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Won-Gi Paeng

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hep-ph nucl-th Artificial Intelligence Machine Learning astro-ph.HE Computation and Language

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preprint2026arXiv

An Axiomatic Approach to General Intelligence: SANC(E3) -- Self-organizing Active Network of Concepts with Energy E3

General intelligence must reorganize experience into internal structures that enable prediction and action under finite resources. Existing systems implicitly presuppose fixed primitive units -- tokens, subwords, pixels, or predefined sensor channels -- thereby bypassing the question of how representational units themselves emerge and stabilize. This paper proposes SANC(E3), an axiomatic framework in which representational units are not given a priori but instead arise as stable outcomes of competitive selection, reconstruction, and compression under finite activation capacity, governed by the explicit minimization of an energy functional E3. SANC(E3) draws a principled distinction between system tokens -- structural anchors such as {here, now, I} and sensory sources -- and tokens that emerge through self-organization during co-occurring events. Five core axioms formalize finite capacity, association from co-occurrence, similarity-based competition, confidence-based stabilization, and the reconstruction-compression-update trade-off. A key feature is a pseudo-memory-mapped I/O mechanism, through which internally replayed Gestalts are processed via the same axiomatic pathway as external sensory input. As a result, perception, imagination, prediction, planning, and action are unified within a single representational and energetic process. From the axioms, twelve propositions are derived, showing that category formation, hierarchical organization, unsupervised learning, and high-level cognitive activities can all be understood as instances of Gestalt completion under E3 minimization.

preprint2026arXiv

Why Geometric Continuity Emerges in Deep Neural Networks: Residual Connections and Rotational Symmetry Breaking

Weight matrices in deep networks exhibit geometric continuity -- principal singular vectors of adjacent layers point in similar directions. While this property has been widely observed, its origin remains unexplained. Through experiments on toy MLPs and small transformers, we identify two mechanisms: residual connections create cross-layer gradient coherence that aligns weight updates across layers, and symmetry-breaking nonlinearities constrain all layers to a shared coordinate frame, preventing the rotation drift that would otherwise destabilize weight structure. Crucially, a nonlinear but rotation-preserving activation fails to retain continuity, isolating symmetry breaking -- not nonlinearity itself -- as the active ingredient. Activation and normalization play distinct roles: activation concentrates continuity in the leading singular direction, while normalization distributes it across multiple directions. In transformers, continuity is projection-specific: Q, K, Gate, and Up (which read from the residual stream) develop input-space ($\mathbf{v}_1$) continuity; O and Down (which write to it) develop output-space ($\mathbf{u}_1$) continuity; V alone, lacking an adjacent nonlinearity, develops only low continuity.

preprint2022arXiv

Cusp in the Symmetry Energy, Speed of Sound in Neutron Stars and Emergent Pseudo-Conformal Symmetry

We review how the "cusp" predicted in the nuclear symmetry energy generated by a topology change at density $n_{1/2}\gsim 2 n_0$ can have a surprising consequence, so far unrecognized in nuclear physics and astrophysics communities, on the structure of dense compact-star matter. The topology change, when translated into nuclear EFT with "effective" QCD degrees of freedom in terms of hidden local and scale symmetries duly taken into account, predicts an EoS that is soft below and stiff above $n\gsim n_{1/2}$, involving no low-order phase transitions, and yields the macrophysical properties of neutron stars consistent -- so far with no tension -- with the astrophysical observations, including the maximum mass $ 2.0\lsim M/ M_\odot\lsim 2.2$ as well as the GW data. Furthermore it describes the interior core of the massive stars populated by baryon-charge-fractionalized quasi-fermions that are neither baryonic nor quarkonic. It is argued that the cusp "buried" in the symmetry energy resulting from strong correlations with hidden heavy degrees of freedom leads, at $n\gsim n_{1/2}$, to what we dubbed "pseudo-conformal" sound speed, $v^2_{pcs}/c^2\approx 1/3$, precociously converged from below at $n_{1/2}$. It is not strictly conformal since the trace of energy-momentum tensor is not zero even in the chiral limit. This observation with the topology change identified with the putative hadron-quark continuity, taking place at at density $\gsim 2 n_0$, implies that the quantities accurately measured at $\sim n_0$ cannot give a stringent constraint for what takes place at the core density of compact stars $\sim (3-7) n_0$. This is because the change of degrees of freedom in effective field theory is involved. We discuss the implication of this on the recent PREX-II "dilemma" in the measured skin thickness of $^{208}$Pb.

