The effect of relative entropy asymmetry is analyzed in the context of empirical risk minimization (ERM) with relative entropy regularization (ERM-RER). Two regularizations are considered: $(a)$ the relative entropy of the measure to be optimized with respect to a reference measure (Type-I ERM-RER); or $(b)$ the relative entropy of the reference measure with respect to the measure to be optimized (Type-II ERM-RER). The main result is the characterization of the solution to the Type-II ERM-RER problem and its key properties. By comparing the well-understood Type-I ERM-RER with Type-II ERM-RER, the effects of entropy asymmetry are highlighted. The analysis shows that in both cases, regularization by relative entropy forces the solution's support to collapse into the support of the reference measure, introducing a strong inductive bias that can overshadow the evidence provided by the training data. Finally, it is shown that Type-II regularization is equivalent to Type-I regularization with an appropriate transformation of the empirical risk function.
相關內容
A growing amount of literature critiques the current operationalizations of empathy based on loose definitions of the construct. Such definitions negatively affect dataset quality, model robustness, and evaluation reliability. We propose an empathy evaluation framework that operationalizes empathy close to its psychological origins. The framework measures the variance in responses of LLMs to prompts using existing metrics for empathy and emotional valence. The variance is introduced through the controlled generation of the prompts by varying social biases affecting context understanding, thus impacting empathetic understanding. The control over generation ensures high theoretical validity of the constructs in the prompt dataset. Also, it makes high-quality translation, especially into languages that currently have little-to-no way of evaluating empathy or bias, such as the Slavonic family, more manageable. Using chosen LLMs and various prompt types, we demonstrate the empathy evaluation with the framework, including multiple-choice answers and free generation. The variance in our initial evaluation sample is small and we were unable to measure convincing differences between the empathetic understanding in contexts given by different social groups. However, the results are promising because the models showed significant alterations their reasoning chains needed to capture the relatively subtle changes in the prompts. This provides the basis for future research into the construction of the evaluation sample and statistical methods for measuring the results.
We provide a complete characterization of the solvability/impossibility of deterministic stabilizing consensus in any computing model with benign process and communication faults using point-set topology. Relying on the topologies for infinite executions introduced by Nowak, Schmid and Winkler (JACM, 2024) for terminating consensus, we prove that semi-open decision sets and semi-continuous decision functions as introduced by Levin (AMM, 1963) are the appropriate means for this characterization: Unlike the decision functions for terminating consensus, which are continuous, semi-continuous functions do not require the inverse image of an open set to be open and hence allow to map a connected space to a disconnected one. We also show that multi-valued stabilizing consensus with weak and strong validity are equivalent, as is the case for terminating consensus. By applying our results to (variants of) all the known possibilities/impossibilities for stabilizing consensus, we easily provide a topological explanation of these results.
Dual continuation, an innovative insight into extending the real-valued functions of real matrices to the dual-valued functions of dual matrices with a foundation of the G\^ateaux derivative, is proposed. Theoretically, the general forms of dual-valued vector and matrix norms, the remaining properties in the real field, are provided. In particular, we focus on the dual-valued vector $p$-norm $(1\!\leq\! p\!\leq\!\infty)$ and the unitarily invariant dual-valued Ky Fan $p$-$k$-norm $(1\!\leq\! p\!\leq\!\infty)$. The equivalence between the dual-valued Ky Fan $p$-$k$-norm and the dual-valued vector $p$-norm of the first $k$ singular values of the dual matrix is then demonstrated. Practically, we define the dual transitional probability matrix (DTPM), as well as its dual-valued effective information (${\rm{EI_d}}$). Additionally, we elucidate the correlation between the ${\rm{EI_d}}$, the dual-valued Schatten $p$-norm, and the dynamical reversibility of a DTPM. Through numerical experiments on a dumbbell Markov chain, our findings indicate that the value of $k$, corresponding to the maximum value of the infinitesimal part of the dual-valued Ky Fan $p$-$k$-norm by adjusting $p$ in the interval $[1,2)$, characterizes the optimal classification number of the system for the occurrence of the causal emergence.
Text toxicity detection systems exhibit significant biases, producing disproportionate rates of false positives on samples mentioning demographic groups. But what about toxicity detection in speech? To investigate the extent to which text-based biases are mitigated by speech-based systems, we produce a set of high-quality group annotations for the multilingual MuTox dataset, and then leverage these annotations to systematically compare speech- and text-based toxicity classifiers. Our findings indicate that access to speech data during inference supports reduced bias against group mentions, particularly for ambiguous and disagreement-inducing samples. Our results also suggest that improving classifiers, rather than transcription pipelines, is more helpful for reducing group bias. We publicly release our annotations and provide recommendations for future toxicity dataset construction.
The Softmax attention mechanism in Transformer models is notoriously computationally expensive, particularly due to its quadratic complexity, posing significant challenges in vision applications. In contrast, linear attention provides a far more efficient solution by reducing the complexity to linear levels. However, compared to Softmax attention, linear attention often experiences significant performance degradation. Our experiments indicate that this performance drop is due to the low-rank nature of linear attention's feature map, which hinders its ability to adequately model complex spatial information. In this paper, to break the low-rank dilemma of linear attention, we conduct rank analysis from two perspectives: the KV buffer and the output features. Consequently, we introduce Rank-Augmented Linear Attention (RALA), which rivals the performance of Softmax attention while maintaining linear complexity and high efficiency. Based on RALA, we construct the Rank-Augmented Vision Linear Transformer (RAVLT). Extensive experiments demonstrate that RAVLT achieves excellent performance across various vision tasks. Specifically, without using any additional labels, data, or supervision during training, RAVLT achieves an 84.4% Top-1 accuracy on ImageNet-1k with only 26M parameters and 4.6G FLOPs. This result significantly surpasses previous linear attention mechanisms, fully illustrating the potential of RALA. Code will be available at //github.com/qhfan/RALA.
