As video transmission increasingly serves machine vision systems (MVS) instead of human vision systems (HVS), video coding for machines (VCM) has become a critical research topic. Existing VCM methods often bind codecs to specific downstream models, requiring retraining or supervised data and thus limiting generalization in multi-task scenarios. Recently, unified VCM frameworks have employed visual backbones (VB) and visual foundation models (VFM) to support multiple video understanding tasks with a single codec. They mainly utilize VB/VFM to maintain semantic consistency or suppress non-semantic information, but seldom explore how to directly link video coding with understanding under VB/VFM guidance. Hence, we propose a Symmetric Entropy-Constrained Video Coding framework for Machines (SEC-VCM). It establishes a symmetric alignment between the video codec and VB, allowing the codec to leverage VB's representation capabilities to preserve semantics and discard MVS-irrelevant information. Specifically, a bi-directional entropy-constraint (BiEC) mechanism ensures symmetry between the process of video decoding and VB encoding by suppressing conditional entropy. This helps the codec to explicitly handle semantic information beneficial for MVS while squeezing useless information. Furthermore, a semantic-pixel dual-path fusion (SPDF) module injects pixel-level priors into the final reconstruction. Through semantic-pixel fusion, it suppresses artifacts harmful to MVS and improves machine-oriented reconstruction quality. Experimental results show our framework achieves state-of-the-art (SOTA) in rate-task performance, with significant bitrate savings over VTM on video instance segmentation (37.41%), video object segmentation (29.83%), object detection (46.22%), and multiple object tracking (44.94%). We will release our code.

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