicting with the planned course of action, enabling humans to act coherently over long horizons. This research (N = 50, 23 boys, ages 5-6, Chinese) explored the cognitive development of commitment to partial plans in a sequential decision-making task, and its correlation to participant capacity for attentional control. Our results suggest that only 6-year-olds committed to partial plans, and moreover, that in both age groups, intentional commitment was positively correlated with the use of proactive control. These findings indicate that intentional commitment does not develop simultaneously with the understanding of intention at infancy, but rather matures gradually in parallel with the development of attentional control

Intentional commitment through an internalized theory of mind: Acting in the eyes of an imagined observer

The ancient Greek hero Ulysses chose to bind himself to resist the temptation of Sirens, highlighting the fact that humans may voluntarily sacrifice their freedom of choice to achieve committed goals. In this work, we propose a computational model for such commitment under the framework of Bayesian Theory of Mind. The model is based on the idea that even when alone, humans act to better demonstrate their intentions to an imagined third-party observer (ITO) censoring their actions. Our model successfully captures the Ulysses-constraint of freedom, as the freedom confuses the ITO’s inference of their intention. We further show that, trajectories generated both by human actors and actors modeled with ITO censorship are easy to interpret both in the eyes of an actual human ob- server and an ITO. The results demonstrate that under conflict- ing desires, humans achieve commitment by spontaneously censoring their actions with an internalized theory of mind

Intention regulates conflicting desires in human decision making

It is an ancient insight that human actions are driven by desires. This insight inspired the formulation that a rational agent acts to maximize expected utility (MEU), which has been widely used in psychology for modeling theory of mind and in artificial intelligence (AI) for controlling machines’ actions. Yet, it's rather unclear how humans act coherently when their desires are complex and often conflicting with each other. Here we show desires do not directly control human actions. Instead, actions are regulated by an intention — a deliberate mental state that commits to a fixed future rather than taking the expected utilities of many futures evaluated by many desires. Our study reveals four behavioral signatures of human intention by demonstrating how human sequential decision-making deviates from the optimal policy based on MEU in a navigation task: “Disruption resistance” as the persistent pursuit of an original intention despite an unexpected change has made that intention suboptimal; “Ulysses-constraint of freedom” as the proactive constraint of one’s freedom by avoiding a path that could lead to many futures, similar to Ulysses’s self-binding to resist the temptation of the Siren’s song; “Enhanced legibility” as an active demonstration of intention by choosing a path whose destination can be promptly inferred by a third-party observer; “Temporal leap” as committing to a distant future even before reaching the proximal one. Our results showed how the philosophy of intention can lead to discoveries of human decision-making, which can also be empirically compared with AI algorithms. The findings showing that to define a theory of mind, intention should be highlighted as a distinctive mental state in between desires and actions, for quarantining conflicting desires from the execution of actions

Intention beyond Desire: Humans Spontaneously Commit to Future Actions

It is an ancient insight that human actions are driven by desires. Yet it misses one mental representation, intention, with which agents regulate conflicting desires by committing to an admissible plan. Here we demonstrate four behavioral signatures of intention only observed in humans: disruption resistance as sticking with a plan despite setbacks; exclusiveness as avoiding paths with temptations of re-planning; deliberation as the gradual emergence of a commitment plan; temporal leap as forming future plans before finishing the current one. Humans were compared against an optimal model formulated as Markov Decision Process (MDP), who acts only to maximize expected future rewards. Conflicting desires are defined as a reward function returning positive rewards for multiple states. It showed none of the behavioral signatures of intention. These results reveal that humans regulate conflicting desires with intentions, which directly drive actions

CEPC Conceptual Design Report: Volume 2 - Physics & Detector

The Circular Electron Positron Collider (CEPC) is a large international scientific facility proposed by the Chinese particle physics community to explore the Higgs boson and provide critical tests of the underlying fundamental physics principles of the Standard Model that might reveal new physics. The CEPC, to be hosted in China in a circular underground tunnel of approximately 100 km in circumference, is designed to operate as a Higgs factory producing electron-positron collisions with a center-of-mass energy of 240 GeV. The collider will also operate at around 91.2 GeV, as a Z factory, and at the WW production threshold (around 160 GeV). The CEPC will produce close to one trillion Z bosons, 100 million W bosons and over one million Higgs bosons. The vast amount of bottom quarks, charm quarks and tau-leptons produced in the decays of the Z bosons also makes the CEPC an effective B-factory and tau-charm factory. The CEPC will have two interaction points where two large detectors will be located. This document is the second volume of the CEPC Conceptual Design Report (CDR). It presents the physics case for the CEPC, describes conceptual designs of possible detectors and their technological options, highlights the expected detector and physics performance, and discusses future plans for detector R&D and physics investigations. The final CEPC detectors will be proposed and built by international collaborations but they are likely to be composed of the detector technologies included in the conceptual designs described in this document. A separate volume, Volume I, recently released, describes the design of the CEPC accelerator complex, its associated civil engineering, and strategic alternative scenarios

CEPC Conceptual Design Report: Volume 2 - Physics & Detector

The Circular Electron Positron Collider (CEPC) is a large international scientific facility proposed by the Chinese particle physics community to explore the Higgs boson and provide critical tests of the underlying fundamental physics principles of the Standard Model that might reveal new physics. The CEPC, to be hosted in China in a circular underground tunnel of approximately 100 km in circumference, is designed to operate as a Higgs factory producing electron-positron collisions with a center-of-mass energy of 240 GeV. The collider will also operate at around 91.2 GeV, as a Z factory, and at the WW production threshold (around 160 GeV). The CEPC will produce close to one trillion Z bosons, 100 million W bosons and over one million Higgs bosons. The vast amount of bottom quarks, charm quarks and tau-leptons produced in the decays of the Z bosons also makes the CEPC an effective B-factory and tau-charm factory. The CEPC will have two interaction points where two large detectors will be located. This document is the second volume of the CEPC Conceptual Design Report (CDR). It presents the physics case for the CEPC, describes conceptual designs of possible detectors and their technological options, highlights the expected detector and physics performance, and discusses future plans for detector R&D and physics investigations. The final CEPC detectors will be proposed and built by international collaborations but they are likely to be composed of the detector technologies included in the conceptual designs described in this document. A separate volume, Volume I, recently released, describes the design of the CEPC accelerator complex, its associated civil engineering, and strategic alternative scenarios