The optimal branch number of MDS matrices has established their importance in designing diffusion layers for various block ciphers and hash functions. As a result, numerous matrix structures, including Hadamard and circulant matrices, have been proposed for constructing MDS matrices. Also, in the literature, significant attention is typically given to identifying MDS candidates with optimal implementations or proposing new constructions across different orders. However, this paper takes a different approach by not emphasizing efficiency issues or introducing new constructions. Instead, its primary objective is to enumerate Hadamard MDS and involutory Hadamard MDS matrices of order $4$ within the field $\mathbb{F}_{2^r}$. Specifically, it provides an explicit formula for the count of both Hadamard MDS and involutory Hadamard MDS matrices of order $4$ over $\mathbb{F}_{2^r}$. Additionally, it derives the count of Hadamard Near-MDS (NMDS) and involutory Hadamard NMDS matrices, each with exactly one zero in each row, of order $4$ over $\mathbb{F}_{2^r}$. Furthermore, the paper discusses some circulant-like matrices for constructing NMDS matrices and proves that when $n$ is even, any $2n \times 2n$ Type-II circulant-like matrix can never be an NMDS matrix. While it is known that NMDS matrices may be singular, this paper establishes that singular Hadamard matrices can never be NMDS matrices. Moreover, it proves that there exist exactly two orthogonal Type-I circulant-like matrices of order $4$ over $\mathbb{F}_{2^r}$.
We give an approach for characterizing interference by lower bounding the number of units whose outcome depends on certain groups of treated individuals, such as depending on the treatment of others, or others who are at least a certain distance away. The approach is applicable to randomized experiments with binary-valued outcomes. Asymptotically conservative point estimates and one-sided confidence intervals may be constructed with no assumptions beyond the known randomization design, allowing the approach to be used when interference is poorly understood, or when an observed network might only be a crude proxy for the underlying social mechanisms. Point estimates are equal to Hajek-weighted comparisons of units with differing levels of treatment exposure. Empirically, we find that the size of our interval estimates is competitive with (and often smaller than) those of the EATE, an assumption-lean treatment effect, suggesting that the proposed estimands may be intrinsically easier to estimate than treatment effects.
Conventional economic and socio-behavioural models assume perfect symmetric access to information and rational behaviour among interacting agents in a social system. However, real-world events and observations appear to contradict such assumptions, leading to the possibility of other, more complex interaction rules existing between such agents. We investigate this possibility by creating two different models for a doctor-patient system. One retains the established assumptions, while the other incorporates principles of reflexivity theory and cognitive social structures. In addition, we utilize a microbial genetic algorithm to optimize the behaviour of the physician and patient agents in both models. The differences in results for the two models suggest that social systems may not always exhibit the behaviour or even accomplish the purpose for which they were designed and that modelling the social and cognitive influences in a social system may capture various ways a social agent balances complementary and competing information signals in making choices.
We study the implementability problem for an expressive class of symbolic communication protocols involving multiple participants. Our symbolic protocols describe infinite states and data values using dependent refinement predicates. Implementability asks whether a global protocol specification admits a distributed, asynchronous implementation, namely one for each participant, that is deadlock-free and exhibits the same behavior as the specification. We provide a unified explanation of seemingly disparate sources of non-implementability through a precise semantic characterization of implementability for infinite protocols. Our characterization reduces the problem of implementability to (co)reachability in the global protocol restricted to each participant. This compositional reduction yields the first sound and relatively complete algorithm for checking implementability of symbolic protocols. We use our characterization to show that for finite protocols, implementability is co-NP-complete for explicit representations and PSPACE-complete for symbolic representations. The finite, explicit fragment subsumes a previously studied fragment of multiparty session types for which our characterization yields a PTIME decision procedure, improving upon a prior PSPACE upper bound.
The recent introduction of geometric partition entropy brought a new viewpoint to non-parametric entropy quantification that incorporated the impacts of informative outliers, but its original formulation was limited to the context of a one-dimensional state space. A generalized definition of geometric partition entropy is now provided for samples within a bounded (finite measure) region of a d-dimensional vector space. The basic definition invokes the concept of a Voronoi diagram, but the computational complexity and reliability of Voronoi diagrams in high dimension make estimation by direct theoretical computation unreasonable. This leads to the development of approximation schemes that enable estimation that is faster than current methods by orders of magnitude. The partition intersection ($\pi$) approximation, in particular, enables direct estimates of marginal entropy in any context resulting in an efficient and versatile mutual information estimator. This new measure-based paradigm for data driven information theory allows flexibility in the incorporation of geometry to vary the representation of outlier impact, which leads to a significant broadening in the applicability of established entropy-based concepts. The incorporation of informative outliers is illustrated through analysis of transient dynamics in the synchronization of coupled chaotic dynamical systems.
注冊地址： 北京市海淀區羊坊店路18號2幢3層301-191