In what has become a tradition, I compiled Tensorflow for my no-avx CPU. This time, the installation was more complicated because of a dependency on jaxlib. I had installed jax either through pip3 or through Debian's repositories (apt-get tool). The jaxlib was compiled with AVX support and would not work on my computer.
So I spent some time getting Jax sources and compiling those without AVX support.
Here are the two files for older Intel CPUs:
jaxlib-0.1.76-cp38-none-manylinux2010_x86_64.whl
tensorflow-2.8.0rc0-cp38-cp38-linux_x86_64.whl
Unless you have compiled your own jaxlib, you will need to download both. The jaxlib should be useful with the native 'jax' install from pip3 since the jax library only contains Python code. As I understand, the jax library does not contain native code.
You could also use the jaxlib in isolation for playing with Jax.
To install them, download the whl files to disk, and run
pip3 install filenameHere.whl
These were compiled on a cpu with the following flags in the output of /proc/cpuinfo:
flags : fpu vme de pse tsc msr pae mce cx8 apic sep mtrr pge mca cmov pat pse36 clflush dts acpi mmx fxsr sse sse2 ss ht tm pbe syscall nx pdpe1gb rdtscp lm constant_tsc art arch_perfmon pebs bts rep_good nopl xtopology tsc_reliable nonstop_tsc cpuid aperfmperf tsc_known_freq pni pclmulqdq dtes64 ds_cpl vmx est tm2 ssse3 sdbg cx16 xtpr pdcm sse4_1 sse4_2 x2apic movbe popcnt tsc_deadline_timer aes xsave rdrand lahf_lm 3dnowprefetch cpuid_fault cat_l2 ibrs ibpb stibp tpr_shadow vnmi flexpriority ept vpid ept_ad fsgsbase tsc_adjust smep erms mpx rdt_a rdseed smap clflushopt intel_pt sha_ni xsaveopt xsavec xgetbv1 xsaves dtherm ida arat pln pts md_clear arch_capabilities
Both these wheels work great on my Core 2 duo and another Pentium CPU that didn't have AVX support. Compiled with Python 3.8, they should work for most Linux distributions, assuming the dependencies (numpy, absl-py, scipy, flatbuffers, tensorboard, ...) are installed. pip3 should get the dependencies you don't have. None of the dependencies contain any native code that requires AVX instructions.