preprint2016arXiv

Scale-Invariant Hidden Local Symmetry, Topology Change and Dense Baryonic Matter

When scale symmetry is implemented into hidden local symmetry in low-energy strong interactions to arrive at a scale-invariant hidden local symmetric (HLS) theory, the scalar $f_0(500)$ may be interpreted as pseudo-Nambu-Goldstone (pNG) boson, i.e., dilaton, of spontaneously broken scale invariance, joining the pseudo-scalar pNG bosons $π$ and the matter fields $V=(ρ,ω)$ as relevant degrees of freedom. Implementing the skyrmion-half-skyrmion transition predicted at large $N_c$ in QCD at a density roughly twice the nuclear matter density found in the crystal simulation of dense skyrmion matter, we determine the intrinsically density-dependent (IDD) "bare parameters" of the scale-invariant HLS Lagrangian matched to QCD at a matching scale $Λ_M$. The resulting effective Lagrangian, with the parameters scaling with the density of the system, is applied to nuclear matter and dense baryonic matter relevant to massive compact stars by means of the double-decimation renormalization-group $V_{lowk}$ formalism. We satisfactorily post-dict the properties of normal nuclear matter and more significantly {\it predict} the EoS of dense compact-star matter that quantitatively accounts for the presently available data coming from both the terrestrial and space laboratories. We interpret the resulting structure of compact-star matter as revealing how the combination of hidden-scale symmetry and hidden local symmetry manifests itself in compressed baryonic matter.

preprint2015arXiv

Kaon Condensation in Baryonic Fermi Liquid at High Density

We formulate kaon condensation in dense baryonic matter with anti-kaons fluctuating from the Fermi-liquid fixed point. This entails that in the Wilsonian RG approach, the decimation is effectuated in the baryonic sector to the Fermi surface while in the meson sector to the origin. In writing the kaon-baryon (KN) coupling, we will take a generalized hidden local symmetry Lagrangian for the meson sector endowed with a "mended symmetry" that has the unbroken symmetry limit at high density in which the Goldstone $π$, scalar $s$, and vectors $ρ$ (and $ω$) and $a_1$ become massless. The vector mesons $ρ$ (and $ω$) and $a_1$ can be identified as emergent (hidden) local gauge fields and the scalar $s$ as the dilaton field of the spontaneously broken scale invariance at chiral restoration. In matter-free space, when the vector mesons and the scalar meson -- whose masses are much greater than that of the pion -- are integrated out, then the resulting KN coupling Lagrangian consists of the leading chiral order ($O(p^1)$) Weinberg-Tomozawa term and the next chiral order ($O(p^2)$) $Σ_{KN}$ term. In addressing kaon condensation in dense nuclear matter in chiral perturbation theory (ChPT), one makes an expansion in the "small" Fermi momentum $k_F$. We argue that in the Wilsonian RG formalism with the Fermi-liquid fixed point, the expansion is on the contrary in $1/k_F$ with the "large" Fermi momentum $k_F$. The kaon-quasinucleon interaction resulting from integrating out the massive mesons consists of a "relevant" term from the scalar exchange (analog to the $Σ_{KN}$ term) and an "irrelevant" term from the vector-meson exchange (analog to the Weinberg-Tomozawa term). It is found that the critical density predicted by the latter approach, controlled by the relevant term, is three times less than that predicted by chiral perturbation theory.

preprint2015arXiv

Scalar Pseudo-Nambu-Goldstone Boson in Nuclei and Dense Nuclear Matter

The notion that the scalar listed as $f_0 (500)$ in the particle data booklet is a pseudo-Nambu-Goldstone (NG) boson of spontaneously broken scale symmetry, explicitly broken by a small departure from an infrared fixed point, is explored in nuclear dynamics. That notion which puts the scalar -- that we shall identify as a "dilaton" -- on the same footing as the pseudo-scalar pseudo-NG bosons, i.e., octet $π$, while providing a simple explanation for the $ΔI=1/2$ rule for kaon decay, generalizes the standard chiral perturbation theory (S$χ$PT) to "scale chiral perturbation theory," denoted $χ$PT$_σ$, with {\it one infrared mass scale for both symmetries}, with the $σ$ figuring as a chiral singlet NG mode in non-strange sector. Applied to nuclear dynamics, it is seen to provide possible answers to various hitherto unclarified nuclear phenomena such as the success of one-boson-exchange potentials (OBEP), the large cancellation of strongly attractive scalar potential by strongly repulsive vector potential in relativistic mean field theory of nuclear systems and in-medium QCD sum rules, the interplay of the dilaton and the vector meson $ω$ in dense skyrmion matter, the BPS skyrmion structure of nuclei accounting for small binding energies of medium-heavy nuclei, and the suppression of hyperon degrees of freedom in compact-star matter.

preprint2013arXiv

Interplay between ω-Nucleon Interaction and Nucleon Mass in Dense Baryonic Matter

