Does semantic communication require a semantic information theory parallel to Shannon's information theory, or can Shannon's work be generalized for semantic communication? This paper advocates for the latter and introduces a semantic generalization of Shannon's information theory (G theory for short). The core idea is to replace the distortion constraint with the semantic constraint, achieved by utilizing a set of truth functions as a semantic channel. These truth functions enable the expressions of semantic distortion, semantic information measures, and semantic information loss. Notably, the maximum semantic information criterion is equivalent to the maximum likelihood criterion and similar to the Regularized Least Squares criterion. This paper shows G theory's applications to daily and electronic semantic communication, machine learning, constraint control, Bayesian confirmation, portfolio theory, and information value. The improvements in machine learning methods involve multilabel learning and classification, maximum mutual information classification, mixture models, and solving latent variables. Furthermore, insights from statistical physics are discussed: Shannon information is similar to free energy; semantic information to free energy in local equilibrium systems; and information efficiency to the efficiency of free energy in performing work. The paper also proposes refining Friston's minimum free energy principle into the maximum information efficiency principle. Lastly, it compares G theory with other semantic information theories and discusses its limitation in representing the semantics of complex data.

Language is an interface to the outside world.

Recent advances in deep learning suggest that we need to maximize and minimize two different kinds of information simultaneously. The Information Max-Min (IMM) method has been used in deep learning, reinforcement learning, and maximum entropy control. Shannon's information rate-distortion function is the theoretical basis of Minimizing Mutual Information (MMI) and data compression, but it is not enough to solve the IMM problem. The author has proposed the semantic information G theory (i.e., Shannon-Lu theory), including the semantic information G measure and the information rate fidelity function R(G) (R is the MMI for the given G of semantic mutual information). The parameter solution of the R(G) function provides a general method to improve the information efficiency, G/R. This paper briefly introduces the semantic information G measure and the parametric solution of the R(G) function. Two examples reveal that the parametric solution can help us optimize range control with the tradeoff between purposiveness (i.e., semantic mutual information) and information efficiency. It seems that the R(G) function can serve as the theoretical basis of IMM methods, but we still need further research in combination with deep learning, reinforcement learning, and constraint control.

The Variational Bayesian method (VB) is used to solve the probability distributions of latent variables with the minimum free energy criterion. This criterion is not easy to understand, and the computation is complex. For these reasons, this paper proposes the Semantic Variational Bayes' method (SVB). The Semantic Information Theory the author previously proposed extends the rate-distortion function R(D) to the rate-fidelity function R(G), where R is the minimum mutual information for given semantic mutual information G. SVB came from the parameter solution of R(G), where the variational and iterative methods originated from Shannon et al.'s research on the rate-distortion function. The constraint functions SVB uses include likelihood, truth, membership, similarity, and distortion functions. SVB uses the maximum information efficiency (G/R) criterion, including the maximum semantic information criterion for optimizing model parameters and the minimum mutual information criterion for optimizing the Shannon channel. For the same tasks, SVB is computationally simpler than VB. The computational experiments in the paper include 1) using a mixture model as an example to show that the mixture model converges as G/R increases; 2) demonstrating the application of SVB in data compression with a group of error ranges as the constraint; 3) illustrating how the semantic information measure and SVB can be used for maximum entropy control and reinforcement learning in control tasks with given range constraints, providing numerical evidence for balancing control's purposiveness and efficiency. Further research is needed to apply SVB to neural networks and deep learning.

We propose a new perspective on deep ReLU networks, namely as circuit counterparts of Lukasiewicz infinite-valued logic -- a many-valued (MV) generalization of Boolean logic. An algorithm for extracting formulae in MV logic from deep ReLU networks is presented. As the algorithm applies to networks with general, in particular also real-valued, weights, it can be used to extract logical formulae from deep ReLU networks trained on data.