The dilaton-limit fixed point and the scaling properties of hadrons in the close vicinity of the fixed point in dense baryonic matter uncovered in hidden local symmetry implemented with spontaneously broken scale symmetry are shown to reveal a surprisingly intricate interplay, hitherto unsuspected, between the origin of the bulk of proton mass and the renormalization-group flow of the ω-nuclear interactions. This rends a theoretical support to the previous (phenomenologically) observed correlation between the dropping nucleon mass and the behavior of the ω-nuclear interactions in dense matter described in terms of half skyrmions that appear at a density denoted $n_{1/2}$ in skyrmion crystals. The role of the ω-meson degree of freedom in the source for nucleon mass observed in this paper is highly reminiscent of its important role in the skyrmion description of nucleon mass in hidden local symmetric theory. One of the most notable novel results found in this paper is that the nucleon mass in dense baryonic medium undergoes a drop roughly linear in density up to a density (denoted $\tilde{n}$) slightly above nuclear matter density ($n_0$) and then stays more or less constant up to the dilaton limit fixed point. The possibility that we entertain is that $\tilde{n}$ coincides with or at least close to $n_{1/2}$. We note that this feature can be economically captured by the parity-doublet model for nucleons with the chiral-invariant mass $m_0\sim (0.7-0.8) m_N$. It is found in one-loop renormalization-group analysis with the Lagrangian adopted that while the ρ-NN coupling "runs" in density, the ω-NN coupling does not scale: it will scale at two-loop or higher-loop order, but at a slower pace, so it is more appropriate to say it "walks" rather than runs.

preprint2013arXiv

Pair Production of Majorana Neutrinos by Annihilation of Charged Particles in High Energy Collision

Assuming that neutrinos have non-vanishing magnetic moments, we discuss the possibility of pair production through annihilation of charged fermions in high-energy collisions. Adopting the Pauli interaction for photon-neutrino coupling, we calculate the neutrino pair production cross section in the photon channel and compare the result with the standard model in $ Z^{0} $ channel. we demonstrated that the enhancement of the production rate for Majorana neutrino pairs over the standard model rate can be possible at the center-of-mass energy of $10 - 100$ TeV for the Large Hadron Collider or the ultra-high-energy cosmic Ray when the transition magnetic moment is not smaller than $10^{-9} - 10^{-10} μ_B$.

preprint2012arXiv

Dilaton-Limit Fixed Point in Hidden Local Symmetric Parity Doublet Model

We study nucleon structure with positive and negative parities using a parity doublet model endowed with hidden local symmetry (HLS) with the objective to probe dense baryonic matter. The model -- that we shall refer to as "PDHLS model" for short -- allows a chiral-invariant mass of the nucleons unconnected to spontaneously broken chiral symmetry which comes out to be m_0 ~ 200 MeV at tree level from fitting to the decay width of the parity doubler, N(1535), to nucleon-pion and nucleon axial coupling g_A=1.267. The presence of a substantial m_0 that remains non-vanishing at chiral restoration presents a deep issue for the origin of the nucleon mass as well as will affect nontrivially the equation of state for dense baryonic matter relevant for compact stars. We construct a chiral perturbation theory at one-loop order and explore the phase structure of the model using renormalization group equations. We find a fixed point that corresponds exactly to the "dilaton limit" at which the HLS vector mesons decouple from the nucleons before reaching the vector manifestation fixed point. We suggest that cold baryonic system will flow to this limit as density increases toward that of chiral restoration.

preprint2011arXiv

Conformal anomaly and the vector coupling in dense matter

We construct an effective chiral Lagrangian for hadrons implemented by the conformal invariance and discuss the properties of nuclear matter at high density. The model is formulated based on two alternative assignment, "naive" and mirror, of chirality to the nucleons. It is shown that taking the dilaton limit, in which the mended symmetry of Weinberg is manifest, the vector-meson Yukawa coupling becomes suppressed and the symmetry energy becomes softer as one approaches the chiral phase transition. This leads to softer equations of state (EoS) and could accommodate the EoS without any exotica consistent with the recent measurement of a $1.97 \pm 0.04\,M_\odot$ neutron star.

preprint2010arXiv

Toward an Effective Field Theory for Cold Compressed Baryonic Matter

This is an extended version of the note taken by the first author (W.-G.P.) on a lecture given by the second author (M.R.) as a first part of the series on "Hadronic Matter Under Extreme Conditions," the principal theme of the WCU-Hanyang Program. It covers the attempts to go in a framework anchored on effective field theory of QCD from zero density to the nuclear matter density and slightly beyond, with the ultimate goal of arriving at the density relevant to compact stars, including chiral phase transition and quark matter. The focus is on the conceptual aspects rather than detailed "fitting" of the data on the kinds of physics that are being addressed to in radioactive-ion-beam machines in operation as well as in project (such as `KoRIA' in Korea) and will be explored at such forthcoming accelerators as FAIR/GSI. The approach presented here is basically different from the standard ones found in the literature in that the notion of hidden local symmetry -- which underlies the chiral symmetry of the strong interactions -- and its generalization to dual gravity description involving infinite tower of hidden gauge fields are closely relied on.