A new trend in deep learning, represented by Mutual Information Neural Estimation (MINE) and Information Noise Contrast Estimation (InfoNCE), is emerging. In this trend, similarity functions and Estimated Mutual Information (EMI) are used as learning and objective functions. Coincidentally, EMI is essentially the same as Semantic Mutual Information (SeMI) proposed by the author 30 years ago. This paper first reviews the evolutionary histories of semantic information measures and learning functions. Then, it briefly introduces the author's semantic information G theory with the rate-fidelity function R(G) (G denotes SeMI, and R(G) extends R(D)) and its applications to multi-label learning, the maximum Mutual Information (MI) classification, and mixture models. Then it discusses how we should understand the relationship between SeMI and Shan-non's MI, two generalized entropies (fuzzy entropy and coverage entropy), Autoencoders, Gibbs distributions, and partition functions from the perspective of the R(G) function or the G theory. An important conclusion is that mixture models and Restricted Boltzmann Machines converge because SeMI is maximized, and Shannon's MI is minimized, making information efficiency G/R close to 1. A potential opportunity is to simplify deep learning by using Gaussian channel mixture models for pre-training deep neural networks' latent layers without considering gradients. It also discusses how the SeMI measure is used as the reward function (reflecting purposiveness) for reinforcement learning. The G theory helps interpret deep learning but is far from enough. Combining semantic information theory and deep learning will accelerate their development.

Language is an interface to the outside world. In order for embodied agents to use it, language must be grounded in other, sensorimotor modalities. While there is an extended literature studying how machines can learn grounded language, the topic of how to learn spatio-temporal linguistic concepts is still largely uncharted. To make progress in this direction, we here introduce a novel spatio-temporal language grounding task where the goal is to learn the meaning of spatio-temporal descriptions of behavioral traces of an embodied agent. This is achieved by training a truth function that predicts if a description matches a given history of observations. The descriptions involve time-extended predicates in past and present tense as well as spatio-temporal references to objects in the scene. To study the role of architectural biases in this task, we train several models including multimodal Transformer architectures; the latter implement different attention computations between words and objects across space and time. We test models on two classes of generalization: 1) generalization to randomly held-out sentences; 2) generalization to grammar primitives. We observe that maintaining object identity in the attention computation of our Transformers is instrumental to achieving good performance on generalization overall, and that summarizing object traces in a single token has little influence on performance. We then discuss how this opens new perspectives for language-guided autonomous embodied agents. We also release our code under open-source license as well as pretrained models and datasets to encourage the wider community to build upon and extend our work in the future.

After long arguments between positivism and falsificationism, the verification of universal hypotheses was replaced with the confirmation of uncertain major premises. Unfortunately, Hemple discovered the Raven Paradox (RP). Then, Carnap used the logical probability increment as the confirmation measure. So far, many confirmation measures have been proposed. Measure F among them proposed by Kemeny and Oppenheim possesses symmetries and asymmetries proposed by Elles and Fitelson, monotonicity proposed by Greco et al., and normalizing property suggested by many researchers. Based on the semantic information theory, a measure b* similar to F is derived from the medical test. Like the likelihood ratio, b* and F can only indicate the quality of channels or the testing means instead of the quality of probability predictions. And, it is still not easy to use b*, F, or another measure to clarify the RP. For this reason, measure c* similar to the correct rate is derived. The c* has the simple form: (a-c)/max(a, c); it supports the Nicod Criterion and undermines the Equivalence Condition, and hence, can be used to eliminate the RP. Some examples are provided to show why it is difficult to use one of popular confirmation measures to eliminate the RP. Measure F, b*, and c* indicate that fewer counterexamples' existence is more essential than more positive examples' existence, and hence, are compatible with Popper's falsification thought.

Bayesian Inference (BI) uses the Bayes' posterior whereas Logical Bayesian Inference (LBI) uses the truth function or membership function as the inference tool. LBI was proposed because BI was not compatible with the classical Bayes' prediction and didn't use logical probability and hence couldn't express semantic meaning. In LBI, statistical probability and logical probability are strictly distinguished, used at the same time, and linked by the third kind of Bayes' Theorem. The Shannon channel consists of a set of transition probability functions whereas the semantic channel consists of a set of truth functions. When a sample is large enough, we can directly derive the semantic channel from Shannon's channel. Otherwise, we can use parameters to construct truth functions and use the Maximum Semantic Information (MSI) criterion to optimize the truth functions. The MSI criterion is equivalent to the Maximum Likelihood (ML) criterion, and compatible with the Regularized Least Square (RLS) criterion. By matching the two channels one with another, we can obtain the Channels' Matching (CM) algorithm. This algorithm can improve multi-label classifications, maximum likelihood estimations (including unseen instance classifications), and mixture models. In comparison with BI, LBI 1) uses the prior P(X) of X instead of that of Y or {\theta} and fits cases where the source P(X) changes, 2) can be used to solve the denotations of labels, and 3) is more compatible with the classical Bayes' prediction and likelihood method. LBI also provides a confirmation measure between -1 and 1 for induction.